The penalty in data driven Neyman's tests

Data driven Neyman's tests are based on two elements: Neyman's smooth tests in finite dimensional submodels and a selection rule to choose the "right'' submodel. As selection rule usually (a modification of) Schwarz's rule is applied. In this paper we consider data driven Neyman's tests with selection rules allowing also other penalties than the one in Schwarz's rule. It is shown that the nice properties of consistency against very large classes of alternatives and the more deep result of asymptotic optimality in the sense of vanishing shortcoming continue to hold for other penalties as well, including the one corresponding to Akaike's selection rule

Estimation and testing in large binary contingency tables

Very sparse contingency tables with a multiplicative structure are studied. The number of unspecified parameters and the number of cells are growing with the number of observations. Consistency and asymptotic normality of natural estimators are established. Also uniform convergence of the estimators to the parameters is investigated, and an application to the construction of confidence intervals is presented. Further, a family of goodness-of-fit tests is proposed for testing multiplicativity. It is shown that the test statistics are asymptotically normal. The results can be applied in such different fields as production testing or psychometrics

The penalty in data driven Neyman's tests

Data driven Neyman's tests are based on two elements: Neyman's smooth tests in finite dimensional submodels and a selection rule to choose the ``right'' submodel. As selection rule usually (a modification of) Schwarz's rule is applied. In this paper we consider data driven Neyman's tests with selection rules allowing also other penalties than the one in Schwarz's rule. It is shown that the nice properties of consistency against very large classes of alternatives and the more deep result of asymptotic optimality in the sense of vanishing shortcoming continue to hold for other penalties as well, including the one corresponding to Akaike's selection rule

Inequalities for noncentral chi-square distributions

An upper and lower bound are presented for the difference between the distribution functions of noncentral chi-square variables with the same degrees of freedom and different noncentralities. The inequalities are applied in a comparison of two approximations to the power of Pearson's chi-square test

Motor unit properties in the biceps brachii of stroke patients assessed with surface array EMG

As a consequence of a stroke, both motor control as well as motor unit (MU) characteristics may change, e.g. MU size has been reported to increase due to reinnervation. The aim of the present study was to investigate how differences between the affected and unaffected side of hemiparetic stroke patients are reflected in surface array electomyography parameters

Limiting values of large deviation probabilities of quadratic statistics

Application of exact Bahadur efficiencies in testing theory or exact inaccuracy rates in estimation theory needs evaluation of large deviation probabilities. Because of the complexity of the expressions, frequently a local limit of the nonlocal measure is considered. Local limits of large deviation probabilities of general quadratic statistics are obtained by relating them to large deviation probabilities of sums of k-dimensional random vectors. The results are applied, e.g., to generalized Cramér-von Mises statistics, including the Anderson-Darling statistic, Neyman's smooth tests, and likelihood ratio tests