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Random thresholds for linear model selection

Marc Lavielle, Carenne Ludeña (2008)

ESAIM: Probability and Statistics

A method is introduced to select the significant or non null mean terms among a collection of independent random variables. As an application we consider the problem of recovering the significant coefficients in non ordered model selection. The method is based on a convenient random centering of the partial sums of the ordered observations. Based on L-statistics methods we show consistency of the proposed estimator. An extension to unknown parametric distributions is considered. Simulated examples...

Randomized goodness of fit tests

Friedrich Liese, Bing Liu (2011)

Kybernetika

Classical goodness of fit tests are no longer asymptotically distributional free if parameters are estimated. For a parametric model and the maximum likelihood estimator the empirical processes with estimated parameters is asymptotically transformed into a time transformed Brownian bridge by adding an independent Gaussian process that is suitably constructed. This randomization makes the classical tests distributional free. The power under local alternatives is investigated. Computer simulations...

Rank tests in regression model based on minimum distance estimates

Radim Navrátil (2015)

Kybernetika

In this paper a new rank test in a linear regression model is introduced. The test statistic is based on a certain minimum distance estimator, however, unlike classical rank tests in regression it is not a simple linear rank statistic. Its exact distribution under the null hypothesis is derived, and further, the asymptotic distribution both under the null hypothesis and the local alternative is investigated. It is shown that the proposed test is applicable in measurement error models. Finally, a...

Rank tests of symmetry and R-estimation of location parameter under measurement errors

Radim Navrátil (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

This paper deals with the hypotheses of symmetry of distributions with respect to a location parameter when the response variables are subject to measurement errors. Rank tests of hypotheses about the location parameter and the related R-estimators are studied in an asymptotic set up. It is shown, when and under what conditions, these rank tests and R-estimators can be used effectively, and the effect of measurement errors on the power of the test and on the efficiency of the R-estimators is indicated....

Rank theory approach to ridge, LASSO, preliminary test and Stein-type estimators: Comparative study

A. K. Md. Ehsanes Saleh, Radim Navrátil (2018)

Kybernetika

In the development of efficient predictive models, the key is to identify suitable predictors for a given linear model. For the first time, this paper provides a comparative study of ridge regression, LASSO, preliminary test and Stein-type estimators based on the theory of rank statistics. Under the orthonormal design matrix of a given linear model, we find that the rank based ridge estimator outperforms the usual rank estimator, restricted R-estimator, rank-based LASSO, preliminary test and Stein-type...

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