Thesis advisor: Zhijie Xiao / In recent years, quantile regression has achieved increasing prominence as a quantitative method of choice in applied econometric research. The methodology focuses on how the quantile of the dependent variable is influenced by the regressors, thus providing the researcher with much information about variations in the relationship between the covariates. In this dissertation, I consider two quantile regression models where the information set may contain quantiles of the regressors. Such frameworks thus capture the dependence between quantiles - the quantile of the dependent variable and the quantile of the regressors - which I call models of quantile dependence. These models are very useful from the applied researcher's perspective as they are able to further uncover complex dependence behavior and can be easily implemented using statistical packages meant for standard quantile regressions. The first chapter considers an application of the quantile dependence model in empirical finance. One of the most important parameter of interest in risk management is the correlation coefficient between stock returns. Knowing how correlation behaves is especially important in bear markets as correlations become unstable and increase quickly so that the benefits of diversification are diminished especially when they are needed most. In this chapter, I argue that it remains a challenge to estimate variations in correlations. In the literature, either a regime-switching model is used, which can only estimate correlation in a finite number of states, or a model based on extreme-value theory is used, which can only estimate correlation between the tails of the returns series. Interpreting the quantile of the stock return as having information about the state of the financial market, this chapter proposes to model the correlation between quantiles of stock returns. For instance, the correlation between the 10th percentiles of stock returns, say the U.S. and the U.K. returns, reflects correlation when the U.S. and U.K. are in the bearish state. One can also model the correlation between the 60th percentile of one series and the 40th percentile of another, which is not possible using existing tools in the literature. For this purpose, I propose a nonlinear quantile regression where the regressor is a conditional quantile itself, so that the left-hand-side variable is a quantile of one stock return and the regressor is a quantile of the other return. The conditional quantile regressor is an unknown object, hence feasible estimation entails replacing it with the fitted counterpart, which then gives rise to problems in inference. In particular, inference in the presence of generated quantile regressors will be invalid when conventional standard errors are used. However, validity is restored when a correction term is introduced into the regression model. In the empirical section, I investigate the dependence between the quantile of U.S. MSCI returns and the quantile of MSCI returns to eight other countries including Canada and major equity markets in Europe and Asia. Using regression models based on the Gaussian and Student-t copula, I construct correlation surfaces that reflect how the correlations between quantiles of these market returns behave. Generally, the correlations tend to rise gradually when the markets are increasingly bearish, as reflected by the fact that the returns are jointly declining. In addition, correlations tend to rise when markets are increasingly bullish, although the magnitude is smaller than the increase associated with bear markets. The second chapter considers an application of the quantile dependence model in empirical macroeconomics examining the money-output relationship. One area in this line of research focuses on the asymmetric effects of monetary policy on output growth. In particular, letting the negative residuals estimated from a money equation represent contractionary monetary policy shocks and the positive residuals represent expansionary shocks, it has been widely established that output growth declines more following a contractionary shock than it increases following an expansionary shock of the same magnitude. However, correctly identifying episodes of contraction and expansion in this manner presupposes that the true monetary innovation has a zero population mean, which is not verifiable. Therefore, I propose interpreting the quantiles of the monetary shocks as having information about the monetary policy stance. For instance, the 10th percentile shock reflects a restrictive stance relative to the 90th percentile shock, and the ranking of shocks is preserved regardless of shifts in the shock's distribution. This idea motivates modeling output growth as a function of the quantiles of monetary shocks. In addition, I consider modeling the quantile of output growth, which will enable policymakers to ascertain whether certain monetary policy objectives, as indexed by quantiles of monetary shocks, will be more effective in particular economic states, as indexed by quantiles of output growth. Therefore, this calls for a unified framework that models the relationship between the quantile of output growth and the quantile of monetary shocks. This framework employs a power series method to estimate quantile dependence. Monte Carlo experiments demonstrate that regressions based on cubic or quartic expansions are able to estimate the quantile dependence relationships well with reasonable bias properties and root-mean-squared errors. Hence, using the cubic and quartic regression models with M1 or M2 money supply growth as monetary instruments, I show that the right tail of the output growth distribution is generally more sensitive to M1 money supply shocks, while both tails of output growth distribution are more sensitive than the center is to M2 money supply shocks, implying that monetary policy is more effective in periods of very low and very high growth rates. In addition, when non-neutral, the influence of monetary policy on output growth is stronger when it is restrictive than expansive, which is consistent with previous findings on the asymmetric effects of monetary policy on output. / Thesis (PhD) — Boston College, 2009. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Economics.

Thesis advisor: Zhijie Xiao / This dissertation contains three essays. It provides an application of quantile regression in Financial Economics. The first essay investigates whether tail dependence makes a difference in the estimation of systemic risk. This chapter develops a common framework based on a copula model to estimate several popular return-based systemic risk measures: Delta Conditional Value at Risk (ΔCoVaR) and its modification; and Marginal Expected Shortfall (MES) and its extension, systemic risk measure (SRISK). By eliminating the discrepancy of the marginal distribution, copula models provide the flexibility to concentrate only on the effects of dependence structure on the systemic risk measure. We estimate the systemic risk contributions of four financial industries consisting of a large number of institutions for the sample period from January 2000 to December 2010. First, we found that the linear quantile regression estimation of ΔCoVaR, proposed by Adrian and Brunnermeier (AB hereafter) (2011), is inadequate to completely capture the non-linear contagion tail effect, which tends to underestimate systemic risk in the presence of lower tail dependence. Second, ΔCoVaR originally proposed by AB (2011) is in conflict with dependence measures. By comparison, the modified version of ΔCoVaR put forward by Girardi et al. (2011) and MES, proposed by Acharya et al. (2010), are more consistent with dependence measures, which conforms with the widely held notion that stronger dependence strength results in higher systemic risk. Third, the modified ΔCoVaR is observed to have a strong correlation with tail dependence. In contrast, MES is found to have a strong empirical relationship with firms' conditional CAPM beta. SRISK, however, provides further connection with firms' level characteristics by accounting for information on market capitalization and liability. This stylized fact seems to imply that ΔCoVaR is more in line with the ``too interconnected to fail" paradigm, while SRISK is more related to the ``too big to fail" paradigm. In contrast, MES offers a compromise between these two paradigms. The second essay proposes a quantile regression approach to stock return prediction. I show that incorporating distributional information together with combining model information can produce a superior forecast for the conditional mean as well as the entire distribution of future equity premium, which significantly outperforms the forecast that utilizes either source of information alone. Meanwhile, the order of combination strategies appears to make a difference in the efficiency of pooling both distributional information and model information. It turns out that aggregating distributional information in the first step, followed by combining model information in the second step is more advantageous in return forecast than the alternative combination strategies which reverse the order of combination strategy. Furthermore, the forecast based on LASSO model selection can be significantly improved as well if the distributional information is further incorporated. In other word, aggregating distributional information via combining multiple quantiles estimators contributes to the improvement of forecasts obtained either from model combination or model selection. This paper not only investigates the forecast of conditional mean, but also studies the forecast of the whole distribution of future stock returns. The approaches of quantile combination together with either model combination or model selection turn out to deliver statistically and economically significant out-of-sample forecasts relative to a historical average benchmark. The third essay proposes a quantile-based approach to efficiently estimate the conditional beta coefficient without assuming a parametric structure on the distribution of data generating process. Multiple quantiles estimates are combined in a weighting scheme to utilize distributional information across different quantile of the distribution. Monte Carlo simulation demonstrated that combining multiple quantile estimates can substantially improve the estimation efficiency for beta risk estimates in the absence of Gaussian distribution. The robustness of quantile-based beta estimates are pronounced during financial crisis when the distribution of stock returns deviates most from normality. I also explored the performance of different beta estimators in an application of portfolio management analysis and found that beta estimates from the proposed quantile combination approaches are superior to the OLS estimates in constructing Global Minimum Variance Portfolio, which generates lower variance of portfolio but does not come at the expense of persistent lower returns. / Thesis (PhD) — Boston College, 2013. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Economics.

The goal of this thesis is to propose a new quantile regression approach to identify and estimate the quantiles of the private value conditional distribution in ascending and rst price auctions under the Independent Private Value (IPV) paradigm. The quantile regression framework provides a exible and convenient parametrization of the private value distribution, which is not a ected by the curse of dimensionality. The rst Chapter of the thesis introduces a quantile regression methodology for ascending auctions. The Chapter focuses on revenue analysis, optimal reservation price and its associated screening level. An empirical application for the USFS timber auctions suggests an optimal reservation price policy with a probability of selling the good as low as 58% for some auctions with two bidders. The second Chapter tries to address this issue by considering a risk averse seller with a CRRA utility function. A numerical exercise based on the USFS timber auctions shows that increasing the CRRA of the sellers is su cient to give more reasonable policy recommendations and a higher probability of selling the auctioned timber lot. The third Chapter develops a quantile regression methodology for rst-price auction. The estimation method combines local polynomial, quantile regression and additive sieve methods. It is shown in addition that the new quantile regression methodology is not subject to boundary issues. The choice of smoothing parameters is also discussed.

The traffic accident all causes the greatest damage and the loss of the world. There are approximate million people to die and about 10 million people to be injured every year of the traffic accident of the world, but middle develops countries have the highest ratio of accident. According to the National Highway Traffic Safety Administration a preliminary appraisal shows that number of death of drunk driving is highest for 14 years of the United States., 2006. Ruthm(1996) and Wilkinson(1987) indicate that the main reason of all age¡¦s populace is the traffic accident fatality on the United States. Phelp(1988) found that there are 5,100 people death for the serious traffic accident in 1980¡¦s of the United States. Above show drunk driving is serious and necessary of discussion. In the past, the research about drunk driving, the kinds of data are cross-section¡Btime series and panel data. The tradition econometrics data have two estimate methods¡GFirst is the Ordinary Least Square; second is the Least Absolute Deviation. The two way¡¦s common characteristic is comprehensive discussion. Therefore the study draw on Quantile Regression and that is analysis of drunk driving of the United States. By the research, we can find that in different rats of fatality must be to take the different policy measure to improve the fatality of drunk driving. Not like other research only provide the concise suggestion.

Climatic change has been observed in many locations and has been seen to have dramatic impact on a wide range of ecosystems. The traditional method to analyse trends in climatic series is regression analysis. Koenker and Bassett (1978) developed a regression-type model for estimating the functional relationship between predictor variables and any quantile in the distribution of the response variable. Quantile regression has received considerable attention in the statistical literature, but less so in the water resources literature. This study aims to apply quantile regression to problems in water resources and climate change studies. The core of the thesis is made up of three papers of which two have been published and one has been submitted. One paper presents a novel application of quantile regression to analyze the distribution of sea ice extent. Another paper investigates changes in temperature and precipitation extremes over the Canadian Prairies using quantile regression. The third paper presents a Bayesian model averaging method for variable selection adapted to quantile regression and analyzes the relationship of extreme precipitation with large-scale atmospheric variables. This last paper also develops a novel statistical downscaling model based on quantile regression. The various applications of quantile regression support the conclusion that the method is useful in climate change studies.

Climatic change has been observed in many locations and has been seen to have dramatic impact on a wide range of ecosystems. The traditional method to analyse trends in climatic series is regression analysis. Koenker and Bassett (1978) developed a regression-type model for estimating the functional relationship between predictor variables and any quantile in the distribution of the response variable. Quantile regression has received considerable attention in the statistical literature, but less so in the water resources literature. This study aims to apply quantile regression to problems in water resources and climate change studies. The core of the thesis is made up of three papers of which two have been published and one has been submitted. One paper presents a novel application of quantile regression to analyze the distribution of sea ice extent. Another paper investigates changes in temperature and precipitation extremes over the Canadian Prairies using quantile regression. The third paper presents a Bayesian model averaging method for variable selection adapted to quantile regression and analyzes the relationship of extreme precipitation with large-scale atmospheric variables. This last paper also develops a novel statistical downscaling model based on quantile regression. The various applications of quantile regression support the conclusion that the method is useful in climate change studies.

The motivation for this thesis came from the provision of a large data set from Saudi Arabia giving anthropometric measurements of children and adolescents from birth to eighteen years of age, with a requirement to construct growth charts. The construction of these growth charts revealed a number of issues particularly in the respect to statistical inference relating to quantile regression. To investigate a range of different statistical inference procedures in parametric quantile regression in particular the estimation of the confidence limits of the ?th (?? [0, 1]) quantile, a number of sets of simulated data in which various error structures are imposed including homoscedastic and heteroscedastic structures were developed. Methods from the statistical literature were then compared with a method proposed within this thesis based on the idea of Silverman's (1986) kernel smoothing. This proposed bootstrapping method requires the estimation of the conditional variance function of the fitted quantile. The performance of a variety of variance estimation methods combined within the proposed bootstrapping procedure are assessed under various data structures in order to examine the performance of the proposed bootstrapping approach. The validity of the proposed bootstrapping method is then illustrated using the Saudi Arabian anthropometric data.

Climate change studies are crucial to assist decision-makers in understanding future risks and planning adequate adaptation measures. In general, Global/Regional Climate Models (GCMs/RCMs) achieve coarse resolutions, and are thus unable to provide sufficient information to conduct local climate assessments. Downscaling, defined as a method that derives local to regional-scale (10 to 100 km) information from larger-scale models or data analyses, is used to address this deficiency. In this thesis, a particular downscaling technique, known as the Quantile-Quantile transformation, was used to adjust the statistical distribution of RCM variables to match the statistical distribution of the observed variables generated by two RCMs: the Canadian Regional Climate Model version 3.7.1 and the ARPEGE model, on the historical period (1961-2001). The analyses presented in this study were applied to daily precipitation and maximum and minimum temperatures in the South Nation watershed in Eastern Ontario, Canada. The two-sample Kolmogorov–Smirnov test indicated that the Quantile-Quantile transformation improved the shape of the PDF of RCM-simulated climate variables. The results suggest that, under the A1B scenario, temperatures in the watershed would rise significantly and there would be an increment in precipitation occurrence and intensity. Trend analysis was performed on the 1961 to 2001 and 2041 to 2081 timeframes, using the Mann-Kendall test and the Sen's slope estimator. Discernible, often significant, increases of maximum and minimum temperatures were found for the 1961 to 2001 period, and stronger ascending slopes for the 2041 to 2081 period. However, there was marginal evidence of changes in the time series of maximum and accumulated annual precipitation for both periods. The study also outlined how the frequency and intensity of some extreme weather events will evolve in the 2041-2081 period in response to the rise in atmospheric GHG concentrations. Projected impacts were investigated by tracking future changes in four extreme temperature indices and three precipitation indices. It was predicted that heavy precipitation events and warm spells will occur more frequently and intensely, while extreme cold events will be weaker, and some will be hardly observed.

Dans le domaine de la chimie et plus particulièrement en chimio-informatique, les modèles QSAR (pour Quantitative Structure Activity Relationship) sont de plus en plus étudiés. Ils permettent d’avoir une estimation in silico des propriétés des composés chimiques notamment des propriétés éco toxicologiques. Ces modèles ne sont théoriquement valables que pour une classe de composés (domaine de validité) et sont sensibles à la présence de valeurs atypiques. La thèse s’est focalisée sur la construction de modèles globaux robustes (intégrant un maximum de composés) permettant de prédire l’écotoxicité des composés chimiques sur une algue P. Subcapitata et de déterminer un domaine de validité dans le but de déduire la capacité de prédiction d’un modèle pour une molécule. Ces modèles statistiques robustes sont basés sur une approche quantile en régression linéaire et en régression Support Vector Machine. / In chemistry and more particularly in chemoinformatics, QSAR models (Quantitative Structure Activity Relationship) are increasingly studied. They provide an in silico estimation of the properties of chemical compounds including ecotoxicological properties. These models are theoretically valid only for a class of compounds (validity domain) and are sensitive to the presence of outliers. This PhD thesis is focused on the construction of robust global models (including a maximum of compounds) to predict ecotoxicity of chemical compounds on algae P. subcapitata and to determine a validity domain in order to deduce the capacity of a model to predict the toxicity of a compound. These robust statistical models are based on quantile approach in linear regression and regression Support Vector Machine.

Statistics, as a critical component in transportation research, has been widely used to analyze driver safety, travel time, traffic flow and numerous other problems. Many of these popular topics can be interpreted as to establish the statistical models for the latent structure of data. Over the past several years, the interest in latent class models has continuously increased due to their great potential in solving practical problems. In this dissertation, I developed several latent class models to quantitatively analyze the hidden structure of transportation data and addressed related application issues. The first model is focused on the uncertainty of travel time, which is critical for assessing the reliability of transportation systems. Travel time is random in nature, and contains substantial variability, especially under congested traffic conditions. A Bayesian mixture model, with the ability to incorporate the influence from covariates such as traffic volume, has been proposed. This model advances the previous multi-state travel time reliability model in which the relationship between response and predictors was lacking. The Bayesian mixture travel time model, however, lack the power to accurately predict the future travel time. The analysis indicates that the independence assumption, which is difficult to justify in real data, could be a potential issue. Therefore, I proposed a Hidden Markov model to accommodate dependency structure, and the modeling results were significantly improved. The second and third parts of the dissertation focus on the driver safety identification. Given the demographic information and crash history, the number of crashes, as a type of count data, is commonly modeled by Poisson regression. However, the over-dispersion issue within the data implies that a single Poisson distribution is insufficient to depict the substantial variability. Poisson mixture model is proposed and applied to identify risky and safe drivers. The lower bound of the estimated misclassification rate is evaluated using the concept of overlap probability. Several theoretical results have been discussed regarding the overlap probability. I also introduced quantile regression based on discrete data to specifically model the high-risk drivers. In summary, the major objective of my research is to develop latent class methods and explore the hidden structure within the transportation data, and the approaches I employed can also be implemented for similar research questions in other areas. / Ph. D.