662 research outputs found
Statistical Treatment Choice Based on Asymmetric Minimax Regret Criteria
This paper studies the problem of treatment choice between a status quo treatment with a known outcome distribution and an innovation whose outcomes are observed only in a representative finite sample. I evaluate statistical decision rules, which are functions that map sample outcomes into the planner’s treatment choice for the population, based on regret, which is the expected welfare loss due to assigning inferior treatments. I extend previous work that applied the minimax regret criterion to treatment choice problems by considering decision criteria that asymmetrically treat Type I regret (due to mistakenly choosing an inferior new treatment) and Type II regret (due to mistakenly rejecting a superior innovation). I derive exact finite sample solutions to these problems for experiments with normal, Bernoulli and bounded distributions of individual outcomes. In conclusion, I discuss approaches to the problem for other classes of distributions. Along the way, the paper compares asymmetric minimax regret criteria with statistical decision rules based on classical hypothesis tests.treatment effects, loss aversion, statistical decisions, hypothesis testing.
Optimal Rates of Statistical Seriation
Given a matrix the seriation problem consists in permuting its rows in such
way that all its columns have the same shape, for example, they are monotone
increasing. We propose a statistical approach to this problem where the matrix
of interest is observed with noise and study the corresponding minimax rate of
estimation of the matrices. Specifically, when the columns are either unimodal
or monotone, we show that the least squares estimator is optimal up to
logarithmic factors and adapts to matrices with a certain natural structure.
Finally, we propose a computationally efficient estimator in the monotonic case
and study its performance both theoretically and experimentally. Our work is at
the intersection of shape constrained estimation and recent work that involves
permutation learning, such as graph denoising and ranking.Comment: V2 corrects an error in Lemma A.1, v3 corrects appendix F on unimodal
regression where the bounds now hold with polynomial probability rather than
exponentia
On deconvolution of distribution functions
The subject of this paper is the problem of nonparametric estimation of a
continuous distribution function from observations with measurement errors. We
study minimax complexity of this problem when unknown distribution has a
density belonging to the Sobolev class, and the error density is ordinary
smooth. We develop rate optimal estimators based on direct inversion of
empirical characteristic function. We also derive minimax affine estimators of
the distribution function which are given by an explicit convex optimization
problem. Adaptive versions of these estimators are proposed, and some numerical
results demonstrating good practical behavior of the developed procedures are
presented.Comment: Published in at http://dx.doi.org/10.1214/11-AOS907 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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