Zur bestimmung von bayes-lösungen bei messender prüfung

A model of sampling inspection by variables is presented, where the loss function and the a priori distribution of the unknown defective fraction are assumed to be known. The existence of a BAYES rule in the class of relevant decision functions (sampling plans) is proved. Furthermore, it is shown that under certain conditions the decision functions "accept without sampling" or "reject without sampling" are BAYESian decision rules. Some numerical examples are presented to illustrate the theory developed in the paper.     

Consistency of the least-squares-estimators for linear stochastic difference equations

Assumptions are given for the strong consistency in the stable case and weak consistency in the instable case of the Least-Square-Estimator of the unknown system-parameters of a inhomogeneous linear stochastic difference equation system with constant coefficients.     

D–optimality of a class of saturated main–effect plans and allied results

This paper applies the theory of unimodular matrices to prove that all saturated main effect plans of an s₁ × s₂ factorial are equivalent from the point of view of D–optimality and are hence all D–optimal. The A– and E–optimal plans in this context have also been derived. An application in sequential experimentation has been considered     

Simultaneous control and estimation of linear stochastic systems with unknown parameters of disturbances

In the present paper methods of the decision theory are applied to determine minimax policies of simultaneous control and estimation for stochastic system (1). There are solved the following cases:

a)when disturbances of the system have the binomial distribution with unknown parameter

b)when disturbances of the system have distribution belonging to an exponential family dependent on natural unknown parameter and the class of prior distributions of parameter is restricted by fixing the second moment

In both cases open analytical forms of minimax policies are given     

Estimation in one–way classification with heteroscedastic error

For an unbalanced one way calssification under the random effect model the problem of estimation of the fixed effect parameter and the variance is considered. Tje error variance which are funtionally related to the above set of parameters are assumed to fall into k classes with constant error varaince for a class. The asymptotic properties of the proposed estimate is established for increasing number of classes k, assuming the number of observations in the classes form a fixed sequence     

Lower Bounds for the Efficiency of Designs with Respect to the D-Criterion when the Observations are Correlated

In the general linear model consider the experimental design problem for the Gauß-Markov estimator or least squares estimator when the observations are correlated. We prove new formulas for the efficiency of an exact design with respect to the D-criterion. For models with intercept term, for example, these formulas are useful to derive better lower bounds for the efficiency than the bounds recently given for an arbitrary linear model. These bounds are applied in examples to symmetrical regular circulants as covariance matrices. A byproduct of the investigations is some insight as to what kinds of designs might retain their optimality or high efficiency (for the uncorrelated homoscedastic case) under correlated observations.     

Robustness of least distances estimate in ultivariate linear models

In this paper, the robustness of the least distances (LD) estimate in multivariate linear models, as defined by Bai, Chen, Miao and Rao (1990), is discussed in terms of the influence function as well as the breakdown point. The LD estimate is shown to be more robust than the least squares (LS) estimate. The robustness of the LD is similar to that of the least absolute deviations (LAD) estimate, a well studied robust estimate in the univariate case. In particular, if there are no outliers in the design matrices, the breakdown point of the LD estimate reaches the highest value, 1/2.     

One-Sample One-Sided Student T-Test Under Contaminants

A paradoxical behavior of the t-test under ε-contamination is presented. The paradox consists in that under a fixed distribution of contaminants an increasing of the probability of the appearance of a contaminant may decrease the violation of the size of the test! A simple explanation of the phenomenon is given. It is revealed which contaminants make the test conservative and which make it liberal: it appears that, in spite of the established opinion, conservatism or liberalism of the test depends not so much on the tails of the contaminating distribution as on where its support is located.     

On the estimation of the stochastic intensity and the parameters of neyman-scott trigger processes

In this paper we are concerned with a class of simple point processes, whose unobservable stochastic intensity is a shot-noise process. We derive a stochastic equation for the conditional moment generating function of the intensity, which can be solved in a recursive way. This yields explicit expression for the minimum variance estimate of the intensity as well as the likelihood ration with respect to the reference measure, on the basis of point process observations.