Bootstrap Based Goodness-Of-Fit-Tests.
Compact hypothesis and extremal set estimators
In extremal estimation theory the estimators are local or absolute extremes of functions defined on the cartesian product of the parameter by the sample space. Assuming that these functions converge uniformly, in a convenient stochastic way, to a limit function g, set estimators for the set ∇ of absolute maxima (minima) of g are obtained under the compactness assumption that ∇ is contained in a known compact U. A strongly consistent test is presented for this assumption. Moreover, when the true...
Comparing the suitability of two factors for stratification in estimating diversity
Comportamiento de los contrastes ADF, PP y KPSS al trabajar con series ajustadas de estacionalidad.
En este trabajo se analiza el comportamiento de los tests de raíces unitarias cuando se utilizan los componentes ciclo-tendencia obtenidos a partir de procedimientos de extracción de señales en lugar de utilizar las series originales. Adicionalmente se intenta detectar las causas finales de los efectos perniciosos observados. Los procedimientos de extracción de señales analizados son el basado en modelos ARIMA y el filtro de líneas aéreas modificado. Un ejercicio de simulación nos permite concluir...
Detecting Changes in a Multivariate Renewal Process.
Detection of transient change in mean – a linear behavior inside epidemic interval
A procedure for testing occurrance of a transient change in mean of a sequence is suggested where inside an epidemic interval the mean is a linear function of time points. Asymptotic behavior of considered trimmed maximum-type test statistics is presented. Approximate critical values are obtained using an approximation of exceedance probabilities over a high level by Gaussian fields with a locally stationary structure.
Efficiency rate and local deficiency of the most powerful tests in the model of contaminacy with general neighbourhoods
Estimators for epidemic alternatives
We introduce and study the behavior of estimators of changes in the mean value of a sequence of independent random variables in the case of so called epidemic alternatives which is one of the variants of the change point problem. The consistency and the limit distribution of the estimators developed for this situation are shown. Moreover, the classical estimators used for `at most change' are examined for the studied situation.
Exact Bahadur Efficiencies of lests for Superadditivity of the Mean Function of a Non-Homogeneous Poisson Process.
Fixed-α and fixed-β efficiencies
Consider testing H0 : F ∈ ω0 against H1 : F ∈ ω1 for a random sample X1, ..., Xn from F, where ω0 and ω1 are two disjoint sets of cdfs on ℝ = (−∞, ∞). Two non-local types of efficiencies, referred to as the fixed-α and fixed-β efficiencies, are introduced for this two-hypothesis testing situation. Theoretical tools are developed to evaluate these efficiencies for some of the most usual goodness of fit tests (including the Kolmogorov–Smirnov tests). Numerical comparisons are provided using several...
Generalization of discrimination-rate theorems of Chernoff and Stein
Global statistical information in exponential experiments and selection of exponential models
The concept of global statistical information in the classical statistical experiment with independent exponentially distributed samples is investigated. Explicit formulas are evaluated for common exponential families. It is shown that the generalized likelihood ratio test procedure of model selection can be replaced by a generalized information procedure. Simulations in a classical regression model are used to compare this procedure with that based on the Akaike criterion.
Goodness-of-fit tests for parametric regression models based on empirical characteristic functions
Test procedures are constructed for testing the goodness-of-fit in parametric regression models. The test statistic is in the form of an L2 distance between the empirical characteristic function of the residuals in a parametric regression fit and the corresponding empirical characteristic function of the residuals in a non-parametric regression fit. The asymptotic null distribution as well as the behavior of the test statistic under contiguous alternatives is investigated. Theoretical results are...
Hellinger integrals, contiguity and entire separation
Hypothesis Testing and Parameter Estimation Based on M-Statistics in k Samples with Unequal Variances.
Influence of contamination level deviations on the test error probabilities
Introduction à la statistique mathématique. IV. Propriétés asymptotiques du modèle statistique
Large deviations for quasi-arithmetically self-normalized random variables
We introduce a family of convex (concave) functions called sup (inf) of powers, which are used as generator functions for a special type of quasi-arithmetic means. Using these means, we generalize the large deviation result on self-normalized statistics that was obtained in the homogeneous case by [Q.-M. Shao, Self-normalized large deviations. Ann. Probab. 25 (1997) 285–328]. Furthermore, in the homogenous case, we derive the Bahadur exact slope for tests using self-normalized statistics.
Least empirical risk procedures in statistical inference
We consider the empirical risk function (for iid ’s) under the assumption that f(α,z) is convex with respect to α. Asymptotics of the minimum of is investigated. Tests for linear hypotheses are derived. Our results generalize some of those concerning LAD estimators and related tests.
Likelihood ratio inequalities with applications to various mixtures