Variance estimation for high-dimensional regression models pdf

Variance estimation for highdimensional varying index. Fast bayesian variable selection for high dimensional linear 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. Indeed, they are widely used for variance components estimation in linear randome ects models e. Variance estimation in highdimensional linear models.

The procedure, termed as selectionassisted partial regression and smoothing spares, utilizes data splitting along. By smoothing over partial regression estimates based on a given variable selection scheme, we reduce the problem to a lowdimensional least squares estimation. The paper is concerned with the problem of variance estimation for a highdimensional regression model. Drawing inferences for highdimensional linear models. The results show that the accuracy n12 of variance estimation can be achieved only under. Error variance estimation in ultrahigh dimensional additive models. In a highdimensional linear regression model, ac curate estimation is unfeasible unless it relies on some special properties of the parameter. You will check on your homework that, for a truly linear underlying model, the bias of the linear regression estimate is exactly 0, and the variance is p. Ex isting literature on highdimensional linear regression models has largely ignored non constant error variances, even though they commonly occur in a variety.

Highdimensional regression with unknown variance project euclid. Error variance estimation plays an important role in statistical inference for high dimensional regression models. However, our analysis is new and it implies that the mles, which were devised for randome ects models, may also perform very well in highdimensional linear models with xede ects, which are more commonly studied in some areas of highdimensional statistics. Marginal solo spike and slab priors chen, su and walker, stephen g.

Variance estimation for highdimensional varying index coefficient models. Variance estimation for highdimensional regression models. The paper is concerned with the problem of variance estimation for a high dimensional regression model. Variance function estimation in highdimensions icml. Gaussian errors e i n0,s2and a two times differentiable regression function f. Variance estimation in high dimensional regression models. Existing results on residual variance estimation in highdimensional linear models depend on sparsity in the underlying signal. Our results require no sparsity assumptions and imply that the residual variance and the proportion of explained variation can be consistently estimated even when d n and the underlying signal itself is nonestimable.

Maximum likelihood for variance estimation in high. Bayesian estimation of sparse signals with a continuous spikeandslab prior rockova, veronika, the annals of statistics, 2018. We treat the problem of variance estimation of the least squares estimate of the parameter in high dimensional linear regression models by using the. Bayesian variable selection and estimation for group lasso xu, xiaofan and ghosh, malay, bayesian analysis, 2015. Estimating the error variance in a highdimensional linear model. Dicker variance estimation in highdimensional linear models 3 andsun and zhang2012 have proposed methods for estimating.