Title page for ETD etd-01052005-021803


Type of Document Dissertation
Author Tabakova, Vera Alexandrova
Author's Email Address vtabak1@lsu.edu
URN etd-01052005-021803
Title Risk Properties of a Stein-Like Estimator for Multinomial Choice Models
Degree Doctor of Philosophy (Ph.D.)
Department Economics
Advisory Committee
Advisor Name Title
R. Carter Hill Committee Chair
Douglas D. Schwalm Committee Member
Eric T. Hillebrand Committee Member
M. Dek Terrell Committee Member
Thomas C. Owen Dean's Representative
Keywords
  • finite sample properties
  • unordered choice
Date of Defense 2004-12-02
Availability unrestricted
Abstract
Stein-rule estimators, also known as shrinkage estimators, combine sample and non-sample information in a way that improves the precision of the estimation process or the quality of subsequent predictions. A Stein-rule estimator is a weighted average of a restricted and an unrestricted estimator, where the weights determine the degree of shrinkage, i.e. the importance that we place on the non-sample information. The existing literature shows that Stein-rule estimators may lead to squared error risk improvements in the linear regression, and in a number of non-linear models.

The dissertation explores Stein-rule estimation in the context of multinomial choice models. It consists of three main parts. First, a Monte Carlo study is conducted to examine the properties of a Stein-rule estimator for the orthonormal conditional logit model. The shrinkage estimator is compared to the maximum likelihood estimator based on different measures of risk, namely squared error risk, weighted error risk, risk of marginal effects, and mean squared error of prediction in-sample and out-of-sample. Secondly, the analysis is extended to a more general data generation process by introducing various degrees of collinearity within alternatives, or between alternative-specific variables. Finally, there are three applications of Stein-rule estimation in multinomial choice models using marketing data.

The main results of the study show that Stein-rule estimators offer significant risk improvement over the maximum likelihood estimator when certain conditions are met. The importance of this research is that shrinkage estimation is an easy to implement alternative to maximum likelihood estimation, which should be preferred in cases where we have good non-sample information, or when we are not sure of the performance of the MLE. The latter refers to data with small number of observations, or collinearity among the regressors, which is often a problem in practical applications.

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