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Detecting atypical data in air pollution studies by using shorth intervals for regression

Cécile Durot, Karelle Thiébot (2010)

ESAIM: Probability and Statistics

To validate pollution data, subject-matter experts in Airpl (an organization that maintains a network of air pollution monitoring stations in western France) daily perform visual examinations of the data and check their consistency. In this paper, we describe these visual examinations and propose a formalization for this problem. The examinations consist in comparisons of so-called shorth intervals so we build a statistical test that compares such intervals in a nonparametric regression model. This...

Detecting atypical data in air pollution studies by using shorth intervals for regression

Cécile Durot, Karelle Thiébot (2005)

ESAIM: Probability and Statistics

To validate pollution data, subject-matter experts in Airpl (an organization that maintains a network of air pollution monitoring stations in western France) daily perform visual examinations of the data and check their consistency. In this paper, we describe these visual examinations and propose a formalization for this problem. The examinations consist in comparisons of so-called shorth intervals so we build a statistical test that compares such intervals in a nonparametric regression model. This...

Estimation and tests in finite mixture models of nonparametric densities

Odile Pons (2009)

ESAIM: Probability and Statistics

The aim is to study the asymptotic behavior of estimators and tests for the components of identifiable finite mixture models of nonparametric densities with a known number of components. Conditions for identifiability of the mixture components and convergence of identifiable parameters are given. The consistency and weak convergence of the identifiable parameters and test statistics are presented for several models.

Exact slopes of the rank statistics for the two-sample case under discrete distributions

Dana Vorlíčková (1981)

Aplikace matematiky

The author studies the linear rank statistics for testing the pypothesis of randomness against the alternative of two samples provided both are drawn grom discrete (integer-valued) distributions. The weak law of large numbers and the exact slope are obtained for statistics with randomized ranks of with averaged scores.

Fuzzy empirical distribution function: Properties and application

Gholamreza Hesamian, S. M. Taheri (2013)

Kybernetika

The concepts of cumulative distribution function and empirical distribution function are investigated for fuzzy random variables. Some limit theorems related to such functions are established. As an application of the obtained results, a method of handling fuzziness upon the usual method of Kolmogorov-Smirnov one-sample test is proposed. We transact the α -level set of imprecise observations in order to extend the usual method of Kolmogorov-Smirnov one-sample test. To do this, the concepts of fuzzy...

Goodness of fit test for isotonic regression

Cécile Durot, Anne-Sophie Tocquet (2001)

ESAIM: Probability and Statistics

We consider the problem of hypothesis testing within a monotone regression model. We propose a new test of the hypothesis H 0 : “ f = f 0 ” against the composite alternative H a : “ f ≠ f 0 ” under the assumption that the true regression function f is decreasing. The test statistic is based on the 𝕃 1 -distance between the isotonic estimator of f and the function f 0 , since it is known that a properly centered and normalized version of this distance is asymptotically standard normally distributed under H 0 . We study the asymptotic...

Goodness of fit test for isotonic regression

Cécile Durot, Anne-Sophie Tocquet (2010)

ESAIM: Probability and Statistics

We consider the problem of hypothesis testing within a monotone regression model. We propose a new test of the hypothesis H0: “ƒ = ƒ0” against the composite alternative Ha: “ƒ ≠ ƒ0” under the assumption that the true regression function f is decreasing. The test statistic is based on the 𝕃 1 -distance between the isotonic estimator of f and the function f0, since it is known that a properly centered and normalized version of this distance is asymptotically standard normally distributed under H0....

Goodness of fit tests for the skew-Laplace distribution.

Pedro Puig, Michael A. Stephens (2007)

SORT

The skew-Laplace distribution is frequently used to fit the logarithm of particle sizes and it is also used in Economics, Engineering, Finance and Biology. We show the Anderson-Darling and Cramér-von Mises goodness of fit tests for this distribution.

Goodness of fit tests with weights in the classes based on ( h , φ ) -divergences

Elena Landaburu, Leandro Pardo (2000)

Kybernetika

The aim of the paper is to present a test of goodness of fit with weigths in the classes based on weighted h , φ -divergences. This family of divergences generalizes in some sense the previous weighted divergences studied by Frank et al [frank] and Kapur [kapur]. The weighted h , φ -divergence between an empirical distribution and a fixed distribution is here investigated for large simple random samples, and the asymptotic distributions are shown to be either normal or equal to the distribution of a linear...

Goodness-of-fit test for the family of logistic distributions.

N. Aguirre, Mikhail S. Nikulin (1994)

Qüestiió

Chi-squared goodness-of-fit test for the family of logistic distributions id proposed. Different methods of estimation of the unknown parameters θ of the family are compared. The problem of homogeneity is considered.

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