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Simple random walk and rank order statistics

Igor Očka (1977)

Aplikace matematiky

The distributions of rank order statistics are studied for the case of arbitrary sample sizes in the two sample problem. The method applied is a generalization of Dwass's method from his paper in Ann. Math. Statist. 38 (1967), based on the analogy of rank order statistics and functions on a simple random walk.

Simultaneous rank test procedures

Marie Hušková (1980)

Aplikace matematiky

Simultaneous rank test procedures are proposed for testing of randomness concerning some marginals. The considered test procedures are analogous to those introduced by Krishnaiah for classical normal theory (see Krishnaiah (1965) Ann. Inst. Statist. Math. 17, 35-53).

Smoothing and preservation of irregularities using local linear fitting

Irène Gijbels (2008)

Applications of Mathematics

For nonparametric estimation of a smooth regression function, local linear fitting is a widely-used method. The goal of this paper is to briefly review how to use this method when the unknown curve possibly has some irregularities, such as jumps or peaks, at unknown locations. It is then explained how the same basic method can be used when estimating unsmooth probability densities and conditional variance functions.

Smoothing dichotomy in randomized fixed-design regression with strongly dependent errors based on a moving average

Artur Bryk (2014)

Applicationes Mathematicae

We consider a fixed-design regression model with errors which form a Borel measurable function of a long-range dependent moving average process. We introduce an artificial randomization of grid points at which observations are taken in order to diminish the impact of strong dependence. We show that the Priestley-Chao kernel estimator of the regression fuction exhibits a dichotomous asymptotic behaviour depending on the amount of smoothing employed. Moreover, the resulting estimator is shown to exhibit...

Smoothness of Metropolis-Hastings algorithm and application to entropy estimation

Didier Chauveau, Pierre Vandekerkhove (2013)

ESAIM: Probability and Statistics

The transition kernel of the well-known Metropolis-Hastings (MH) algorithm has a point mass at the chain’s current position, which prevent direct smoothness properties to be derived for the successive densities of marginals issued from this algorithm. We show here that under mild smoothness assumption on the MH algorithm “input” densities (the initial, proposal and target distributions), propagation of a Lipschitz condition for the iterative densities can be proved. This allows us to build a consistent...

Some adaptive estimators for slope parameter

Tran Quoc Viet (1993)

Commentationes Mathematicae Universitatis Carolinae

An adaptive estimator (of a slope parameter) based on rank statistics is constructed and its asymptotic optimality is studied. A complete orthonormal system is incorporated in the adaptive determination of the score generating function. The proposed sequential procedure is based on a suitable stopping rule. Various properties of the sequential adaptive procedure and the stopping rule are studied. Asymptotic linearity results of linear rank statistics are also studied and some rates of the convergence...

Some applications of probability generating function based methods to statistical estimation

Manuel L. Esquível (2009)

Discussiones Mathematicae Probability and Statistics

After recalling previous work on probability generating functions for real valued random variables we extend to these random variables uniform laws of large numbers and functional limit theorem for the empirical probability generating function. We present an application to the study of continuous laws, namely, estimation of parameters of Gaussian, gamma and uniform laws by means of a minimum contrast estimator that uses the empirical probability generating function of the sample. We test the procedure...

Some consistent exponentiality tests based on Puri-Rubin and Desu characterizations

Marija Cuparić, Bojana Milošević, Yakov Yu. Nikitin, Marko Obradović (2020)

Applications of Mathematics

We present new goodness-of-fit tests for the exponential distribution based on equidistribution type characterizations. For the construction of the test statistics, we employ an L 2 -distance between the corresponding V-empirical distribution functions. The resulting test statistics are V-statistics, free of the scale parameter. The quality of the tests is assessed through local Bahadur efficiencies as well as the empirical power for small and moderate sample sizes. According to both criteria, for...

Some Diagnostic Tools in Robust Econometrics

Jan Kalina (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Highly robust statistical and econometric methods have been developed not only as a diagnostic tool for standard methods, but they can be also used as self-standing methods for valid inference. Therefore the robust methods need to be equipped by their own diagnostic tools. This paper describes diagnostics for robust estimation of parameters in two econometric models derived from the linear regression. Both methods are special cases of the generalized method of moments estimator based on implicit...

Some limit behavior for linear combinations of order statistics

Yu Miao, Mengyao Ma (2021)

Kybernetika

In the present paper, we establish the moderate and large deviations for the linear combinations of uniform order statistics. As applications, the moderate and large deviations for the k -th order statistics from uniform distribution, Gini mean difference statistics and the k -th order statistics from general continuous distribution are obtained.

Some remarks on permutation type tests in linear models

Marie Husková, Jan Picek (2004)

Discussiones Mathematicae Probability and Statistics

The paper discusses applications of permutation arguments in testing problems in linear models. Particular attention will be paid to the application in L₁-test procedures. Theoretical results will beaccompanied by a simulation study.

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