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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...
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...
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...
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...
The paper studies polynomial approximation models with a new type of constraints that enable to get estimates with significant properties. Recently we enhanced a representation of polynomials based on three reference points. Here we propose a two-part cubic smoothing scheme that leverages this representation. The presence of these points in the model has several consequences. The most important one is the fact that by appropriate location of the reference points the resulting approximant of two...
Interpolating and approximating polynomials have been living separately more than two centuries. Our aim is to propose a general parametric regression model that incorporates both interpolation and approximation. The paper introduces first a new -point transformation that yields a function with a simpler geometrical structure than the original function. It uses reference points and decreases the polynomial degree by . Then a general representation of polynomials is proposed based on reference...
Bad conditioned matrix of normal equations in connection with small values of model parameters is a source of problems in parameter estimation. One solution gives the ridge estimator. Some modification of it is the aim of the paper. The behaviour of it in models with constraints is investigated as well.
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