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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...

Recursive bias estimation for multivariate regression smoothers

Pierre-André Cornillon, N. W. Hengartner, E. Matzner-Løber (2014)

ESAIM: Probability and Statistics

This paper presents a practical and simple fully nonparametric multivariate smoothing procedure that adapts to the underlying smoothness of the true regression function. Our estimator is easily computed by successive application of existing base smoothers (without the need of selecting an optimal smoothing parameter), such as thin-plate spline or kernel smoothers. The resulting smoother has better out of sample predictive capabilities than the underlying base smoother, or competing structurally...

Recursive estimates of quantile based on 0-1 observations

Pavel Charamza (1992)

Applications of Mathematics

The objective of this paper is to introduce some recursive methods that can be used for estimating an L D - 50 value. These methods can be used more generally for the estimation of the γ -quantile of an unknown distribution provided we have 0-1 observations at our disposal. Standard methods based on the Robbins-Monro procedure are introduced together with different approaches of Wu or Mukerjee. Several examples are also mentioned in order to demonstrate the usefulness of the methods presented.

Redescending M-estimators in regression analysis, cluster analysis and image analysis

Christine H. Müller (2004)

Discussiones Mathematicae Probability and Statistics

We give a review on the properties and applications of M-estimators with redescending score function. For regression analysis, some of these redescending M-estimators can attain the maximum breakdown point which is possible in this setup. Moreover, some of them are the solutions of the problem of maximizing the efficiency under bounded influence function when the regression coefficient and the scale parameter are estimated simultaneously. Hence redescending M-estimators satisfy several outlier robustness...

Refined rates of bias convergence for generalized L-Statistics in the i.i.d. case

George Anastassiou, Tomasz Rychlik (1999)

Applicationes Mathematicae

Using tools of approximation theory, we evaluate rates of bias convergence for sequences of generalized L-statistics based on i.i.d. samples under mild smoothness conditions on the weight function and simple moment conditions on the score function. Apart from standard methods of weighting, we introduce and analyze L-statistics with possibly random coefficients defined by means of positive linear functionals acting on the weight function.

Remarks on optimum kernels and optimum boundary kernels

Jitka Poměnková (2008)

Applications of Mathematics

Kernel smoothers belong to the most popular nonparametric functional estimates used for describing data structure. They can be applied to the fix design regression model as well as to the random design regression model. The main idea of this paper is to present a construction of the optimum kernel and optimum boundary kernel by means of the Gegenbauer and Legendre polynomials.

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