Analysis of the cross-effects in a cross-lagged panel study

Panel studies are statistical studies in which two or more variables are observed for two or more subjects at two or more points in time. Cross-lagged panel studies are comprised of continuous variables which divide naturally into two sets, and otten the primary statistical issue Is to estimate and test the cross-effects which indicate the degree to which each set is related to the other over time. By taking a regression approach to modeling the relationships, we apply multivariate regression methodology to make inferences about the regression coefficients in a cross-lagged panel model. In particular we develop a test of the hypothesis that the regression coefficients indicating the cross-effects are equal and develop simultaneous confidence bounds for various linear combinations of these regression coefficients.     

Orthogonal series estimators and cross-validation

The use of cross-validation is considered in conjunction with orthogonal series estimators for a probability density function. We attempt to establish a data-based procedure which will select both the optimal choice of series, and the best trade-off between bias-squared and variance, i.e. series length. Although the expected value of the estimator looks promising, the rate of convergence is very slow. Simulations illustrate the theoretical results.     

A Bivariate Generalization of the Noncentral Negative Binomial Distribution

This article proposes a bivariate generalization of the noncentral negative binomial distribution which arises as a model in photon and neural counting. This bivariate generalization is derived as a mixed shifted bivariate negative binomial distribution. Various properties and parameter estimation, especially by a minimum distance method based on the probability generating function, are considered. To show the practical usefulness of the bivariate distribution proposed, an application to model low-flux astronomical images is discussed and a real data set has been analyzed.     

Convergence of normalized quadratic forms

The asymptotic behavior of quadratic forms of stationary sequences plays an important role in statistics, for example, in the context of the Whittle approximation to maximum likelihood. The quadratic form, appropriately normalized, may have Gaussian or non-Gaussian limits. Under what circumstances will the limits be of one type or another? And if the limits are non-Gaussian, what are they? The goal of this paper is to describe the historical development of the problem and provide further extensions of recent results.     

Bayesian density estimation using bernstein polynomials

We propose a Bayesian nonparametric procedure for density estimation, for data in a closed, bounded interval, say [0,1]. To this aim, we use a prior based on Bemstein polynomials. This corresponds to expressing the density of the data as a mixture of given beta densities, with random weights and a random number of components. The density estimate is then obtained as the corresponding predictive density function. Comparison with classical and Bayesian kernel estimates is provided. The proposed procedure is illustrated in an example; an MCMC algorithm for approximating the estimate is also discussed.     

A matrix variance inequality

In the course of solving a variational problem Chernoff (Ann. Probab. 9 (1981) 533) obtained what appears to be a specialized inequality for a variance, namely, that for a standard normal variable X, Var[g(X)]E[g^′(X)]². However, both the simplicity and usefulness of the inequality has generated a plethora of extensions, as well as alternative proofs. All previous papers have focused on a single function. We provide here an inequality for the covariance matrix of k functions, which leads to a matrix inequality in the sense of Loewner.     

关于Bernstein定理的推广

本文对Bernsstem定理进行了推广,得到了一种新型的Bernstein多项式。     

A review of representation issues and modeling challenges with influence diagrams

Since their introduction in the mid 1970s, influence diagrams have become a de facto standard for representing Bayesian decision problems. The need to represent complex problems has led to extensions of the influence diagram methodology designed to increase the ability to represent complex problems. In this paper, we review the representation issues and modeling challenges associated with influence diagrams. In particular, we look at the representation of asymmetric decision problems including conditional distribution trees, sequential decision diagrams, and sequential valuation networks. We also examine the issue of representing the sequence of decision and chance variables, and how it is done in unconstrained influence diagrams, sequential valuation networks, and sequential influence diagrams. We also discuss the use of continuous chance and decision variables, including continuous conditionally deterministic variables. Finally, we discuss some of the modeling challenges faced in representing decision problems in practice and some software that is currently available.     

On comparing several straight lines under heteroscedasticity and robustness with respect to departure from normality

This article considers the problem of testing slopes in k straight lines with'heterogeneous variances. The statistic Fβ is proposed and the null and non-null distributions of Fβ derived under normality assumption. The power function values are then approximated by Laguerre polynomial expansion for normal and non-normal universes. For the example given in Graybill ‘1976, p. 295’, it is shown that the Satterthwaite approximation provides a close approximation to the null and non-null distributions in all the cases; it is also shown that the Fβ test is quite robust with respect to departure from normality in the case of mixtures of two normals.     

A Note on the Noncentral Beta Distribution Function

The noncentral beta and the related noncentral F distributions have received much attention during the last decade, as is evident from the works of Norton, Lenth, Frick, Lee, Posten, Chattamvelli, and Chattamvelli and Shanmugam. This article reviews the existing algorithms for computing the cumulative distribution function (cdf) of a noncentral beta random variable, and proposes a simple algorithm, based on a sharp error bound, for computing the cdf. A variation of the noncentral beta random variable when the noncentrality is associated only with the denominator χ² and its computational details are also discussed.