Two-Step Estimation of Incomplete Information Social Interaction Models With Sample Selection

ABSTRACT

This article considers linear social interaction models under incomplete information that allow for missing outcome data due to sample selection. For model estimation, assuming that each individual forms his/her belief about the other members’ outcomes based on rational expectations, we propose a two-step series nonlinear least squares estimator. Both the consistency and asymptotic normality of the estimator are established. As an empirical illustration, we apply the proposed model and method to National Longitudinal Study of Adolescent Health (Add Health) data to examine the impacts of friendship interactions on adolescents’ academic achievements. We provide empirical evidence that the interaction effects are important determinants of grade point average and that controlling for sample selection bias has certain impacts on the estimation results. Supplementary materials for this article are available online.     

Superiority comparisons between mixed regression estimators

This paper gives necessary and sufficient conditions for a mixed regression estimator to be superior to another mixed estimator. The comparisons are based on the mean square error matrices of the estimators. Both estimators are allowed to be biased.     

Some improved ratio type estimators of population mean and ratio in finite population sample surveys

In this paper we present a class of ratio type estimators of the population mean and ratio in a finite population sample surveys with without replacement simple random sampling design, where information on an auxiliary variate x positively correlated with the main variate y is available. Large sample approximations to mean square errors (MSE) of these estimatorsare evaluated and their MSE's are compared with the MSE of the usual ratio estimator [ybar]_R of [ybar] the population mean of y. It is shown that under certain conditions these estimators are more efficient than [ybar]_R. When a prior knowledge of the value of thecoefficient of variation, c_y, of y is at hand, ratio type estimator, say [ybar]₁ of [ybar] is proposed. It is shown, under certain conditions, that [ybar]₁ is more efficient than [ybar]_R. When values of c_y, c_x and the population correlation coefficient ρ is at hand, then we have proposed another estimator, say [ybar]₂ of [ybar], which is always better than [ybar]_R as far as the efficiency is concerned. In fact, is [ybar] ₂ is shown to be even better than [ybar]₁. Finally estimators better than the usual ratio estimator [ybar]/[xbar] of [Ybar] are given.     

Some tests for the power series distibutions in one parameter using the kullback-leibler information measure

The purpose of the article is, in case of one sample, to obtain tests concerning the parameter in the power series distribution in one parameter using Ku11back-Leibier information measure. The class of power series distibutions contains a host of discrete distributions. Ve illustrate the general results obtained in case of the geometric distibution.     

Estimation of gene/haplotype frequencies in genetic marker systems based on phenotype data

Two equivalent methods (gene counting and maximum likelihood) for estimating gene frequencies in a general genetic marker system based on observed phenotype data are derived. Under the maximum likelihood approach, an expression is given for the estimated covariance matrix from which estimated standard errors of the estimators can be found. In addition, consideration is given to the problem of estimating gene frequencies when there are available several independent population data sets.     

Accelerated test system strength models based on Birnbaum–Saunders distribution: a complete Bayesian analysis and comparison

Several models for studies related to tensile strength of materials are proposed in the literature where the size or length component has been taken to be an important factor for studying the specimens’ failure behaviour. An important model, developed on the basis of cumulative damage approach, is the three-parameter extension of the Birnbaum–Saunders fatigue model that incorporates size of the specimen as an additional variable. This model is a strong competitor of the commonly used Weibull model and stands better than the traditional models, which do not incorporate the size effect. The paper considers two such cumulative damage models, checks their compatibility with a real dataset, compares them with some of the recent toolkits, and finally recommends a model, which appears an appropriate one. Throughout the study is Bayesian based on Markov chain Monte Carlo simulation.     

VARIATIONAL BAYESIAN ANALYSIS FOR HIDDEN MARKOV MODELS

The variational approach to Bayesian inference enables simultaneous estimation of model parameters and model complexity. An interesting feature of this approach is that it also leads to an automatic choice of model complexity. Empirical results from the analysis of hidden Markov models with Gaussian observation densities illustrate this. If the variational algorithm is initialized with a large number of hidden states, redundant states are eliminated as the method converges to a solution, thereby leading to a selection of the number of hidden states. In addition, through the use of a variational approximation, the deviance information criterion for Bayesian model selection can be extended to the hidden Markov model framework. Calculation of the deviance information criterion provides a further tool for model selection, which can be used in conjunction with the variational approach.     

Data-driven tests of uniformity on product manifolds

Data-driven versions of Sobolev tests of uniformity on compact Riemannian manifolds are reviewed and their large-sample asymptotic properties are given. A variant which is suitable for product manifolds is introduced. Data-driven goodness-of-fit tests of multivariate distributions are derived from data-driven tests of uniformity on tori.