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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 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...

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...

Reference points based recursive approximation

Martina Révayová, Csaba Török (2013)

Kybernetika

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...

Reference points based transformation and approximation

Csaba Török (2013)

Kybernetika

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 r -point transformation that yields a function with a simpler geometrical structure than the original function. It uses r ≥ 2 reference points and decreases the polynomial degree by r - 1 . Then a general representation of polynomials is proposed based on r ≥ 1 reference...

Reflexiones sobre la estrategia de medida de los cambios en probabilidad en modelos de elección binarios.

M.ª Teresa Aparicio Aspas, Inmaculada Villanúa Martín (1998)

Qüestiió

Este trabajo se centra en la evaluación de la medida que, en el marco de los modelos de elección binarios o dicotómicos, se utiliza para reflejar el cambio en la probabilidad ante la variación de una de las variables explicativas. La opción de cuantificación más común ha consistido en utilizar el vector de valores medios de las variables explicativas, lo que podemos entender como poner el énfasis en el comportamiento de un "individuo medio". Frente a esta práctica habitual, efectuamos una propuesta...

Relative Measurement and Its Generalization in Decision Making. Why Pairwise Comparisons are Central in Mathematics for the Measurement of Intangible Factors. The Analytic Hierarchy/Network Process.

Thomas L. Saaty (2008)

RACSAM

According to the great mathematician Henri Lebesgue, making direct comparisons of objects with regard to a property is a fundamental mathematical process for deriving measurements. Measuring objects by using a known scale first then comparing the measurements works well for properties for which scales of measurement exist. The theme of this paper is that direct comparisons are necessary to establish measurements for intangible properties that have no scales of measurement. In that case the value...

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