Sharper Sub-Weibull Concentrations

Constant-specified and exponential concentration inequalities play an essential role in the finite-sample theory of machine learning high-dimensional statistics area. We obtain sharper constants-specified for sum independent sub-Weibull random variables, which leads to a mixture two tails: sub-Gaussian small deviations large from mean. These bounds are new improve existing with constants. In addition, parameter is also proposed, enables recovering tight inequality variable (vector). For statistical applications, we give ?2-error estimated coefficients negative binomial regressions when heavy-tailed covariates distributed sparse structures, result regressions. applying matrices, derive non-asymptotic versions Bai-Yin’s theorem entries tail bounds. Finally, by demonstrating confidence region log-truncated Z-estimator without second-moment condition, discuss define type robust estimator observations {Xi}i=1n exponential-moment conditions.