Abstract. The problem of estimating a normal mean with unknown variance is considered under an asymmetric loss function such that the associated risk is bounded from above by a known quantity. In the absence of a fixed sample size rule, a sequential stopping rule and two sequential estimators of the mean are proposed and second-order asymptotic expansions of their risk functions are derived. It is...

Abstract. Two characterizations of normal distributions based on the third conditional moment and the fourth conditional moment, respectively, are given. These results theoretically support the goodness-of-fit tests for normal distributions using the sample skewness and the sample kurtosis.

Abstract. Given that no false alarm was made, the CUSUM process behaves like a stationary process. The corresponding transition density is derived for Erlang distributed random variables. Then a representation for the so-called average delay and a geometric approximation for the CUSUM run length distribution is obtained.

Abstract. General sufficient and necessary conditions for minimax design are here reconsidered in a form allowing application in various optimal design problems. In combination with the Elfving theorem they are used to find maximin efficient designs for a two-dimensional linear extrapolation, and to find the optimum design for estimating the maximum point of a quadratic response function with intercept...

Abstract. Box-Behnken designs and central composite designs are efficient designs for fitting second order polynomials to response surfaces, because they use relatively small numbers of observations to estimate the parameters. In this paper we investigate the robustness of Box-Behnken designs to the unavailability of observations, in the sense of finding tmax, the maximum number of arbitrary rows...

Abstract. Some nonstationary sequences having independent vector of ranks and vector of order statistics are under consideration. We extend some characterizations in a class of independent r.v.s to a class of Archimedean copula processes and construct the interpretation which gives us a simple way for simulating Archimedean copula processes.

Abstract. Dependent observations commonly arise in factorial experiments. Apart from main-effects two-level designs formed by the Cheng Steinberg reverse foldover algorithm, which are known to be very efficient designs under dependence using the D-criterion, little is known about other designs, models and criteria, and the range of possible behaviour. In this paper, we investigate in detail 8-run...

Abstract. In the present paper we propose a direct approach to prediction in the linear model E[Y]=X, where some but not all of the coordinates of Y are observable, X is a known design matrix, is an unknown parameter vector, and Var[Y] is known and positive definite. To construct a predictor Y*2 of the non-observable part Y2 of Y such that E[Y*2]=E[Y2] and Y*2=B*Y1, where B* is a matrix and Y1 is...

Abstract. The problem of estimation of the scale matrix of a class of elliptical distributions is considered. We propose an improved class of estimators for scale matrix. The exact forms of the risk functions are derived as well. The relative merits of the class of improved estimators to the usual one are appraised in the light of a quadratic loss function. The conditions under which the class of...

Abstract. In this paper, an alternative estimator for estimating population totals in multi-character survey sampling has been suggested when certain variables have poor positive correlation and others have poor negative correlation with selection probabilities. The estimators proposed by Hansen and Hurwitz (1943), Rao (1966) and Sahoo et al. (1994) are shown as special cases of the proposed estimator...

Abstract. We consider a particular two dimensional model, which has a wide applications in statistical signal processing and texture classifications. We prove the consistency of the least squares estimators of the model parameters and also obtain the asymptotic distribution of the least squares estimators. We observe the strong consistency of the least squares estimators when the errors are independent...

Abstract. This article investigates asymptotic properties of the maximum likelihood estimators (MLE) of parameters in the bivariate exponential distribution (BVE) of Marshall and Olkin (1967) based on the following mixed censored data. In life-testing two-component parallel systems (A, B), a cost-saving procedure is to stop the testing experiment after observing the first r failure times of component...

Abstract. This paper considers the estimation of the ratio of population means when some observations are missing. Four estimators are presented and their bias and mean square error properties are studied.

Abstract. Let X1,X2,,Xn be a random sample from a continuous distribution with the corresponding order statistics X1:nX2:nXn:n. All the distributions for which E(Xk+r: n|Xk:n)=aXk:n+b are identified, which solves the problem stated in Ferguson (1967).

Abstract. In the estimation problem of unknown variance of a multivariate normal distribution, a new class of minimax estimators is obtained. It is noted that a sequence of estimators in our class converges to the Steins truncated estimator.

Abstract. It is often required to estimate a quadratic form in survey sampling, especially when one has to estimate the mean squared error of a linear estimator of the population total. In this note we consider the problem of obtaining uniformly nonnegative quadratic unbiased estimators for nonnegative definite quadratic forms. The estimators considered here are necessarily quadratic.

Abstract. In survival analysis, a simple model of informative censoring is the so-called Koziol-Green (KG) model, where the survival function of the censoring times is supposed to be a power of the survival function of the lifetimes. It is well known that this model does not fit well to real data sets. Therefore, in this paper, we propose a generalization of this KG model, where only a part of the...

Abstract. Let X1, X2, be i.i.d. random variables with two-parameter exponential distribution, and suppose that given a sample of size n, the reward is Yn=max {X1, , Xn}cn. When the scale parameter is unknown, the optimal fixed sample size nc* for maximizing the expected reward E (Yn) cannot be found. This paper deals with the problem of approximating the optimal fixed sample size expected reward Rnc*...

Abstract. This paper presents a new widely applicable omnibus test for discrete distributions which is based on the difference between the integrated distribution function (t)=t (1F(x))dx and its empirical counterpart. A bootstrap version of the test for common lattice models has accurate error rates even for small samples and exhibits high power with respect to competitive procedures over a large...

Abstract. In this paper a new approach is presented for testing statistical hypotheses when the hypotheses are fuzzy rather than crisp. In order to establish optimality criteria, we first give new definitions for probability of type I and type II errors. Then, we state and prove the Neyman-Pearson Lemma, on the basis of these new errors, for testing fuzzy hypotheses, and we give a few examples.