# 2016-Statistical Methods and Applications 3

Statistical Methods and Applications 3
Chair: Anand N. Vidyashankar (George Mason University)
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Simulation-based Estimation in Regression Models with Ordinal Response Variable and Mismeasured Covariates  [PDF]

A common problem in regression analysis is that some covariates are measured with errors. We present a simulation-based approach for the inference in the cumulative logit model for ordinal response variable and mismeasured covariates. We propose a simulation-based approach to overcome the computational difficulty of minimizing an objective function which involves multiple integrals and thus obtaining estimators for unknown parameters. This method does not require parametric assumptions for the distributions of the unobserved covariates and error components. Consistency and asymptotically normality for the proposed estimator are derived under some regularity conditions. Finally, the methodology is illustrated through simulation studies.

REN MINGCHEN, University of Calgary
Likelihood Estimation of the Gaussian Copula Distribution for Mixed Data via PX-MCEM  [PDF]

I employ the Gaussian copula distribution (GCD) to construct a joint distribution for mixed variables, where I adopt latent variable description of the binary variables. The model generalizes the grouped continuous model (GCM) or the multivariate probit model for binary data and its extension, the conditional GCM (CGCM), to mixed data. I used the parameter-expanded EM algorithm (PX-MCEM) to estimate the parameters. I also carried out a simulation study to investigate the finite-sample properties of the estimates. This is a joint work with A. R. de Leon and Y. Yan.

BOUCHRA NASRI, INRS-ETE
Copula-Based Quantile Regression and Inference [PDF]

In this work, we introduce a new approach for nonlinear quantile regression modelling based on the copula function. The main idea of this approach is to describe the conditional quantile by using the link between the conditional distribution of the variable of interest given the covariate with the copulas function and the marginal distribution. The quantile estimation will be done by estimating the parametres of the copula function and marginal distributions. Parametric and a semi-parametric estimators for the quantile functions are proposed and their asymptotic normality are established. Simulation results show the performance of theses proposed estimators.

MONSUR CHOWDHURY, University of Manitoba
Optimal Designs for Maximum Likelihood Estimation  [PDF]

There are many problems in statistics, which demand the calculation of one or more optimizing probability distributions. We consider one such problem in which we determine maximum likelihood estimates of cell probabilities under the hypothesis of marginal homogeneity in square contingency tables. This is a maximization problem subject to satisfying several constraints. We first formulate the Lagrangian function and then transform the problem to that of maximizing some functions of the cell probabilities simultaneously. Finally, we apply the methodologies in some real data sets. The methodologies are quite flexible and could be applied to a wide class of optimization problems.

MAYSUM PANJU, University of Waterloo
Topic Modelling in Natural Language Processing [PDF]

Documents written in natural language typically are not just structured sequences of randomly selected words. The underlying distribution determining which words might be found in a given document typically depends on some latent factors describing the overall domain of the document, which we can refer to as topics''. Using statistical methods, these hidden topics can be discovered and identified based on the words that are observed across various documents. In this talk, we'll explore a high-level overview of some of these methods, which ultimately allow machines to infer the central topics and concepts that shape a body of text.