Influence analysis of covariance matrix disturbance on Stein ridge type principal component estimator. (Chinese. English summary) Zbl 1438.62134
Summary: In this paper, the issue of influence analysis of covariance matrix disturbance on Stein ridge type principal components estimator (SRPCE) in linear regression model is studied. We prove that in the data deletion model, some limits of \(\boldsymbol{\hat \beta (P)_G}\) in the regression model with covariance matrix disturbance are SRPCE. Then, we set up the relationships between \(\boldsymbol{\hat \beta (P)_G}\) and \(\boldsymbol{\hat \beta (P)}\). Next, we define the distance measure \({D_G}\), which can be assessed by the disturbing influence. Afterwards, we give several calculation formulas of \({D_G}\). Finally, a practical example is presented to illustrate the effectiveness of this method.
MSC:
62J07 | Ridge regression; shrinkage estimators (Lasso) |
62H25 | Factor analysis and principal components; correspondence analysis |
62H12 | Estimation in multivariate analysis |