Likelihood ratio tests for a class of non-oblique hypotheses

Hu, Xiaomi; Wright, F. T.

doi:10.1007/bf00773599

Cited by 5 publications

(6 citation statements)

References 10 publications

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“…The non-obliqueness condition, first introduced by Warrack et al [52], is also motivated by the fact that are many instances of oblique cone pairs for which the GLRT is known to dominated by other tests. Menendez et al [32] provide an explanation for this dominance in a very general context; see also the papers [34,21] for further studies of non-oblique cone pairs. A nested pair of closed convex cones C 1 ⊂ C 2 is said to be non-oblique if we have the successive projection property…”

Section: Cone-based Glrts and Non-oblique Pairsmentioning

confidence: 99%

“…Thus, past work has studied conditions on the cone pair under which the null distribution has a simple characterization. One such condition is a certain nonobliqueness property that is common to much past work on the GLRT (e.g., [52,33,34,21]). The non-obliqueness condition, first introduced by Warrack et al [52], is also motivated by the fact that are many instances of oblique cone pairs for which the GLRT is known to dominated by other tests.…”

Section: Cone-based Glrts and Non-oblique Pairsmentioning

confidence: 99%

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The geometry of hypothesis testing over convex cones: Generalized likelihood ratio tests and minimax radii

Wei¹,

Wainwright²,

Guntuboyina³

2019

Ann. Statist.

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We consider a compound testing problem within the Gaussian sequence model in which the null and alternative are specified by a pair of closed, convex cones. Such cone testing problem arises in various applications, including detection of treatment effects, trend detection in econometrics, signal detection in radar processing, and shape-constrained inference in nonparametric statistics. We provide a sharp characterization of the GLRT testing radius up to a universal multiplicative constant in terms of the geometric structure of the underlying convex cones. When applied to concrete examples, this result reveals some interesting phenomena that do not arise in the analogous problems of estimation under convex constraints. In particular, in contrast to estimation error, the testing error no longer depends purely on the problem complexity via a volume-based measure (such as metric entropy or Gaussian complexity); other geometric properties of the cones also play an important role. In order to address the issue of optimality, we prove information-theoretic lower bounds for the minimax testing radius again in terms of geometric quantities. Our general theorems are illustrated by examples including the cases of monotone and orthant cones, and involve some results of independent interest.

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Section: Cone-based Glrts and Non-oblique Pairsmentioning

confidence: 99%

Section: Cone-based Glrts and Non-oblique Pairsmentioning

confidence: 99%

The geometry of hypothesis testing over convex cones: Generalized likelihood ratio tests and minimax radii

Wei¹,

Wainwright²,

Guntuboyina³

2019

Ann. Statist.

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“…We say that C 0 and C a are non-oblique if this iterative projection property holds for every α. The terminology of non-obliqueness was first used by Warrack & Robertson (1984) and later studied by Menendez, Rueda & Salvador (1992), and Hu & Wright (1994). When C 0 and C a are non-oblique, the LRT statistic (3.1) is of D(x, ↔ x ) type, where ↔ x is the isotonic regression of x.…”

Section: Test Statisticsmentioning

confidence: 99%

Tests for Monotonic Intensity in a Poisson Process

2000

Aus NZ J of Statistics

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“…Under suitable regularity conditions, the distribution of T has proven to be conditionally distributed as a χ 2 d when r t 1 = · · · = r tn (in what follows we denote r 0 a vector whose components are equal), and d is the observed value of D , i.e, Menéndez et al, 1992 andHu andWright, 1994). The conditional α level test rejects when…”

Section: The Conditional Likelihood Ratio Testmentioning

confidence: 99%

Checking unimodality using isotonic regression: an application to breast cancer mortality rates

Rueda

Ugarte

Militino

2015

Stoch Environ Res Risk Assess

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In some diseases it is well-known that a unimodal mortality pattern exists. A clear example in developed countries is breast cancer, where mortality increased sharply until the nineties and then decreased. This clear unimodal pattern is not necessarily applicable to all regions within a country. In this paper, we develop statistical tools to check if the unimodality pattern persists within regions using order restricted inference. Break points as well as confidence intervals are also provided. In addition, a new test for checking monotonicity against unimodality is derived allowing to discriminate between a simple increasing pattern and an up-then-down response pattern. A comparison with the widely used joinpoint regression technique under unimodality is provided. We show that the joinpoint technique could fail when the underlying function is not piecewise linear. Results will be illustrated using age-specific breast cancer mortality data from Spain in the period 1975-2005.

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Likelihood ratio tests for a class of non-oblique hypotheses

Abstract: Inferences subject to inequality constraints, iterated projection property, non-oblique cones, order restricted inferences,

Cited by 5 publications

References 10 publications

The geometry of hypothesis testing over convex cones: Generalized likelihood ratio tests and minimax radii

The geometry of hypothesis testing over convex cones: Generalized likelihood ratio tests and minimax radii

Tests for Monotonic Intensity in a Poisson Process

Checking unimodality using isotonic regression: an application to breast cancer mortality rates

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