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La distinción entre copulativas ecuativas (p.e. Ana es la única mujer) y predicativas (p.e. Ana es una mujer) se basa en criterios sintácticos. En las ecuativas, la concordancia de género entre el sujeto y el complemento no es obligatoria (p.e. Pepe era la chica de azul sentada allá) y éste se reemplaza por un pronombre nominativo (p.e. Pepe es el chico sentado allá/Pepe es él). En las predicativas, la concordancia de género y número entre el sujeto y el complemento, aparentemente, es obligatoria (p.e. Ana es linda/*-o,*-as,*-os) y éste se reemplaza por el indeclinable lo (p.e. Ana lo/*ella/*la/*le es). Propongo que estos datos sirven de base para postular que ecuativas y predicativas no comparten una estructura sintáctica común en el español. Perelstvaig (2000), a partir de datos del ruso y del italiano, explica que la diferencia entre predicativas y ecuativas se debe a que las primeras incluyen una Cláusula Reducida (CR) cuyo núcleo es una categoría funcional predicativa (Ø) (p.e. cópula [FDet-(Ø)-FN]) y las segundas no tienen tal núcleo (p.e. cópula [FDet₁-FDet₂]). En la misma línea, Haegeman (1994) propone que las predicativas incluyen una categoría funcional –concordancia de género y número (Conc)– en su CR (p.e. cópula [FDet-(Conc)-FN]) y las ecuativas no. Los datos del español no sostienen ambas propuestas ya que no es posible argumentar que en las CRs de las predicativas hay una categoría funcional: no hay necesidad de concordancia de género (e.g. el león(i.masc) es [t(i), una fiera(fem)]) ni de número (e.g. los cuchillos(i.masc) son [ti, una amenaza(fem)]). Por otro lado, la literatura no reconoce que las ecuativas presentan una semejanza con las predicativas: no hay necesidad de concordancia de género (e.g. Ellas(fem) son los invitados(masc) disfrazados de esa mesa). Sánchez y Camacho (1993) plantearon una diferencia estructural entre ecuativas y predicativas; pero su explicación es incompleta porque no incluyen las restricciones de Caso que se imponen a los nominales. Mi propuesta sí considera tales restricciones y se basa en: a) la exigencia teórica de que los nominales deben estar marcados con Caso y b) la evidencia interlingüística proveniente de lenguas como el sinhala, el islandés, el árabe, el latín y el ruso, que marcan con Caso los nominales de las copulativas; a diferencia de éstas, la marcación de Caso en español se hace evidente en la distribución pronominal. Propongo que el patrón casual ecuativo es NOM-NOM (p.e. Ana es la monja/ Ella es la monja/Ana es ella) y que el patrón predicativo es NOM-Predicativo(PRE). PRE es un nuevo rasgo que el indeclinable lo evidencia (p.e. Ana es una monja/Ella es una monja/Ana lo es). Crucialmente, los datos de la copulativas rusas en pretérito (Perelstvaig,2000) presentan ambos patrones; pero en vez de PRE el Caso es Instrumental (INS) (p.e. (NOM)[Oleg] cópula (NOM)[direktor] en las ecuativas, y (NOM)[Oleg] cópula (INS)[direktorom] en las predicativas). En español, el rasgo NOM y el rasgo PRE de los nominales postcopulares se licencian mediante la operación Agree (Chomsky 2000,2001). El rasgo NOM se licencia gracias a T° y el rasgo PRE se legitima gracias a Asp°, núcleo de la FAsp propuesta por Zagona (2002), que es parte del verbo aspectual ser.

This thesis considers statistical issues in the analysis of data in the studies of chronic diseases which involve modeling dependencies between life history processes using copula functions. Many disease processes feature recurrent events which represent events arising from an underlying chronic condition; these are often modeled as point processes. In addition, however, there often exists a random variable which is realized upon the occurrence of each event, which is called a mark of the point process. When considered together, such processes are called marked point processes. A novel copula model for the marked point process is described here which uses copula functions to govern the association between marks and event times. Specifically, a copula function is used to link each mark with the next event time following the realization of that mark to reflect the pattern in the data wherein larger marks are often followed by longer time to the next event. The extent of organ damage in an individual can often be characterized by ordered states, and interest frequently lies in modeling the rates at which individuals progress through these states. Risk factors can be studied and the effect of therapeutic interventions can be assessed based on relevant multistate models. When chronic diseases affect multiple organ systems, joint modeling of progression in several organ systems is also important. In contrast to common intensity-based or frailty-based approaches to modelling, this thesis considers a copula-based framework for modeling and analysis. Through decomposition of the density and by use of conditional independence assumptions, an appealing joint model is obtained by assuming that the joint survival function of absorption transition times is governed by a multivariate copula function. Different approaches to estimation and inference are discussed and compared including composite likelihood and two-stage estimation methods. Special attention is paid to the case of interval-censored data arising from intermittent assessment. Attention is also directed to use of copula models for more general scenarios with a focus on semiparametric two-stage estimation procedures. In this approach nonparametric or semiparametric estimates of the marginal survivor functions are obtained in the first stage and estimates of the association parameters are obtained in the second stage. Bivariate failure time models are considered for data under right-censoring and current status observation schemes, and right-censored multistate models. A new expression for the asymptotic variance of the second-stage estimator for the association parameter along with a way of estimating this for finite samples are presented under these models and observation schemes.

Pastaruoju metu, investavimui tampant vis populiaresniu, atsiranda poreikis skaičiuoti portfelių rizikuojamąją vertę (angl. Value at Risk, toliau tekste VaR). Pastaroji gali būti skaičiuojama portfeliams sudarytiems iš skirtingų finansinių instrumentų. Tačiau iškyla problemų, kai finansiniai instrumentai yra tarpusavyje susiję (priklausomi). Šiai situacijai išspręsti naudojame VaR, kuris skaičiuojamas jungčių (angl. Copula) pagalba. Darbo tikslas – nagrinėjamiems portfeliams parinkti jungtis, kurios geriausiai atspindėtų bendrą duomenų pasiskirstymą. Tada, turint jungtis, apskaičiuoti VaR. Gavome, kad vertinant 1 portfelį ateinančiu laiko momentu mūsų didžiausias tikėtinas nuostolis yra intervale tarp 4.34 ir 4.70 litų. 2 portfelio nuostolis yra intervale (2.88, 3.42), 3 portfelio – (3.29, 5.28 ). / Recently, investments acquire vogue and it’s necessary to compute the Value at Risk of portfolio. VaR can be computed for portfolio which is made from different finance instruments. But the problem arises when these instruments are interdependent. In order to solve this problem, we compute VaR using copulas. The aim of this work is to pick copulas for real data which is the best for the distribution of the data. At that point compute VaR using selected copulas. The results are: in future time the biggest loss for first portfolio is in the interval 4.43 ant 4.7 Litas, for second portfolio the biggest loss – (2.88, 3.42) ant for third portfolio – (3.29, 5.28).

Asymmetric dependence (AD) is defined as dependence that differs across opposing regions of the joint return distribution. Recent evidence of AD between equity returns suggests that dependence can be decomposed into a linear component, captured by the correlation matrix, and a higher order component. When these higher order terms are characterised by increased correlation in bear or bull markets, the effectiveness of diversification strategies is reduced. To the extent that an investor is unable to completely diversify these higher order terms of dependence, it follows that they should be reflected in asset prices and managed explicitly during the portfolio construction process. The aim of this thesis is to determine the extent of AD amongst asset returns, to investigate whether AD is priced and to develop a means of managing AD in the portfolio. I justify the existence of AD and the separation of AD from linear dependence via the bivariate Edgeworth expansion, finding that the joint return distribution may be described by an infinite number of higher order co-moments. Correlation (and hence β) describes one dimension of an infinite number of higher dimensions describing dependence. To determine the importance of AD in finance, I first develop measures that can detect AD independent of the level of linear dependence and idiosyncratic risk. These measures are used to determine the extent of AD amongst US stock returns and the market, to obtain an understanding of how AD changes through time and to re-examine the evidence of AD between equity portfolios. By measuring AD separate from linear dependence, I demonstrate several findings. First, I find evidence of non-stationary AD that can exists irrespective of the magnitude of linear dependence, measured by β. This time-varying AD consists of both significant upper tail dependence (UTD) and significant lower tail dependence (LTD), although LTD is found to occur more frequently than UTD, especially for small stocks and stocks displaying high idiosyncratic risk. Significant time-varying AD is also detected between domestic equity indices and international equity markets, implying that if a portfolio is weighted towards certain industries or countries, portfolio construction methods may need to be adjusted in order too meet risk and return targets, particularly if future AD cannot be adequately forecasted. Next, I investigate whether AD is priced in US equities using the Fama and MacBeth (1973) regression methodology in conjunction with my β invariant AD metrics. I find that AD is as important as linear dependence in explaining the variation in returns. In particular, a positive relationship between LTD and return is found. I document an AD risk premium of 2.7% pa, compared to a β risk premium of 6.18% pa. The AD risk premium increases to 6.9% pa for stocks with significant LTD. This result holds after controlling for size, book-to-market ratio, downside β and coskewness. I also find past AD is a significant variable in predicting the future returns of small firms, whilst neither AD nor linear dependence predict the future returns of large firms. I subsequently demonstrate a means of incorporating AD structures during the portfolio construction process using copula functions. I then investigate how asymmetric return dependencies affect the efficient frontier and subsequent portfolio performance under a dynamic rebalancing framework. By considering the problem of tactically allocating a small set of domestic equity indices, I demonstrate several findings. First, I show that a Mean-Variance efficient frontier differs from the efficient frontier constructed under AD. Constructing paper portfolios based upon these differences, I find that real economic value lies in correctly accounting for AD structures. The primary source of this economic value stems from the ability to better protect portfolio value and reduce the size of any erosion in return relative to the normal portfolio. Finally, I document the benefits of actively managing AD during the portfolio construction process and determine a number of portfolio management principles required to successfully manage AD. I illustrate that managing asymmetry risk in a portfolio of international equity indices results in increased return, decreased risk and decreased transaction costs. I show that in order to yield these benefits, investors must actively and dynamically manage their portfolio. Furthermore, I illustrate that the ability to short-sell assets provides most of the benefits described.

Asymmetric dependence (AD) is defined as dependence that differs across opposing regions of the joint return distribution. Recent evidence of AD between equity returns suggests that dependence can be decomposed into a linear component, captured by the correlation matrix, and a higher order component. When these higher order terms are characterised by increased correlation in bear or bull markets, the effectiveness of diversification strategies is reduced. To the extent that an investor is unable to completely diversify these higher order terms of dependence, it follows that they should be reflected in asset prices and managed explicitly during the portfolio construction process. The aim of this thesis is to determine the extent of AD amongst asset returns, to investigate whether AD is priced and to develop a means of managing AD in the portfolio. I justify the existence of AD and the separation of AD from linear dependence via the bivariate Edgeworth expansion, finding that the joint return distribution may be described by an infinite number of higher order co-moments. Correlation (and hence β) describes one dimension of an infinite number of higher dimensions describing dependence. To determine the importance of AD in finance, I first develop measures that can detect AD independent of the level of linear dependence and idiosyncratic risk. These measures are used to determine the extent of AD amongst US stock returns and the market, to obtain an understanding of how AD changes through time and to re-examine the evidence of AD between equity portfolios. By measuring AD separate from linear dependence, I demonstrate several findings. First, I find evidence of non-stationary AD that can exists irrespective of the magnitude of linear dependence, measured by β. This time-varying AD consists of both significant upper tail dependence (UTD) and significant lower tail dependence (LTD), although LTD is found to occur more frequently than UTD, especially for small stocks and stocks displaying high idiosyncratic risk. Significant time-varying AD is also detected between domestic equity indices and international equity markets, implying that if a portfolio is weighted towards certain industries or countries, portfolio construction methods may need to be adjusted in order too meet risk and return targets, particularly if future AD cannot be adequately forecasted. Next, I investigate whether AD is priced in US equities using the Fama and MacBeth (1973) regression methodology in conjunction with my β invariant AD metrics. I find that AD is as important as linear dependence in explaining the variation in returns. In particular, a positive relationship between LTD and return is found. I document an AD risk premium of 2.7% pa, compared to a β risk premium of 6.18% pa. The AD risk premium increases to 6.9% pa for stocks with significant LTD. This result holds after controlling for size, book-to-market ratio, downside β and coskewness. I also find past AD is a significant variable in predicting the future returns of small firms, whilst neither AD nor linear dependence predict the future returns of large firms. I subsequently demonstrate a means of incorporating AD structures during the portfolio construction process using copula functions. I then investigate how asymmetric return dependencies affect the efficient frontier and subsequent portfolio performance under a dynamic rebalancing framework. By considering the problem of tactically allocating a small set of domestic equity indices, I demonstrate several findings. First, I show that a Mean-Variance efficient frontier differs from the efficient frontier constructed under AD. Constructing paper portfolios based upon these differences, I find that real economic value lies in correctly accounting for AD structures. The primary source of this economic value stems from the ability to better protect portfolio value and reduce the size of any erosion in return relative to the normal portfolio. Finally, I document the benefits of actively managing AD during the portfolio construction process and determine a number of portfolio management principles required to successfully manage AD. I illustrate that managing asymmetry risk in a portfolio of international equity indices results in increased return, decreased risk and decreased transaction costs. I show that in order to yield these benefits, investors must actively and dynamically manage their portfolio. Furthermore, I illustrate that the ability to short-sell assets provides most of the benefits described.

This thesis uses statistical modelling to better understand the relationship between insured losses and hazard footprint characteristics for European windstorms (extra- tropical cyclones). The footprint of a windstorm is defined as the maximum wind gust speed to occur at a set of spatial locations over the duration of the storm. A better understanding of this relationship is required because the most damaging historical windstorms have had footprints with differing characteristics. Some have a large area of relatively low wind gust speeds, while others have a smaller area of higher wind gust speeds. In addition, this insight will help to explain the surprising, sharp decline in European wind related losses in the mid 1990’s. This novel exploration is based on 5730 high resolution model generated historical footprints (1979-2012) representing the whole European domain. Functions of extreme footprint wind gust speeds, known as storm severity measures, are developed to represent footprint characteristics. Exploratory data analysis is used to compare which storm severity measures are most successful at classifying 23 extreme windstorms, known to have caused large insured losses. Summarising the footprint using these scalar severity measures, however, fails to capture different combinations of spatial scale and local intensity characteristics. To overcome this, a novel statistical model for windstorm footprints is developed, initially for pairs of locations using a bivariate Gaussian copula model; subsequently extended to represent the whole European domain using a geostatistical spatial model. Throughout, the distribution of wind gust speeds at each location is modelled using a left-truncated Generalised Extreme Value (GEV) distribution. Synthetic footprints, simulated from the geostatistical model, are then used in a sensitivity study to explore whether the local intensity or spatial dependence structure of a footprint has the most influence on insured loss. This contributes a novel example of sensitivity analysis applied to a stochastic natural hazards model. The area of the footprint exceeding 25ms−1 over land is the most successful storm severity measure at classifying extreme loss windstorms, ranking all 23 within the top 18% of events. Marginally transformed wind gust speeds are identified as being asymptotically independent and second-order stationary, allowing for the spatial dependence to be represented by a geostatistical covariance function. The geostatistical windstorm footprint model is able to quickly (∼3 seconds) simulate synthetic footprints which realistically represent joint losses throughout Europe. The sensitivity study identifies that the left-truncated GEV parameters have a greater influence on insured loss than the geostatistical spatial dependence parameters. The observed decline in wind related losses in the 1990’s can therefore be attributed to a change in the local intensity rather than the spatial structure of footprint wind gust speeds.

La alternancia ser/estar ha inspirado numerosos estudios y, consecuentemente, una significativa variedad de conceptos técnicos. Ante este panorama, proponemos avanzar hacia un refinamiento de los parámetros aspectuales empleados, con énfasis en los niveles lingüísticos en los que se originan y en la diferenciación entre semántica léxica/construccional. A partir de diagnósticos específicos, proponemos: primero, que ser y estar se alejan de la noción estándar de cópula y verbo estativo y son cuanto menos ambiguas respecto al tipo eventivo de las construcciones que articulan; segundo, que propiedades asignadas en la literatura no responden a lacópula, sino a la construcción; tercero, que la delimitación [boundedness] capta más eficientemente las situación de ser/estar, como propiedad semántica diferente y lógicamente distinguible de la perfectividad y telicidad. / Spanish copulas have inspired a vast amount of studies involving a significant number of technical concepts in their description. Against this background, we concentrate on the need to refine the technical parameters used, focusing on the linguistic domains where they are encoded and on the distinction between lexical and constructional semantics. Building on specific tests, we propose that ser and estar: (i) depart from both the standard notion of copula (semantically trivial verb) and of stative verb (lacking temporal structure) and are at least ambiguous as for the eventive type of construction they render; (ii) that many properties observed in the literature do not actually ensue from to the copula per se, but rather from the construction they head; (iii) and that the parameter boundedness best captures their situation, as long as it is conceived as a different semantic property, logically distinguishable from perfectivity telicity.

abstract: The presence of two copula verbs (ser and estar) in Spanish has caused a semantic competition between the two. This semantic competition has been documented from the XII century (Vañó-Cerdá, 1982). Some scholars (Brown & Cortés-Torres, 2012; Cortés-Torres, 2004; Gutiérrez, 1992; Ortiz-López, 2000; Silva-Corvalán, 1994) have demonstrated the presence of this competition in which estar has been occupying structures traditionally reserved for ser in different Spanish varieties. This study investigates the extent to which the extension of estar to contexts previously limited to ser is present in the Spanish of Puerto Rico in adjectival structures (copula + adjective). The investigation analyzed 21 Puerto Rican Spanish speakers, who completed five different instruments (interview, description of a picture, 2 questionnaires and grammar judgment). Nine of the participants completed the five tasks and the other 12 completed the 2 questionnaires. A multi-variable and qualitative analysis were employed to examine the linguistics (class or individual frame of reference, copulas the adjective allows, animacy, susceptibility to change, and type of adjective) and social factors (sex, age, level of education, and bilingualism) that favor the phenomenon. The results showed that type of adjective, copulas the adjective allows, susceptibility to change, and type of questionnaire favored the innovative use of estar. Both analyses showed a clear tendency of the linguistics factors that favor the innovative use of estar. The results of this study concur with previous studies (Cortés-Torres, 2004; Gutiérrez, 1992; Ortiz-López, 2000; Silva-Corvalán, 1994) about the phenomenon in other monolingual and bilingual Spanish dialects. This study confirms Puerto Rican Spanish follows the internal change tendency in Spanish language about the uses of ser and estar. The use of different instruments for data collection provides a clear view of the phenomenon in Puerto Rican Spanish. The use of questionnaires with confirmed estar predictors shows that some adjectives resist the phenomenon more; even with the perfect conditions for the use of estar, the participants did not allowed its use. / Dissertation/Thesis / M.A. Spanish 2013

Quantile function modeling is a more robust, comprehensive, and flexible method of statistical analysis than the commonly used mean-based methods. More and more data are collected in the form of multivariate, functional, and multivariate functional data, for which many aspects of quantile analysis remain unexplored and challenging. This thesis presents a set of quantile analysis methods for multivariate data and multivariate functional data, with an emphasis on environmental applications, and consists of four significant contributions. Firstly, it proposes bivariate quantile analysis methods that can predict the joint distribution of bivariate response and improve on conventional univariate quantile regression. The proposed robust statistical techniques are applied to examine barley plants grown in saltwater and freshwater conditions providing interesting insights into barley’s responses, informing future crop decisions. Secondly, it proposes modeling and visualization of bivariate functional data to characterize the distribution and detect outliers. The proposed methods provide an informative visualization tool for bivariate functional data and can characterize non-Gaussian, skewed, and heavy-tailed distributions using directional quantile envelopes. The radiosonde wind data application illustrates our proposed quantile analysis methods for visualization, outlier detection, and prediction. However, the directional quantile envelopes are convex by definition. This feature is shared by most existing methods, which is not desirable in nonconvex and multimodal distributions. Thirdly, this challenge is addressed by modeling multivariate functional data for flexible quantile contour estimation and prediction. The estimated contours are flexible in the sense that they can characterize non-Gaussian and nonconvex marginal distributions. The proposed multivariate quantile function enjoys the theoretical properties of monotonicity, uniqueness, and the consistency of its contours. The proposed methods are applied to air pollution data. Finally, we perform quantile spatial prediction for non-Gaussian spatial data, which often emerges in environmental applications. We introduce a copula-based multiple indicator kriging model, which makes no distributional assumptions on the marginal distribution, thus offers more flexibility. The method performs better than the commonly used variogram approach and Gaussian kriging for spatial prediction in simulations and application to precipitation data.