Single index models are a special type of nonlinear regression model that are partially linear and play an important role in fields that employ multidimensional regression models. A wavelet series is thought of as a good approximation to any function in the space. There are two ways to represent the function: one in which all wavelet coefficients are used in the series, and another that allows for shrinkage rules. We propose posterior inference for the two wavelet representations of the function. To implement posterior inference, we define a hierarchial (mixture) prior model on the scaling(wavelet) coefficients. Since from the two representations a non-zero coefficient has information about the features of the function at a certain scale and location, a prior model for the coefficient should depend on its resolution level. In wavelet shrinkage rules we use "pseudo-priors" for a zero coefficient. In single index models a direction theta affects estimates of the function. Transforming theta to a spherical polar coordinate is a convenient way of imposing the constraint. The posterior distribution of the direction is unknown and we employ a Metropolis algorithm and an independence sampler, which require a proposal distribution. A normal distribution is proposed as the proposal distribution for the direction. We introduce ways to choose its mode (mean) using the independence sampler. For Monte Carlo simulations and real data we compare performances of the Metropolis algorithm and independence samplers for the direction and two functions: the cosine function is represented only by the smooth part in the wavelet series and the Doppler function is represented by both smooth and detail parts of the series.

A passive investment management model was developed via a critical literature review of portfolio methodologies. This model was developed based on the fundamental models originated by both Markowitz and Sharpe. The passive model was automated via the development of a computer programme that can be used to generate the required outputs as suggested by Markowitz and Sharpe. For this computer programme MATLAB is chosen and the model’s logic is designed and validated. The demonstration of the designed programme using securities traded is performed on Johannesburg Securities Exchange. The selected portfolio has been sub-categorised into six components with a total of twenty- seven shares. The shares were grouped into different components due to the investors’ preferences and investment time horizon. The results demonstrate that a test portfolio outperforms a risk- free money market instrument (the government R194 bond), but not the All Share Index for the period under consideration. This design concludes the reason for this is due in part to the use of the error term from Sharpe’s single index model. An investor following the framework proposed by this design may use this to determine the risk- return relationship for selected portfolios, and hopefully, a real return.

This thesis explores the association between a response variable and various regressors in dairy cattle breeding data using the various survival models in general and the partially linear single index survival model (PLSISM) in particular. In this study calf survival data and culling data were used. The calf survival data contains the following information: survival time, birth weight, weaning weight, calving ease score, average daily gain, number of disease incidences and serum total protein content. The culling data include, survival time, herd size variation, production level (milk, fat and protein), type of supervision, body condition score and age at first calving. Both data sets contain herd, year and season of calving and were analyzed using the various survival models. The Weibull model, however, was used for detailed analyses of the data sets. The nonparametric vector of PLSISM includes body weight, total serum protein and average daily gain for calf survival data and age at first calving, fat production and body condition core for culling data. The parametric vector of PLSISM consists of the rest of the covariates. The results show that the estimates of the parametric component are similar in the two models (Weibull and PLSISM). However, the estimates of the nonparametric component differ from parametric analysis. This difference may be attributed largely to the nonlinearity of the estimated function indicating the standard linear survival model does not adequately describe the underlying association between the response variable and the various covariates in this study. This is the first implementation and application of this complex model, PLSISM, with large real censored data.

Different from the standard treatment discovery framework which is used for finding single treatments for a homogenous group of patients, personalized medicine involves finding therapies that are tailored to each individual in a heterogeneous group. In this paper, we propose a new semiparametric additive single-index model for estimating individualized treatment strategy. The model assumes a flexible and nonparametric link function for the interaction between treatment and predictive covariates. We estimate the rule via monotone B-splines and establish the asymptotic properties of the estimators. Both simulations and an real data application demonstrate that the proposed method has a competitive performance.

[pt] Muitos dos trabalhos em finanças, como os que envolvem modelos financeiros,concentram-se na busca de formas de rejeitar as suposições sobre as quais estes se baseiam. Contudo, uma questão importante, é verificar se um determinado modelo supera ou é superado pelas alternativas existentes.Assim foi feito nesta pesquisa, que tem como objetivo principal mostrar que o gerenciamento ativo de carteiras dos fundos de pensão, com todas as limitações constantes em sua legislação cria valor, se comparado ao gerenciamento passivo. Ou seja, o gerenciamento ativo supera o gerenciamento passivo de carteiras.Basicamente, neste trabalho são apresentadas as limitantes presentes na legislação dos fundos de pensão e metodologias para a construção de carteiras.A carteira passiva foi construída segundo os conceitos presentes no algoritmo de Elton, Gruber e Padberg.A carteira ativa foi construída segundo um processo proposto por Grinold e Kahn de transformar sinais / informações em alphas / previsões.Para a segunda etapa do processo de geração de uma carteira ativa foram utilizadas três técnicas de construção de carteiras: a metodologia das janelas; a metodologia da estratificação; e a metodologia de programação quadrática onde foi utilizado o programa AEGIS 3.0 da consultoria BARRA. Após a construção das carteiras uma comparação, entre ambas, valida o objetivo proposto. / [en] Many of the works in finance, as the ones that involves financial models, are concentrated in fetching the forms to reject the assumptions on which these are based.However, an important question is to verify if one specific model surpasses or is surpassed by the other alternatives. Thus, it was made in this work, which main objective is showing that the active pension funds portfolio management, with all those legislation restrictions, creates value when it was compared to the passive management. In other words, the active portfolio management surpasses the passive management. Basically, in this work, we present the restrictions of the pension funds legislation and the methodology of the portfolio construction.The passive portfolio was built according to the concepts presented in the Elton, Gruber and Padberg algorithm. The active portfolio was built according to the process considered by Grinold and Kahn to transform signs / information into alphas / forecasts. For the second step of the process of the portfolio construction, there are three generic classes of procedures that cover the vast majority of institutional portfolio management, that are used: Screens; Stratification; and Quadratic Programming, in which we used AEGIS 3.0 of BARRA consult. After the portfolio construction we match the results to validate the main objective.

Preview:     SEB Investment Strategy is the function in SEB that supports business units SEB      Private Banking and SEB Retail with investment philosophy and investment            process. The framework of SEB Investment Strategy encompasses to manage a     structured investment philosophy and process to produce a range of investment                    options and portfolios for different target groups. From January 2006 to October        2009 forty “Proposal for fund portfolios” were produced each containing         writing on market condition and expectations plus portfolio recommendations.        Each time four portfolios consisting of six mutual funds was recommended,                    Fund Portfolio 30, 50, 70 and 100. Fund Portfolio 30 (FP30) contained           30% equity fund and 70% fixed-income funds. By same reasoning FP50           contains 50/50 equity- and fixed-income funds, FP70, 70% equity funds and         30% fixed-income funds and FP100 only equity funds.   Purpose:      The aim of this work is to evaluate these SEB Investment Strategy recommended       portfolios for private SEB Retail clients from January 2006 to December 2009.    Evaluation is done by comparing the performance of recommended portfolios       with portfolios produced by applying Vasicek´s Technique and simplified   optimization technique.   Method:     To allow work with Vasicek´s Technique in which we are dependent on a market        portfolio, I have created an Index which includes SEB Mutual Funds and their         share of the Index is determined from each fund´s total assets in relation to the    sum of the total assets under management of all funds inclusive in the Index.   Index consists of 40 mutual funds 2002-2007 and 37 mutual funds 2008         and 2009. The total supply of funds has been reduced to the above numbers by             the following criteria:   Clients must be able to invest in funds through conventional SEB Fund Account. No initiation fees or sales charges. Minimum historical Net Asset Value prices (NAV-prices) from 2nd January 2002. Daily trading and at least 300 million SEK in assets under management. No Fund-in-Fund products. Only SEB or SEB Choice funds.   The closing daily NAV-prices (time series) of these funds have been obtained from seb.se/fonder from 2nd January 2002 to 28th December 2009. With prices daily returns are calculated and used for estimation of historical and average values of variables needed for computing forecasted Alphas and Betas according to Vasicek´s Technique. Mutual funds are then ranked with respect to excess return over forecasted Beta given risk free rate equal to Swedish government 1 month treasury-bill (SSVX1M) at time for optimisation. Top six ranked funds are included in the optimization process. The first optimized portfolio given actual T-bill is then compared to FP100 recommended by SEB Investment Strategy. In order to find optimized solutions to other recommended portfolios premiums are added to actual T-bill rate.

Cette thèse s'intéresse à deux modèles de régression semi-paramétrique permettant de contourner le problème classique du "fléau de la dimension" inhérent aux approches non-paramétriques usuelles. La première partie du travail concerne l'étude d'un modèle de régression dit partiellement linéaire ; le but est d'identifier les régresseurs qui composent la partie non-linéaire de la fonction de régression ainsi que d'estimer tous les paramètres du modèle. Pour ce faire nous définissons des quantités caractéristiques du modèle qui mesurent la linéarité des régresseurs puis nous développons un test du nombre de composantes non-linéaires basé sur cette mesure. La seconde partie porte sur l'étude d'un modèle dit à direction révélatrice unique et consiste à estimer, via des propriétés géométriques, l'axe du modèle et d'en déduire un test convergent et puissant sous une suite d'alternatives locales.

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