Consider testing whether F = F0 for a continuous cdf on R = (-∞,∞) and for a random sample X1,..., Xn from F. We derive expansions of the associated asymptotic power based on the Cramer-von Mises, Kolmogorov-Smirnov and Kuiper statistics. We provide numerical illustrations using a double-exponential example with a shifted alternative.
Outliers in a time series often cause problems in fitting a suitable model to the data. Hence predictions based on such models are liable to be erroneous. In this paper we consider a stable first-order autoregressive process and suggest two methods of substituting an outlier by imputed values and then predicting on the basis of it. The asymptotic properties of both the process parameter estimators and the predictors are also studied.
Predictive sample reuse methods usually applied in low structure aparametric paradigms are shown to be useful in certain high structure situations when conjoined with a Bayesian approach. Particular attention is focused on the incomplete data situation for which two alternative sample reuse approaches are devised. The first involves differential weighting and the second a recursive sample reuse algorithm. These are applied to censored exponential survival data. The exponential approach appears to...
A method for estimation of probability distribution of transformed random variables is presented. The proposed approach admits an approximation of the transformation of the random variables. The approximate probability density function (pdf) is corrected to obtain a resulting pdf which incorporates a prior knowledge of approximation errors. The corrected pdf is not contaminated by any uncontrollable approximation. The method is applied to pattern recognition. It is shown that class conditional pdf...
Consideramos la conexión que existe entre la información de Kullback y los tests admisibles óptimos en el conjunto de riesgos de Neyman-Pearson, usando para ello el estudio de problemas de programación matemática de tipo infinito. Se obtienen resultados que caracterizan un subconjunto de soluciones Bayes como consecuencia del conocimiento de la información, así como una medida de discriminación entre hipótesis para el conjunto de riesgos.
La connaissance de la robustesse des méthodes usuelles d'inférence statistique vis-à-vis de divers types d'écarts par rapport au modèle de base est essentielle pour leur bonne utilisation. Dans cet article sont exposés un certain nombre de résultats (pour la plupart classiques. mais parfois mal connus) concernant la robustesse de ces méthodes vis-à-vis de la non-normalité (pour les comparaisons de moyennes, puis pour les comparaisons de variances), vis-à-vis de la non-équidistribution et de la non-indépendance,...
Le conflit robustesse-efficacité se trouve posé notamment chaque fois que l'on a à choisir entre deux méthodes d'inférence statistique dont l'une est privilégiée sous un modèle plus spécifique et l'autre sous un modèle plus général. Ce conflit est étudié dans le cas de la comparaison de deux moyennes (groupes indépendants), à propos du choix entre le modèle (spécifique) postulant l'égalité des variances intra-groupes et le modèle (général) à variances quelconques. On montre que le choix n'est crucial...
The properly recorded standard deviation of the estimator and the properly recorded estimate are introduced. Bounds for the locally best linear unbiased estimator and estimate and also confidence regions for a linearly unbiasedly estimable linear functional of unknown parameters of the mean value are obtained in a special structure of nonlinear regression model. A sufficient condition for obtaining the properly recorded estimate in this model is also given.
We introduce and analyze a class of estimators for distribution parameters based on the relationship between the distribution function and the empirical distribution function. This class includes the nonlinear least squares estimator and the weighted nonlinear least squares estimator which has been used in parameter estimation for lifetime data (see e.g. [6, 8]) as well as the generalized nonlinear least squares estimator proposed in [3]. Sufficient conditions for consistency and asymptotic normality...