In this article, we are interested in deriving the asymptotic distributional risk function of a class of estimator concerning the mean parameter matrix of matrices variate random sample. The proposed result is useful in decision theory, more precisely in risk analysis of a class of some robust estimators such as Stein-rule types estimators.

Trisomies are numerical chromosomal anomalies (aneuploidies) which are common causes of mental retardation, pregnancy losses and fetal death. The determination of the meiosis I nondisjunction fraction plays an important role in the identification of possible factors which could generate such aneuploidies. In this article, more flexible misclassification models for the number of peaks in a polymorphic locus of trisomic individuals are considered. They are compared to some others proposed in the literature. Estimation and tests for the nondisjunction fraction in meiosis I and for the misclassification errors are introduced extending previous works. Using the Decision Theory approach, we also build a criterion for making decisions under Jeffreys and Pereira–Stern tests. We apply the results to Down Syndrome data that is the most prevalent trisomy in humans.

We give Cornish–Fisher expansions for general smooth functions of the sample cross-moments of a stationary linear process. Examples include the distributions of the sample mean, the sample autocovariance and the sample autocorrelation.

Linear dynamic mixed models are commonly used for continuous panel data analysis in economic statistics. There exists generalized method of moments (GMM) and generalized quasi-likelihood (GQL) inferences for binary and count panel data models, the GQL estimation approach being more efficient than the GMM approach. The GMM and GQL estimating equations for the linear dynamic mixed model can not, however, be obtained from the respective estimating equations under the nonlinear models for binary and count data. In this paper, we develop the GMM and GQL estimation approaches for the linear dynamic mixed models and demonstrate that the GQL approach is more efficient than the GMM approach, also under such linear models. This makes the GQL approach uniformly more efficient than the GMM approach in estimating the parameters of both linear and nonlinear dynamic mixed models.

The important problem of the ratio of gamma and beta distributed random variables is considered. Six motivating applications (from efficiency modeling, income modeling, clinical trials, hydrology, reliability and modeling of infectious diseases) are discussed. Exact expressions are derived for the probability density function, cumulative distribution function, hazard rate function, shape characteristics, moments, factorial moments, variance, skewness, kurtosis, conditional moments, L moments, characteristic function, mean deviation about the mean, mean deviation about the median, Bonferroni curve, Lorenz curve, percentiles, order statistics and the asymptotic distribution of the extreme values. Estimation procedures by the methods of moments and maximum likelihood are provided and their performances compared by simulation. For maximum likelihood estimation, the Fisher information matrix is derived and the case of censoring is considered. Finally, an application is discussed for efficiency of warning-time systems.

In this paper we establish the almost sure, in law, and uniform convergence over compact subsets on ℝ of a fuzzy set estimator of the density function, based on n i.i.d. random variable.