Scholarlink

<p>We tackle estimating sparse coefficients in a linear regression when the covariates are sampled from an <i>L</i>-subexponential random vector. Such vectors follow a class of distributions that exhibit heavier tails than Gaussian random vectors. Previous studies have established error bounds similar to those derived for Gaussian random vectors. However, these methods require stronger conditions than those used for Gaussian random vectors to derive the error bounds. In the present study, we present an error bound identical to the one obtained for Gaussian random vectors up to constant factors without imposing stronger conditions, for covariates drawn from an <i>L</i>-subexponential random vector. Of special interest, we employ an <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\ell _1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ℓ</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>-penalized Huber regression, which is known for its robustness against heavy-tailed random noises rather than covariates. We believe that this study reveals a new aspect of the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\ell _1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ℓ</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>-penalized Huber regression method.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Estimation of sparse linear regression coefficients under L-subexponential covariates

  • 期刊论文

  • 发表日期：

    2026年7月29日

查看全文
  • Takeyuki Sasai

摘要

We tackle estimating sparse coefficients in a linear regression when the covariates are sampled from an L-subexponential random vector. Such vectors follow a class of distributions that exhibit heavier tails than Gaussian random vectors. Previous studies have established error bounds similar to those derived for Gaussian random vectors. However, these methods require stronger conditions than those used for Gaussian random vectors to derive the error bounds. In the present study, we present an error bound identical to the one obtained for Gaussian random vectors up to constant factors without imposing stronger conditions, for covariates drawn from an L-subexponential random vector. Of special interest, we employ an \(\ell _1\) ℓ 1 -penalized Huber regression, which is known for its robustness against heavy-tailed random noises rather than covariates. We believe that this study reveals a new aspect of the \(\ell _1\) ℓ 1 -penalized Huber regression method.