Zhu, Ying (2018): Statistical inference and feasibility determination: a nonasymptotic approach.
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Abstract
We develop nonasymptotically justified methods for hypothesis testing about the pdimensional coefficients in (possibly nonlinear) regression models, where the hypotheses can also be nonlinear in the coefficients. Our (nonasymptotic) control on the Type I and Type II errors holds for fixed n and does not rely on wellbehaved estimation error or prediction error; in particular, when the number of restrictions in the null hypothesis is large relative to pn, we show it is possible to bypass the sparsity assumption on the coefficients (for both Type I and Type II error control), regularization on the estimates of the coefficients, and other inherent challenges in an inverse problem. We also demonstrate an interesting link between our framework and Farkas' lemma (in math programming) under uncertainty, which points to some potential applications of our method outside traditional hypothesis testing.
Item Type:  MPRA Paper 

Original Title:  Statistical inference and feasibility determination: a nonasymptotic approach 
Language:  English 
Keywords:  Nonasymptotic validity; hypothesis testing; confidence regions; concentration inequalities; high dimensional regressions; Farkas' lemma 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C12  Hypothesis Testing: General C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C21  CrossSectional Models ; Spatial Models ; Treatment Effect Models ; Quantile Regressions 
Item ID:  94645 
Depositing User:  Ms Ying Zhu 
Date Deposited:  24 Jun 2019 06:43 
Last Modified:  27 Sep 2019 16:04 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/94645 
Available Versions of this Item

Concentration Based Inference in High Dimensional Generalized Regression Models (I: Statistical Guarantees). (deposited 21 Aug 2018 01:27)

Concentration Based Inference for High Dimensional (Generalized) Regression Models: New Phenomena in Hypothesis Testing. (deposited 02 Oct 2018 03:23)
 Statistical inference and feasibility determination: a nonasymptotic approach. (deposited 24 Jun 2019 06:43) [Currently Displayed]

Concentration Based Inference for High Dimensional (Generalized) Regression Models: New Phenomena in Hypothesis Testing. (deposited 02 Oct 2018 03:23)