Approximate Inference for the Factor Loading of a Simple Factor Analysis Model

We study a factor analysis model with two normally distributed observations and one factor. Two approximate conditional inference procedures for the factor loading are developed. The first proposal is a very simple procedure but it is not very accurate. The second proposal gives extremely accurate results even for very small sample size. Moreover, the calculations require only the signed log-likelihood ratio statistic and a measure of the standardized maximum likelihood departure. Simulations are used to study the accuracy of the proposed procedures.     

Simple and accurate inference for the mean of the gamma model

The two-parameter gamma model is widely used in reliability, environmental, medical and other areas of statistics. It has a two-dimensional sufficient statistic, and a two-dimensional parameter which can be taken to describe shape and mean. This makes it closely comparable to the normal model, but it differs substantially in that the exact distribution for the minimal sufficient statistic is not available. Some recently developed asymptotic theory is used to derive an approximation for observed levels of significance and confidence intervals for the mean parameter of the model. The approximation is as easy to apply as first-order methods, and substantially more accurate.     

Generalized Score Test of Homogeneity Based on Correlated Random Effects Models

We present a family of tests based on correlated random effects models which provides a synthesis and a generalization of recent work on homogeneity testing. In these models each subject has a particular random effect, but the random effects between subjects are correlated. We derive the general form of the score statistic for testing that the random effects have a variance equal to 0. We apply this result to both parametric and semi-parametric models. In both cases we show that under certain conditions the score statistic has an asymptotic normal distribution. We consider several applications of this theory, including overdispersion, heterogeneity between groups, spatial correlations and genetic linkage.     

The impact of negative affectivity on stressor-strain relations: A replication and extension

The present study was a replication and extension of the results of Brief et al. (1988), who found that partialling out negative affectivity reduced the magnitude of stressor-strain correlations considerably. The effect of both trait anxiety and dispositional optimism was partialled out from stressor-strain correlations. Unlike Brief et al. (1988), however, work stress was measured with specific stressor scales rather than life events. Results from two samples of university employees showed that partialling out trait anxiety, dispositional optimism, or both, reduced the magnitude of stressor-strain correlations very little. Thus, it does not appear that stressor-strain correlations can be attributed to negative affectivity. The possibility that the results of the study by Brief et al. (1988) may have been due to problems with the life events approach used to measure work stress is discussed. Future research on the impact of dispositions is suggested.     

Integer-valued moving average (INMA) process

A simple model for a stationary sequence of dependent integer-valued random variables {X_n} is given. The sequence to be called integer-valued moving average (INMA) process, is taken as the “survivals” of i.i.d. non-negative integervalued random variables. It is argued that the model’s structure reflects to some extent the mechanism generating real life data for many counting process and consequently it is useful for modelling such processes. Various properties for the special case in which {X_n} is Poisson INMA (1) process, such as the joint distribution, regression, time reversibility, along with the conditional and partial correlations, are discussed in details. Extension of the INMA of first order to higher order moving average is considered.     

广义经典力学的非等时变分方程和积分不变量

给出了广义经典力学的正则方程，研究了其非等时变分方程，讨论了它们的解，并证明可由第一积分构造相应的积分不变量．     

单变量时间序列模型识别方法的实证研究

时间序列分析就是通过研究时间序列中数值上的统计关系,来揭示系统的动态结构特征及其发展变化规律,是一种重要的现代统计分析方法,广泛地应用于自然领域、社会领域的科学研究和思维。在时间序列变量建模的过程中,一般分为模型识别、模型估计和诊断以及模型预测三个步骤,其中模     

On efficient inferences in familial-longitudinal binary models with two variance components

When a generalized linear mixed model (GLMM) with multiple (two or more) sources of random effects is considered, the inferences may vary depending on the nature of the random effects. For example, the inference in GLMMs with two independent random effects with two distinct components of dispersion will be different from the inference in GLMMs with two random effects in a two factor factorial design set-up. In this paper, we consider a familial-longitudinal model for repeated binary data where the binary response of an individual member of a family at a given time point is assumed to be influenced by the past responses of the member as well as two but independent sources of random family effects. For the estimation of the parameters of the proposed model, we discuss the well-known maximum-likelihood (ML) method as well as a generalized quasi-likelihood (GQL) approach. The main objective of the paper is to examine the relative asymptotic efficiency performance of the ML and GQL estimators for the regression effects, dynamic (longitudinal) dependence and variance parameters of the random family effects from two sources.     

Parallel analysis approach for determining dimensionality in canonical correlation analysis

ABSTRACT

Canonical correlations are maximized correlation coefficients indicating the relationships between pairs of canonical variates that are linear combinations of the two sets of original variables. The number of non-zero canonical correlations in a population is called its dimensionality. Parallel analysis (PA) is an empirical method for determining the number of principal components or factors that should be retained in factor analysis. An example is given to illustrate for adapting proposed procedures based on PA and bootstrap modified PA to the context of canonical correlation analysis (CCA). The performances of the proposed procedures are evaluated in a simulation study by their comparison with traditional sequential test procedures with respect to the under-, correct- and over-determination of dimensionality in CCA.     

ESTIMATION OF FAMILIAL CORRELATIONS UNDER AUTOREGRESSIVE CIRCULAR COVARIANCE

Circular covariance matrices play an important role in modeling phenomena in numerous epidemiological, communications and physical contexts. In this article, we propose a parsimonious, autoregressive type of circular covariance structure for modeling correlations between the “siblings” of a “family”. This structure, similar to AR(1) structure used in time series models, involves only two parameters. We derive the maximum likelihood estimators of these parameters, and discuss testing of hypotheses about the autoregressive parameter. Estimation of “parent-sib” correlation, namely, the interclass correlation, is also considered. Estimation of the parameters when there are unequal numbers of siblings in different families is also discussed.