arXiv subjects

Lutz Dümbgen

Publications and source records attributed to Lutz Dümbgen.

3 recordsLinked to original sources

arXiv2023

Covariate Selection Based on a Assumpton-free Approach to Linear Regression with Exact Probabilities

In this paper we give a completely new approach to the problem of covariate selection in linear regression. A covariate or a set of covariates is included only if it is better in the sense of least squares than the same number of Gaussian covariates consisting of i.i.d. $N(0,1)$ random variables. The Gaussian P-value is defined as the probability that the Gaussian covariates are better. It is given in terms of the Beta distribution, it is exact and it holds for all data. The covariate selection procedures based on this require only a cut-off value $α$ for the Gaussian P-value: the default value in this paper is $α=0.01$. The resulting procedures are very simple, very fast, do not overfit and require only least squares. In particular there is no regularization parameter, no data splitting, no use of simulations, no shrinkage and no post selection inference is required. The paper includes the results of simulations, applications to real data sets and theorems on the asymptotic behaviour under the standard linear model. Here the stepwise procedure performs overwhelmingly better than any other procedure we are aware of. An R-package {\it gausscov} is available.

stat.ME↗

arXiv2022

Characteristic kernels on Hilbert spaces, Banach spaces, and on sets of measures

We present new classes of positive definite kernels on non-standard spaces that are integrally strictly positive definite or characteristic. In particular, we discuss radial kernels on separable Hilbert spaces, and introduce broad classes of kernels on Banach spaces and on metric spaces of strong negative type. The general results are used to give explicit classes of kernels on separable $L^p$ spaces and on sets of measures.

stat.ML↗

arXiv2022

Covariate Selection Based on a Model-free Approach to Linear Regression with Exact Probabilities

In this paper we give a completely new approach to the problem of covariate selection in linear regression. A covariate or a set of covariates is included only if it is better in the sense of least squares than the same number of Gaussian covariates consisting of i.i.d. $N(0,1)$ random variables. The Gaussian P-value is defined as the probability that the Gaussian covariates are better. It is given in terms of the Beta distribution, it is exact and it holds for all data making it model-free free. The covariate selection procedures require only a cut-off value $α$ for the Gaussian P-value: the default value in this paper is $α=0.01$. The resulting procedures are very simple, very fast, do not overfit and require only least squares. In particular there is no regularization parameter, no data splitting, no use of simulations, no shrinkage and no post selection inference is required. The paper includes the results of simulations, applications to real data sets and theorems on the asymptotic behaviour under the standard linear model. Here the step-wise procedure performs overwhelmingly better than any other procedure we are aware of. An R-package {\it gausscov} is available.

stat.ME↗