Robust testing with generalized partial linear models for longitudinal data

By approximating the nonparametric component using a regression spline in generalized partial linear models (GPLM), robust generalized estimating equations (GEE), involving bounded score function and leverage-based weighting function, can be used to estimate the regression parameters in GPLM robustly for longitudinal data or clustered data. In this paper, score test statistics are proposed for testing the regression parameters with robustness, and their asymptotic distributions under the null hypothesis and a class of local alternative hypotheses are studied. The proposed score tests reply on the estimation of a smaller model without the testing parameters involved, and perform well in the simulation studies and real data analysis conducted in this paper.     

Interpreting DNA Mixtures with Related Contributors in Subdivided Populations

Abstract.  In this paper, we study the statistical interpretation of forensic DNA mixtures with related contributors in subdivided populations. Compact general formulae for match probabilities are obtained for two situations: a relative of one tested person is an unknown contributor of a DNA mixture; and two related unknowns are contributors. The effect of kinship and population structure is illustrated using a real case example.     

Influence diagnostics and outlier tests for semiparametric mixed models

Summary. Semiparametric mixed models are useful in biometric and econometric applications, especially for longitudinal data. Maximum penalized likelihood estimators (MPLEs) have been shown to work well by Zhang and co-workers for both linear coefficients and nonparametric functions. This paper considers the role of influence diagnostics in the MPLE by extending the case deletion and subject deletion analysis of linear models to accommodate the inclusion of a nonparametric component. We focus on influence measures for the fixed effects and provide formulae that are analogous to those for simpler models and readily computable with the MPLE algorithm. We also establish an equivalence between the case or subject deletion model and a mean shift outlier model from which we derive tests for outliers. The influence diagnostics proposed are illustrated through a longitudinal hormone study on progesterone and a simulated example.     

Generalized Leverage and its Applications

The generalized leverage of an estimator is defined in regression models as a measure of the importance of individual observations. We derive a simple but powerful result, developing an explicit expression for leverage in a general M -estimation problem, of which the maximum likelihood problems are special cases. A variety of applications are considered, most notably to the exponential family non-linear models. The relationship between leverage and local influence is also discussed. Numerical examples are given to illustrate our results     

Further influence measures in factor analysis

Various influence measures are discussed for sensitivity analysis in factor analysis. The internal norm is used to characterize the vector-valued influence curves in factor analysis. Influence curves for the chi-square goodness of fit test, and the determinants of the model covariance matrix and unique variance matrix are derived. They are found to have simple formulas which are easy to be interpreted and have nice distributions for calibration. The likelihood displacement is also applied to sensitivity analysis in maximum likelihood factor analysis.     

On moments and cumulants of the D compound Poisson distribution

This note provides more results on moments and cumulants of the D compound Poisson distribution through the properties of the multivariate generalized power series distribution.     

An analysis of two probabilistic model induction techniques

Two probabilistic model induction techniques, cart and constructor, are compared, via a series of experiments, in terms of their ability to induce models that are both interpretable and predictive. The experiments show that, although both algorithms are able to deliver classifiers with predictive performance close to that of the optimal Bayes rule,constructor is able to generate a probabilistic model that is more easily interpretable than the cart model. On the other hand, cart is a more mature algorithm and is capable of handling many more situations (e.g., real-valued training sets) thanconstructor. A variety of characteristics of both algorithms are compared, and suggestions for future research are made.     

The dependence of voter shares under a two-vote system

In an electoral system where each voter is allowed to select up to two candidates in a double-seat constituency, the combination of votes forms a special kind of contingency table. The usual hypothesis of complete independence of the voter shares for the candidates is of interest, but it is shown to be almost unattainable. The correlation coefficient of the voter shares is constructed. It is shown to be equivalent to Pearson's phi coefficient. The limitations of the coefficient are discussed. It is found that the use of conditional probabilities gives a better understanding of the dependence of the voter shares under the system considered.     

A more generalized stirling distribution of the second kind

A more generalized stirling distribution of the second kind (MGSDSK) is introduced in this paper as the distribution of the sum of the independent but not identically distributed left truncated Poisson variables. Properties of MGSDSK are studied. The recursion relation and decomposition of MGSDSK are obtained. The rth moment is also found and a new recurrence relationship for them are given. A new incomplete exponential function is utilized in the derivations. A MVU estimate of the p, d, f. of MGSDSK is obtained.     

Bowling Alone in Taiwan? Political Trust and Civic Participation of Taiwanese and Their Appraisal of Liberal Democracy and Personal Wellbeing

Social Indicators Research - Based on a nationwide survey dataset collected by Taiwan’s Executive Yuan (2017) (N?=?2737) and adopting structural equation modelling with...