The conditional test is compared with other relevant test procedures for testing parameters of Normal and Exponential populations. It is seen that under certain conditions the conditional test is more powerful than the relevant unconditional tests. An example is provided where the conditional test given the ancillary is uniformaly more powerful than the obvious unconditional test.
In analysing a well known data set from the literature which can be thought of as a two-way layout it transpires that a robust adaptive regression approach for identifying outliers fails to be sensitive enough to detect the possible interchange of two observations. On the other hand if one takes the classical approach of diagnostic checking one may also stop too early and be satisfied with a model that falls short of a more detailed analysis that takes account of heteroscedasticity in the data....
Regression and scale invariant -test procedures are developed for detection of structural changes in linear regression model. Their limit properties are studied under the null hypothesis.
Regression- and scale-invariant -test procedures for detection of structural changes in linear regression model was developed and their limit behavior under the null hypothesis was studied in Hušková [9]. In the present paper the limit behavior under local alternatives is studied. More precisely, it is shown that under local alternatives the considered test statistics have asymptotically normal distribution.
This paper is concerned with the study of some properties of the distance between statistical individuals based on representations on the dual tangent space of a parametric manifold representation of a statistical model. Explicit expressions for distances are obtained for well-known families of distributions. We have also considered applications of the distance to parameter estimation, testing statistical hypotheses and discriminant analysis.
We consider a measure of the diversity of a population based on the λ-measure of hypoentropy introduced by Ferreri (1980). Our purpose is to study its asymptotic distribution for testing hypotheses. A numerical example based on real data is given.
Two concepts of optimality corresponding to Bayesian robust analysis are considered: conditional Γ-minimaxity and stability. Conditions for coincidence of optimal decisions of both kinds are stated.
Necessary and sufficient conditions are derived for the inclusions and to be fulfilled where , and , are some classes of invariant linearly sufficient statistics (Oktaba, Kornacki, Wawrzosek (1988)) corresponding to the Gauss-Markov models and , respectively.
This paper deals with stability of stochastic optimization problems in a general setting. Objective function is defined on a metric space and depends on a probability measure which is unknown, but, estimated from empirical observations. We try to derive stability results without precise knowledge of problem structure and without measurability assumption. Moreover, -optimal solutions are considered. The setup is illustrated on consistency of a --estimator in linear regression model.