Half-sample variance estimation

This paper studies an alternative to the jackknife variance estimator, the half-sample variance estimator. Both theoretical and Monte Carlo comparisons between the half-sample variance estimator and the jackknife variance estimator indicate that the former is better in some situations.     

James - stein regression estimation in a prediction context

Two types of shrunken estimators of regression coefficients are studied in the context of stochastic predictor variables. Emphasis is placed on the choice of the shrinkage parameters, using a ‘deleted-observation’ concept which is motivated by predictive ability.     

Affiliation networks with an increasing degree sequence

Affiliation network is one kind of two-mode social network with two different sets of nodes (namely, a set of actors and a set of social events) and edges representing the affiliation of the actors with the social events. Although a number of statistical models are proposed to analyze affiliation networks, the asymptotic behaviors of the estimator are still unknown or have not been properly explored. In this article, we study an affiliation model with the degree sequence as the exclusively natural sufficient statistic in the exponential family distributions. We establish the uniform consistency and asymptotic normality of the maximum likelihood estimator when the numbers of actors and events both go to infinity. Simulation studies and a real data example demonstrate our theoretical results.     

Uniformly minimum variance unbiased estimation in lognormal and related distributions

The uniformly mimimum variance unbiased estimators and their variances from independent samples of lognormal distributions are concisely expressed using the hypergeometric functions     

A time series model with random coefficients

There are many time series applications where an experi­menter observes the simultaneous responses of several sub­systems over time. In these instances one is often not interested in the parameters of individual subsystems, but rather in an overall characterization of the system in question. Under the assumption that subsystems are independent and first order autoregressive, the present paper presents two methods for estimating the distribution of the subsystem coefficients.     

Anova and minque type of estimators for the one-way random effects model

The one-way random effects model with unequal variances and unequal sample sizes is considered. Estimation of the variances, variance of a single observation (total variance), and the standard error of the unweighted mean are considered. Precision of the Analysis of Variance and Unweighted Sums of Squares type of estimators and the Minimum Norm Quadratic Unbiased Estimators with a priori weights are examined.     

Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models

Outlier detection algorithms are intimately connected with robust statistics that down‐weight some observations to zero. We define a number of outlier detection algorithms related to the Huber‐skip and least trimmed squares estimators, including the one‐step Huber‐skip estimator and the forward search. Next, we review a recently developed asymptotic theory of these. Finally, we analyse the gauge, the fraction of wrongly detected outliers, for a number of outlier detection algorithms and establish an asymptotic normal and a Poisson theory for the gauge.     

A Note on Superiority Comparisons of Homogeneous Linear Estimators

This note extends some results on homogeneous linear estimators to the general, even nonlinear case.A Sufficient condition for the difference of mean square error matrices of minimum conditional mean square error estimator and minimum average risk linear estimator to be postive definite is derived.     

Parameter estimation for switched counting processes

The paper investigates parameter estimation problems in special Markov modulated counting processes. The events occuring at any state of an underlying Markov chain can be equipped with marks performing additional information on the events. Specifying the model to the case of two-state Markov chain modulation, the so-called switched counting process, some statistical problems are studied:maximum likelihood estimators, Rao-Blackwell optimal estimators, test of equality of the counting intensities of the two states and minimax estimation procedures. Tne consideration could be applied in various practical problems, in particular, in queueing and in reliability models, for example in failure-repair processes with alternatively operating repair systems.     

Estimation of regression models with equi-correlated responses when some observations on the response variable are missing

The present article deals with the problem of estimation of parameters in a linear regression model when some data on response variable is missing and the responses are equi-correlated. The ordinary least squares and optimal homogeneous predictors are employed to find the imputed values of missing observations. Their efficiency properties are analyzed using the small disturbances asymptotic theory. The estimation of regression coefficients using these imputed values is also considered and a comparison of estimators is presented.