Modified minimax estimation of regression coefficients

Working with the linear regression model (1.1) and having the extraneous information (1.2) about regression coefficients the problem exists how to build estimators (1.3) with the risk (1.4) which enable to utilize the known information in order to reduce their risk as compared with the risk (1.6) of the LSE (1.5). Solution of this problem is known for the positive definite matrix T, namely in form for estimators (1.8) and (1.10).First, it is shown that the proposed estimators (2.6),(2.9) and (2.16) based on psedoinversions of the matrix L represent the solution of the problem of the positive semidefinite matrix T=L'L.Further, the problem of interpretability of estimators in the sense of the inequality (3.1) exists; it is shown that all mentioned estimators are at least partially interpretable in the sense of requirements (3.2) or (3.10).     

A bibliography of statistical tolerance regions,II

This bibiliography (completing the previous one, JILEK 1981a) contains about 130 references dealing with statistical tolerance regions. References are classified according to the type of probability distribution concerned and according to some other criteria as well     

Second-Order Approximations to Two Classes of Sequential Estimation Procedures

For the model considered by Chaturvedi, Pandey and Gupta (1991), two classes of sequential procedures are developed to construct confidence regions (which may be interval, ellipsoidal or spherical) of ‘pre-assigned width and coverage probability’ for the parameters of interest and for the minimum risk point estimation (taking loss to be quadratic plus linear cost of sampling) of the nuisance parameter. Second-Order approximations are derived for the expected sample size, coverage probability and ‘regret’ associated with the two classes of sequential procedures. A simple and direct method of obtaining the asymptotic distribution of the stopping time is provided. By means of examples, it is illustrated that several estimation problems can be tackled with the help of proposed classes of sequential procedures.     

Percentile Related Bounds and Estimator for the Mean of the Negative Binomial Distribution

Upper and lower bounds are obtained for the mean of the negative binomial distribution. These bounds are simple functions of a percentile determined by the shape parameter. The result is then used to obtain a robust estimate of the mean when the shape parameter is known.     

A Comparison of Survival Function Estimators in the Koziol–Green Model

In this paper, three competing survival function estimators are compared under the assumptions of the so-called Koziol– Green model, which is a simple model of informative random censoring. It is shown that the model specific estimators of Ebrahimi and Abdushukurov, Cheng, and Lin are asymptotically equivalent. Further, exact expressions for the (noncentral) moments of these estimators are given, and their biases are analytically compared with the bias of the familiar Kaplan–Meier estimator. Finally, MSE comparisons of the three estimators are given for some selected rates of censoring.     

Projection Measures And Estimation Variances Of Intensities

The paper investigates random processes of geometrical objects in Euclidean spaces. General properties of the measure of total projections are derived by means of Palm distribution. Explicit formulas for variances of the projection measure are obtained for Poisson point processes of compact sets.

Intensity estimators of fibre (surface) processes are then studied by means of projection measures. Classification of direct and indirect probes is introduced. The indirect sampling design of vertical sections and projections is generalized and its statistical properties derived.     

A specification strategy for order determination in arma models

In this paper a specification strategy is proposed for the determination of the orders in ARMA models. The strategy is based on two newly defined concepts: the q-conditioned partial auto-regressive function and the p-conditioned partial moving average function. These concepts are similar to the generalized partial autocorrelation function which has been recently suggested for order determination. The main difference is that they are defined and employed in connection with an asymptotically efficient estimation method instead of the rather inefficient generalized Yule-Walker method. The specification is performed by using sequential Wald type tests. In contrast to the traditional testing of hypotheses, these tests use critical values which increase with the sample size at an appropriate rate