Abstract: The problem of component wise estimation of ordered location parameters θ 1 (θ 1 ≤ θ 2) of two independent exponential distributions is investigated. The scale parameters are assumed to be unequal but known. Independent random samples of unequal sample sizes are drawn from two populations and the estimators admissible among the mixed estimators of θ 1 and θ 2 are obtained. It is shown that the minimum risk estimators (MREs) of θ 1 and θ 2 without assuming θ 1 ≤ θ 2 are inadmissible when one does assume that θ 1 ≤ θ 2. The efficiencies of mixed estimators relative to MREs (without assuming θ 1 ≤ θ 2) are tabulated for equal sample sizes and equal scale parameters.

Abstract: Three examples of point processes are given where the autocovariance decays in an inverse power law, but which are not fractal.

Abstract: Recently Gupta and Gupta [3] have discussed point estimation for R= Pr(a′x > b′y) where x p × 1 and y q × 1 are two non-independent multivariate normal variates and a and b are two known vectors. We show how a lower confidence bound can be obtained for R and how this can be used to refine the inference for the application considered by Gupta and Gupta. Furthermore the case of independent x and y is considered and an application of this case is presented.

Abstract: The paper is devoted to the development of the known splitting and Russian roulette method for Markov chains simulation. Representations for variances of unbiased parameter estimates and optimal numbers for branching are obtained. Efficiency of the method applied to M/M/1 queueing system is estimated.

Abstract: The paper develops a general framework for the formulation of generic uniform laws of large numbers. In particular, we introduce a basic generic uniform law of large numbers that contains recent uniform laws of large numbers by Andrews [2] and Hoadley [9] as special cases. We also develop a truncation approach that makes it possible to obtain uniform laws of large numbers for the functions under consideration from uniform laws of large numbers for truncated versions of those functions. The point of the truncation approach is that uniform laws of large numbers for the truncated versions are typically easier to obtain. By combining the basic uniform law of large numbers and the truncation approach we also derive generalizations of recent uniform laws of large numbers introduced in Potscher and Prucha [15, 16].

Abstract: The asymptotic behavior of the MLE of a parameter of partially observed linear system is studied. Using asymptotic expansion of this estimate by the powers of diffusion coefficient the consistency and asymptotic normality of MLE are proved. The time of observation is supposed to be fixed and the asymptotics corresponds to small noises in observed and nonobserved equations.

Abstract: Relative efficiencies of four chain-type estimators using an additional auxiliary variable z in two-phase sampling are studied under a postulated super-population model.

Abstract: The consistency of the maximum likelihood estimator is considered with an approach from its uniform consistency. Regularity conditions for its consistency are given in consideration of the Wald conditions. The relationship among the conditions is also discussed.

Abstract: We consider the multivariate linear and affine functional models for which several observations for each mean are available (replications of observations). In the case of a simple random sampling, which is the assumption made in this study, the number of observations for each mean is a random variable. Let be the sampling covariance matrix Explained by the partition (also called the between covariance matrix) and M a symmetric positive definite p × p matrix that defines a quadratic metric on . The least squares estimation of the parameters of the model in ( , M)amounts to the diagonalization of M The estimators are consistent for any M, but we show that they satisfy an asymptotic efficiency property if and only if we choose for M the inverse of the errors covariance matrix Γ-1. When Γ is unknown and estimated by the sampling Residual covariance matrix (also called the within covariance matrix), we are led to the diagonalization of or (with . A study of the asymptotic properties of the estimators is then f...

Abstract: summary. In Bonneu (1988) a prediction criterion for model selection is defined for Generalized Linear Models (GLM). This criterion, similar to AIC (Akaike, H. (1973)), Sakamoto, Y. and Akaike, H. (1978)) is based on the expected Kullback-Leibler discrepancy (Kullback, S. 1959)), especially defined for prediction. The model selection strategy is employed to select a Nelder's link function (1972) and a small subset of explanatory variables. Data are observed from an experimental design with unequal numbers of replications. This paper deals with the asymptotic estimate of this prediction criterion and compares it with a simulated bootstrap estimate. Usually asymptotic criteria for model selection can be written as the sum of a statistic and a bias (see Linhart, H. and Volkers, P. (1984); Linhart, H. and Zucchini, W. (1986)). In the present paper, asymptotic arguments are investigated in a different way, taking into account the prediction objective and GLM framework with unequal numbers of replicates. Our as...

Abstract: Motivated by circle fitting to spatial distributions, this paper looks at the relationship between the expected distance function and the radial density. Inversion of this relationship is given simply in dimensions 1 and 3 and generally by using Mellin transforms. Examples of variance function behaviour are given and calculations of the coefficient of sphericity shown.

Abstract: We study a mixed linear model with two variance components. We suppose that one component is known. The objective of the paper is the estimation of the unknown component. The usual MINQE estimators seem to be unadapted to the problem. So we propose a new family of quadratic estimators, based on a natural class of estimators and the idea upon which the MINQE theory is built. All the estimators are compared on simulated data.

Abstract: Considering a class of randomized response trials for eliciting sensitive information from a sample survey and a class of ordered sampling designs, a uniformly minimum variance unbiased estimator of population mean (of the sensitive character) has been obtained.

Abstract: It is shown that the number of non-void arrangements of {1, … k}, where is some realization of a random variable X with distribution defined by ,which occur in connection with the rencontre problem (as the probability for m fixed points of permutations of {1, … ,n} selected with probability ), is the uniquely determined unbiased estimator of . Here stands for the one-point mass at zero. Furthermore, the class of all unbiased estimators of n with respect to the family , where the case n = 0 is excluded, is determined and all locally MVU estimators at every in the model are characterized. In particular, it turns out that there does not exist a uniformly MVU resp. a locally MVU estimator for n at every in the model .

Abstract: We consider an experiment with blocks of equal size involving some qualitative treatments, one of which is a control treatment, and some controlled explanatory variables that can vary only from one block to another. The assumed model includes interactions between treatments and explanatory variables. The objective of the experiment is to compare the mean responses of the treatments with the mean response of the control for all possible values of the explanatory variables. First, conditions for a design to be optimal are established in the set-up of exact design theory. Then, the construction of designs that satisfy these conditions is studied. Conditions for a design to be optimal under several models are also given. Finally, an example is presented.

Abstract: This paper deals with the two—sample (unequal sized) problem where F m (x) and G n(x) are the two empirical distribution functions and investigates the null joint and marginal distributions of certain rank order statistics through the extended Dwass technique based on simple random walk with independent steps given by Aneja (1975).

Abstract: Let X 1, …, X n be a sequence of independent real random variables with common distribution function F and density function f. Let be the corresponding order statistics and let denote the associated spacings. Define the empirical distribution function of the spacings. It is known that G n,F converges. We characterize completely the distributions F which give the same G F as well as the set of GF's when f describes the set of all densities on. Moreover, given a limiting function G, we construct all the distributions F for which G F = G. In addition we establish two Tauberian theorems which relate the behaviour of G F at infinity (resp. in 0) to the behaviour of f at infinity (resp. in 0 when f has a singularity at the origin).

Abstract: sLingappaiah (1986) was the first to introduce the idea of Bayesian prediction in life testing when the size of the future sample is a random variable. In this paper we discuss the Bayesion prediction of the sample median when the parent distribution is a generalized Burr distribution (GBD), the old sample is censored type II and the size of the future sample is a random variable. A numerical illustration is provided.

Abstract: We consider the problem of estimating the unknown variance function υ in a nonparametric regression model. As a basis for our estimators we take estimated residuals which are based on a kernel estimator of the mean vector. Then we form with these residuals a kernel estimator of υ. Main emphasis is on a data-driven choice of the bandwidths involved in the procedure. It is shown that the risk of this estimator attains the uniform convergence rate in Sobolev classes for υ under weak smoothness assumptions on the mean. Moreover, we prove that there is asymptotically no loss due to the estimation of the mean.

Abstract: A non-parametric estimation method is proposed for the intensity of the Poisson process associated to a Boolean random function. The case studied is that of marks being half-spheres as primary functions, these half-spheres lying on a given horizontal plane. The proposed method is derived from the method presented in Gyorfi, Hardle, Sarda et Vieu [1989] for the case of time series. An application in soil science is presented.