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

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 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

Are estimated control charts in control?

Standard control chart practice assumes normality and uses estimated parameters. Because of the extreme quantiles involved, large relative errors result. Here simple corrections are derived to bring such estimated charts under control. As a criterion, suitable exceedance probabilities are used. \u

Moderate deviations of maximum likelihood estimators under alternatives

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 the (multivariate) maximum likelihood estimator determined within a proposed model is investigated not only under this model, but also under distributions close to the model. The set-up is quite general, including for instance also discrete distributions

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

Estimation effects on stop-loss premiums under dependence

Even a small amount of dependence in large insurance portfolios can lead to huge errors in relevant risk measures, such as stop-loss premiums. This has been shown in a model where the majority consists of ordinary claims and a small fraction of special claims. The special claims are dependent in the sense that a whole group is exposed to damage. In this model, the parameters have to be estimated. The effect of the estimation step is studied here. The estimation error is dominated by the part of the parameters related to the special claims, because by their nature we do not have many observations of them. Although the estimation error in this way is restricted to a few parameters, it turns out that it may be quite substantial. Upper and lower confidence bounds are given for the stop-loss premium, thus protecting against the estimation effect