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

Moderate deviations of minimum contrast estimators under contamination

Since statistical models are simplifications of reality, it is important in estimation theory to study the behavior of estimators also under distributions (slightly) different from the proposed model. In testing theory, when dealing with test statistics where nuisance parameters are estimated, knowledge of the behavior of the estimators of the nuisance parameters is needed under alternatives to evaluate the power. In this paper the moderate deviation behavior of minimum contrast estimators is investigated not only under the supposed model, but also under distributions close to the model. A particular example is the (multivariate) maximum likelihood estimator determined within the proposed model. The set-up is quite general, including for instance also discrete distributions. \u

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

Control charts using minima instead of averages

Traditional control charts are commonly based on the averages of the inspected groups of observations. It turns out to be quite worthwhile to consider alternative approaches. In particular, a very good proposal is to use instead the group minimum for comparison to some suitable upper limit (and likewise the group maximum for comparison to a lower limit). The power of detection during Out-of-Control of the resulting chart is comparable to that of the standard Shewhart approach, while it offers much better protection to the effects of parameter estimation and/or nonnormality than the traditional methods

Estimation in Shewhart control charts

The influence of the estimation of parameters in Shewhart control charts is investigated. It is shown by simulation and asymptotics that (very) large sample sizes are needed to accurately determine control charts if estimators are plugged in. Correction terms are developed to get accurate control limits for common sample sizes in the in-control situation. Simulation and theory show that the new corrections work very well. The performance of the corrected control charts in the out-of-control situation is studied as well. It turns out that the correction terms do not disturb the behavior of the control charts in the out-of-control situation. On the contrary, for moderate sample sizes the corrected control charts remain powerful and therefore, the recommendation to take at least 300 observations can be reduced to 40 observations when corrected control charts are applied