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De-sparsified lasso : ウィキペディア英語版
De-sparsified lasso

De-sparsified lasso contributes to construct confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in high-dimensional model.
==1 High-dimensional linear model==

Y = X\beta^0 + \epsilon
with n \times p design matrix X =: (X_p ) ( n \times p vectors X_j), \epsilon \sim N_n(0, \sigma^2_\epsilon I) independent of X and unknown regression p \times 1 vector \beta^0.
The usual method to find the parameter is by Lasso:
\hat^n(\lambda) = \underset \ \frac \left\| Y - X \beta \right\| ^ 2 _ 2 + \lambda \left\| \beta \right\| _ 1
The de-sparsified lasso is a method modified from the Lasso estimator which fulfills the Karush-Kuhn-Tucker conditions is as follows:
\hat^n(\lambda,M) = \hat^n(\lambda) + \frac M X^T(Y- X \hat^n (\lambda))
where M \in R ^(p\times p) is an arbitrary matrix. The matrix M is generated using a surrogate inverse covariance matrix.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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