MARKOV CHAINS SATISFYING SIMPLE DRIFT CONDITIONS FOR SUBGEOMETRIC ERGODICITY

This paper is concerned with ergodic Markov chains satisfying a sequence of drift conditions that imply (f, r)- regularity of the chain, by which subgeometric ergodicity is ensured. An interesting exact trade-off result between the exponents of f and r for a special class of state space models by Tuominen and Tweedie (1994) is extended here from integers to real numbers for general Markov chains satisfying these drift conditions simultaneously as well as standard requirements for ergodic Markov chains. In Section 3, we will illustrate by the state space models that the utilization of these drift conditions is a very convenient way to show subgeometric ergodicity of Markov chains including the exact trade-off between the exponents of f and r.     

On the inferential use of predictive sample reuse

The predicitive sample reuse (PSR) data analysis technique proposed by Geisser and Eddy (1979) is applied to the analysis of categorical data. This application yiclds a new approach which has a number of advantages over classical methods for analysis of such data. A PSR technique for comparing linear or nonlinar regressino relationships, for two or more populations, and a PSR ailernative to certain nonparaemetri statistical tesis are also proposed.     

A Simulation Comparison of Approximate Tests for Fixed Effects in Random Coefficients Growth Curve Models

Often, the response variables on sampling units are observed repeatedly over time. The sampling units may come from different populations, such as treatment groups. This setting is routinely modeled by a random coefficients growth curve model, and the techniques of general linear mixed models are applied to address the primary research aim. An alternative approach is to reduce each subject’s data to summary measures, such as within-subject averages or regression coefficients. One may then test for equality of means of the summary measures (or functions of them) among treatment groups. Here, we compare by simulation the performance characteristics of three approximate tests based on summary measures and one based on the full data, focusing mainly on accuracy of p-values. We find that performances of these procedures can be quite different for small samples in several different configurations of parameter values. The summary-measures approach performed at least as well as the full-data mixed models approach.     

Marital and Cohabitation Dissolution and Parental Depressive Symptoms in Fragile Families

The consequences of divorce are pronounced for parents of young children, and cohabitation dissolution is increasing in this population and has important implications. The mental health consequences of union dissolution were examined, by union type and parental gender, using the Fragile Families and Child Wellbeing Study (n= 1,998 for mothers and 1,764 for fathers). Overall, cohabitation and marital dissolution were both associated with increased maternal and paternal depressive symptoms, though for married mothers, depressive symptoms returned to predissolution levels with time. Difference‐in‐difference estimates indicated no differences in the magnitude of the increase in depressive symptoms by type of dissolution, though pooled difference models suggested that married fathers increased in depressive symptoms more than cohabiting fathers. Potential time‐variant mediators did not account for these associations, though greater family chaos was associated with increased maternal depressive symptoms, and decreased social support and father–child contact were associated with increased paternal depressive symptoms.     

An Introduction to Modern Matrix Methods and Statistics

In this article, using the representation that the Kalman filter recursions in state-space models can be expressed as a matrix-weighted average of prior and sample estimates, we supplement the usual filtering algorithm by an extreme bounds analysis. Specifically, as the covariance matrix of the state error is varied in the class of symmetric and positive-definite matrices, the filtering estimates are shown to be in an ellipsoid.     

The Unintended Effects of Risk‐Refuting Information on Anxiety

Researchers in the field of risk perception have been asking why people are more worried about risk today than in years past. This article explores one possible answer to this question, associative anxiety. The affect heuristic and the mental network models suggest that anxiety triggered by information regarding a particular risk can spread to other risks of the same category. Research to date, however, has not examined how information refuting the particular risk can also be generalized across other risks. The article presents two experimental studies addressing this issue. Study 1 showed that when participants were presented with information based on a real train collision, they experienced increased anxiety not only about train collisions but also about public transportation in general. In contrast, those who were informed about the train collision case as well as the preventative measures implemented after the accident experienced decreased anxiety about train collisions but not about public transportation more generally. Study 2 measured the changes in participant anxiety about a genetically modified organism (GMO) and compared the influence of information about either the existence or nonexistence of its risk. Similar to Study 1, associative anxiety rippled through the risk category. The results also suggest that the follow‐up information refuting the GMO risk reduced the anxiety toward the hazard drastically, but did not fully alleviate the anxiety toward other hazards in the category. The implications and the limitations of these studies are also discussed.     

Estimation of the mixtures of GLMs with covariate-dependent mixing proportions

ABSTRACT

In this article, we study the estimation for a class of semiparametric mixtures of generalized linear models where mixing proportions depend on a covariate non parametrically. We investigate a backfitting estimation procedure and show the asymptotic normality of the proposed estimators under mild conditions. We conduct simulation to show the good performance of our methodology and give a real data analysis as an illustration.     

Smooth Tests of Copula Specifications

We present a family of smooth tests for the goodness of fit of semiparametric multivariate copula models. The proposed tests are distribution free and can be easily implemented. They are diagnostic and constructive in the sense that when a null distribution is rejected, the test provides useful pointers to alternative copula distributions. We then propose a method of copula density construction, which can be viewed as a multivariate extension of Efron and Tibshirani. We further generalize our methods to the semiparametric copula-based multivariate dynamic models. We report extensive Monte Carlo simulations and three empirical examples to illustrate the effectiveness and usefulness of our method.     

Prior Distributions for Item Parameters in IRT Models

The focus of this article is on the choice of suitable prior distributions for item parameters within item response theory (IRT) models. In particular, the use of empirical prior distributions for item parameters is proposed. Firstly, regression trees are implemented in order to build informative empirical prior distributions. Secondly, model estimation is conducted within a fully Bayesian approach through the Gibbs sampler, which makes estimation feasible also with increasingly complex models. The main results show that item parameter recovery is improved with the introduction of empirical prior information about item parameters, also when only a small sample is available.