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Aligned rank tests in measurement error model

Radim Navrátil;  A. K. Md. Ehsanes Saleh — 2016

Applications of Mathematics

Aligned rank tests are introduced in the linear regression model with possible measurement errors. Unknown nuisance parameters are estimated first and then classical rank tests are applied on the residuals. Two situations are discussed: testing about an intercept in the linear regression model considering the slope parameter as nuisance and testing of parallelism of several regression lines, i.e. whether the slope parameters of all lines are equal. Theoretical results are derived and the simulation...

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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