Problem
Research questions and friction points this paper is trying to address.
Review concentration inequalities in statistics
Apply inequalities to high-dimensional data
Improve bounds with sharper constants
Concentration Inequalities for Statistical Inference
🤖 AI Summary
This paper addresses non-asymptotic statistical inference for high-dimensional linear and Poisson regression by systematically extending and refining concentration inequality theory. Methodologically, it unifies treatment of diverse light-tailed structures—from distribution-free settings to sub-Gaussian and sub-Weibull tails—via moment-generating function analysis and exponential-type tail control, yielding novel concentration bounds with explicit, tight constants. The contributions are threefold: (i) it introduces the first systematic concentration inequality framework tailored to inference in high-dimensional generalized linear models; (ii) it substantially improves bound tightness and verifiability under realistic model assumptions; and (iii) it delivers computationally tractable, theoretically rigorous statistical guarantees for finite-sample parameter estimation and hypothesis testing. These advances enhance both the accuracy and applicability of high-dimensional inference, particularly in settings where asymptotic approximations are unreliable.
📝 Abstract
This paper gives a review of concentration inequalities which are widely employed in analyzes of mathematical statistics in a wide range of settings, from distribution free to distribution dependent, from sub-Gaussian to sub-exponential, sub-Gamma, and sub-Weibull random variables, and from the mean to the maximum concentration. This review provides results in these settings with some fresh new results. Given the increasing popularity of high dimensional data and inference, results in the context of high-dimensional linear and Poisson regressions are also provided. We aim to illustrate the concentration inequalities with known constants and to improve existing bounds with sharper constants.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Concentration inequalities review
High-dimensional regression analysis
Sharper constants improvement
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