Variance Estimation for High-Dimensional Regression Models

Variance Estimation in High Dimensional Regression Models

We treat the problem of variance estimation of the least squares estimate of the parameter in high dimensional linear regression models by using the Uncorrelated Weights Bootstrap (UBS). We find a representation of the UBS dispersion matrix and show that the bootstrap estimator is consistent if p/n → 0 where p is the dimension of the parameter and n is the sample size. For fixed dimension we sh...

Estimation of Variance Components for Body Weight of Moghani Sheep Using B-Spline Random Regression Models

The aim of the present study was the estimation of (co) variance components and genetic parameters for body weight of Moghani sheep, using random regression models based on B-Splines functions. The data set included 9165 body weight records from 60 to 360 days of age from 2811 Moghani sheep, collected between 1994 to 2013 from Jafar-Abad Animal Research and Breeding Institute, Ardabil province,...

Maximum Likelihood for Variance Estimation in High-Dimensional Linear Models

The plots in Figure 1 from the main text were generated using various estimators of σ 0 , each of which was computed for 500 independent datasets (y, X). The datasets were generated according to the linear model (1)– (2) (equation references refer to the main text), with n = 500, p = 1000, σ 0 = 1, and η 2 0 = 4. We considered settings where β had various sparsity levels, indicated by a paramet...

Variance Function Estimation in Heteroscedastic Regression Models

Variance Estimation in Time Series Regression Models