A note on centering in subsample selection for linear regression

09/30/2022
by   HaiYing Wang, et al.
0

Centering is a commonly used technique in linear regression analysis. With centered data on both the responses and covariates, the ordinary least squares estimator of the slope parameter can be calculated from a model without the intercept. If a subsample is selected from a centered full data, the subsample is typically un-centered. In this case, is it still appropriate to fit a model without the intercept? The answer is yes, and we show that the least squares estimator on the slope parameter obtained from a model without the intercept is unbiased and it has a smaller variance covariance matrix in the Loewner order than that obtained from a model with the intercept. We further show that for noninformative weighted subsampling when a weighted least squares estimator is used, using the full data weighted means to relocate the subsample improves the estimation efficiency.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/29/2019

Centered and non-centered variance inflation factor

This paper analyzes the diagnostic of near multicollinearity in a multip...
research
04/11/2022

Two-step estimation in linear regressions with adaptive learning

Weak consistency and asymptotic normality of the ordinary least-squares ...
research
06/26/2019

Control variate selection for Monte Carlo integration

Monte Carlo integration with variance reduction by means of control vari...
research
09/10/2022

Slice Weighted Average Regression

It has previously been shown that ordinary least squares can be used to ...
research
09/29/2021

Assessing the goodness of fit of linear regression via higher-order least squares

We introduce a simple diagnostic test for assessing the goodness of fit ...
research
10/29/2019

Efficient Computation for Centered Linear Regression with Sparse Inputs

Regression with sparse inputs is a common theme for large scale models. ...
research
07/07/2013

Loss minimization and parameter estimation with heavy tails

This work studies applications and generalizations of a simple estimatio...

Please sign up or login with your details

Forgot password? Click here to reset