arXiv subjects

Myung Geun Kim

Publications and source records attributed to Myung Geun Kim.

3 recordsLinked to original sources

arXiv2022

On deletion diagnostic statistic in regression

The change in the least squares estimator (LSE) of a vector of regression coefficients due to a case deletion is often used for investigating the influence of an observation on the LSE. A normalization of the change in the LSE using the Moore-Penrose inverse of the covariance matrix of the change in the LSE is derived. This normalization turns out to be a square of the internally studentized residual. It is shown that the numerator term of Cook's distance does not in general have a chi-squared distribution except for a single case. An elaborate explanation about the inappropriateness of the choice of a scaling matrix defining Cook's distance is given. By reflecting a distributional property of the change in the LSE due to a case deletion, a new diagnostic measure that is a scalar is suggested. Three numerical examples are given for illustration.

stat.ME↗

arXiv2021

Asymptotic distribution for the proportional covariance model

Asymptotic distribution for the proportional covariance model under multivariate normal distributions is derived. To this end, the parametrization of the common covariance matrix by its Cholesky root is adopted. The derivations are made in three steps. First, the asymptotic distribution of the maximum likelihood estimators of the proportionality coefficients and the Cholesky inverse root of the common covariance matrix is derived by finding the information matrix and its inverse. Next, the asymptotic distributions for the case of the Cholesky root of the common covariance matrix and finally for the case of the common covariance matrix itself are derived using the multivariate $δ$-method. As an application of the asymptotic distribution derived here, a hypothesis for homogeneity of covariance matrices is considered.

math.ST↗

arXiv2020

Sources of high leverage in linear regression model

Some reasons for high leverage are analytically investigated by decomposing leverage into meaningful components. The results in this work can be used for remedial action as a next step of data analysis.

math.ST↗