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Statistical hypothesis testing

About: Statistical hypothesis testing is a research topic. Over the lifetime, 19580 publications have been published within this topic receiving 1037815 citations. The topic is also known as: statistical hypothesis testing & confirmatory data analysis.


Papers
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Journal ArticleDOI
TL;DR: In this article, the authors consider an approach to the Durbin problem involving a martingale transformation of the parametric empirical process suggested by Khmaladze (1981) and show that it can be adapted to a wide variety of inference problems involving quantile regression process.
Abstract: Tests based on the quantile regression process can be formulated like the classical Kolmogorov–Smirnov and Cramer–von–Mises tests of goodness–of–fit employing the theory of Bessel processes as in Kiefer (1959). However, it is frequently desirable to formulate hypotheses involving unknown nuisance parameters, thereby jeopardizing the distribution free character of these tests. We characterize this situation as “the Durbin problem” since it was posed in Durbin (1973), for parametric empirical processes. In this paper we consider an approach to the Durbin problem involving a martingale transformation of the parametric empirical process suggested by Khmaladze (1981) and show that it can be adapted to a wide variety of inference problems involving the quantile regression process. In particular, we suggest new tests of the location shift and location–scale shift models that underlie much of classical econometric inference. The methods are illustrated with a reanalysis of data on unemployment durations from the Pennsylvania Reemployment Bonus Experiments. The Pennsylvania experiments, conducted in 1988–89, were designed to test the efficacy of cash bonuses paid for early reemployment in shortening the duration of insured unemployment spells.

346 citations

Journal ArticleDOI
TL;DR: This article studies the maximum likelihood inference on a class of Wiener processes with random effects for degradation data, one on which n independent subjects, each with a Wiener process with random drift and diffusion parameters, are observed at different times.

346 citations

Journal ArticleDOI
TL;DR: The Dempster-Shafer theory of probabilistic reasoning is presented in terms of a semantics whereby every meaningful formal assertion is associated with a triple (p,q,r).

345 citations

Journal ArticleDOI
TL;DR: In this paper, a method of determining whether all the parameters meet their respective standards is proposed, which consists of testing each parameter individually and deciding that the product is acceptable only if each parameter passes its test.
Abstract: The quality of a product might be determined by several parameters, each of which must meet certain standards before the product is acceptable. In this article, a method of determining whether all the parameters meet their respective standards is proposed. The method consists of testing each parameter individually and deciding that the product is acceptable only if each parameter passes its test. This simple method has some optimal properties including attaining exactly a prespecified consumer's risk and uniformly minimizing the producer's risk. These results are obtained from more general hypothesis-testing results concerning null hypotheses consisting of the unions of sets.

345 citations

Posted Content
TL;DR: This work develops likelihood-free inference methods and highlight hypothesis testing as a principle for learning in implicit generative models, using which it is able to derive the objective function used by GANs, and many other related objectives.
Abstract: Generative adversarial networks (GANs) provide an algorithmic framework for constructing generative models with several appealing properties: they do not require a likelihood function to be specified, only a generating procedure; they provide samples that are sharp and compelling; and they allow us to harness our knowledge of building highly accurate neural network classifiers. Here, we develop our understanding of GANs with the aim of forming a rich view of this growing area of machine learning---to build connections to the diverse set of statistical thinking on this topic, of which much can be gained by a mutual exchange of ideas. We frame GANs within the wider landscape of algorithms for learning in implicit generative models--models that only specify a stochastic procedure with which to generate data--and relate these ideas to modelling problems in related fields, such as econometrics and approximate Bayesian computation. We develop likelihood-free inference methods and highlight hypothesis testing as a principle for learning in implicit generative models, using which we are able to derive the objective function used by GANs, and many other related objectives. The testing viewpoint directs our focus to the general problem of density ratio estimation. There are four approaches for density ratio estimation, one of which is a solution using classifiers to distinguish real from generated data. Other approaches such as divergence minimisation and moment matching have also been explored in the GAN literature, and we synthesise these views to form an understanding in terms of the relationships between them and the wider literature, highlighting avenues for future exploration and cross-pollination.

343 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023267
2022696
2021959
2020998
20191,033
2018943