# Statistics Postgraduate Talks II

Thursday 18th July, 2013 14:00-15:40 Maths 203

#### Description

#### Khuneswari Pillay - Model Selection and Averaging in the Presence of Missing Values (2pm)

Model selection is an important part of the model-building process and cannot be separated from the rest of the analysis in choosing a best model. In statistical modelling, the main issues have traditionally been model-building, model selection and prediction based on the best model. The problem to be analysed in this research is the implementation of model selection for linear models and generalized linear models in the presence of missing data. The missing data should be dealt with appropriately before estimating the model parameters or predicting future values of the response. In this presentation, three main issues will be discussed: choice of imputation method, the effects of imputation and choice of model selection criteria. Simulation studies were conducted on linear models and generalized linear models to explore these issues. As a result of these simulation studies, the "norm.nob" imputation method (MICE package) and two model selection criteria (AICc and BIC) were chosen for future work.

#### Serdar Neslihanoglu - Test of Unconditional and Conditional Forms of CAPMs in Developed and Emerging Markets (2.20pm)

The purpose of this presentation is to assess the appropriateness of the unconditional (time-invariant) form of the Linear Market Model, which is consistent with the unconditional form of the Two-Moment Capital Assets Pricing Model (CAPM). We compare its performance against three alternative forms of unconditional model. The first two are simple polynomial extensions, namely the Quadratic Market Model and the Cubic Market Model, while the third relaxes these assumptions by using a Generalized Additive Model (GAM). These comparisons will enable us to assess the necessity for the unconditional form of Higher-Moment CAPM, which includes systematic risk measures such as the systematic skewness (co-skewness) and systematic kurtosis (co-kurtosis). The models are fitted by maximum likelihood, although in the case of the polynomial models least squares estimation is equivalent. Furthermore, to compare the performance of the unconditional and conditional (time-varying) forms of the Two-Moment CAPM, the Kalman Filter Mean Reverting (KFMR) model is investigated. The models are compared by applying them to data from 9 developed and 9 emerging markets using weekly data over the period July 2002 - July 2012. The MSCI (Morgan Stanley Capital International) World Index is used as a market proxy.

The appropriateness of the models is assessed by overall measures of model fit (using the AIC, BIC, Adjusted $R^2$), by the statistical significance of the regression parameters, and by graphical comparisons of the fitted models to the data. For the unconditional form of CAPMs, the results suggest that the Linear Market Model is appropriate for the data in the vast majority of the covariate space, with the only inadequacies being caused by extreme values at either end. The existence of such extreme values is especially prevalent in the emerging markets. The GAM improves on the linear model in terms of adjusted $R^2$ by on average 1% for developed markets and 4% for the emerging markets. In the comparison of the unconditional and conditional forms of the Two-Moment CAPM, the results suggest that KFMR outperforms the unconditional linear model and the GAM in terms of overall measures of model fit. The conditional form of Linear Market Model, estimated via KFMR, improves on the unconditional form of Linear Market model, fitted by OLS in terms of Adj $R^2$ by an average 10% for developed markets and 25% for the emerging markets.

#### Charalampos Chanialidis - Bayesian mixture models for quantile regression (2.40pm)

Quantile regression provides a better understanding of how the covariates affect the conditional distribution of the response variable, compared to the classic regression that just models the conditional mean. Almost all quantile regression techniques deal with a continuous response. Quantile regression models for count data have so far received little attention. One approach that has been suggested is adding uniform random noise thus overcoming the problem that $Q_Y(p|x) $ ($p$-th quantile of the conditional distribution of $Y$ given $X=x$) is not a continuous function of the parameters of interest. An alternative approach consists of modelling the response as a mixture of discrete distributions like the Conway-Maxwell-Poisson distribution (COM-Poisson). In order to obtain a quantile regression tool, the mixing weights are assumed to be adaptive. The talk will outline Bayesian inference approaches for such models.

#### Gary Napier - A Bayesian hierarchical model for compositional data (3pm)

Compositional data frequently occur in chemistry. One example is the percentage weights corresponding to chemical elements present in glass. Such compositions are subject to a sum constraint, with zero measurements recorded for some elements, that should be taken into account when the data are analysed. An approach to dealing with zeros in glass elemental compositions is presented, and a Bayesian hierarchical model for glass data developed with the purpose of classifying glass for forensic purposes and for assessing the evidential value of glass as transfer evidence.

#### Kirsten Fairlie - Model-based Clustering with Finite Mixture of Betas(3.20pm)

A fundamental goal in educational research is identifying whether children have mastered certain skills and from this, finding groups of children with similar skill set profiles. In previous studies of childrens’ scores in skill based tests, analysis has focused on Gaussian based clustering techniques including K-Means and Model-based clustering however, when examined, the assumption of normality was found not to hold and instead scores data was found to have characteristics of the beta distribution. This project focuses on introducing a new clustering algorithm based on mixtures of beta distributions and uses a simulation study to test its accuracy.

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