Testing non-oblique hypotheses

Menéndnez, J.A.; Rueda, Cristina; Salvador, Bonifacio

doi:10.1080/03610929208830789

Cited by 10 publications

(9 citation statements)

References 7 publications

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“…i.e., U & C and C are non-oblique in the terminology of Menendez, Rueda and Salvador [7] and Warrack and Robertson [10]. This iterative projection approach can not be used here since, as shown by the next example, B & C and C are not non-oblique.…”

Section: Two Inequalitiesmentioning

confidence: 93%

Application of the Limit of Truncated Isotonic Regression in Optimization Subject to Isotonic and Bounding Constraints

1999

Journal of Multivariate Analysis

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An isotonic regression truncated by confining its domain to a union of its level sets is the isotonic regression in the reduced function space. When some of the weights with which the inner product system is defined go to infinity, the truncated isotonic regression converges. This limit can be used in discribing the projection onto the set of vectors which satisfy an order restriction and have one or more of its coordinates bounded above andÂor below. Through this characterization, two inequalities associated with the projection are established and found useful in order and bound restricted statistical inference. The results obtained show that for an exponential distribution family the inequalities lead to the linkage of the order and bound restricted MLE with the projection of the unrestricted MLE, and the dominance of the order and bound restricted MLE over the unrestricted MLE with respect to two classes of loss functions and risks as well as Bayes risks. 1999Academic Press AMS 1991 subject classifications: 62F10, 62C99.

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Section: Two Inequalitiesmentioning

confidence: 93%

Application of the Limit of Truncated Isotonic Regression in Optimization Subject to Isotonic and Bounding Constraints

1999

Journal of Multivariate Analysis

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“…There are many non-oblique cone pairs in which neither cone is a subspace; the cone pairs (4) and (5), as discussed in Example 1 on treatment testing, are two such examples. (We refer the reader to Section 5 of the paper [34] for verification of these properties.) More generally, there are various non-oblique cone pairs that do not sandwich a subspace L.…”

Section: Cone-based Glrts and Non-oblique Pairsmentioning

confidence: 94%

“…Based on observing y, our goal is to test whether a given parameter θ belongs to the smaller cone C 1 -corresponding to the null hypothesis-or belongs to the larger cone C 2 . Cone testing problems of this type arise in many different settings, and there is a fairly substantial literature on the behavior of the GLRT in application to such problems (e.g., see the papers and books [8,25,40,39,41,44,35,33,34,14,47,52], as well as references therein).…”

Section: Introductionmentioning

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 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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“…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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Testing non-oblique hypotheses

Cited by 10 publications

References 7 publications

Application of the Limit of Truncated Isotonic Regression in Optimization Subject to Isotonic and Bounding Constraints

Application of the Limit of Truncated Isotonic Regression in Optimization Subject to Isotonic and Bounding Constraints

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

Tests for Monotonic Intensity in a Poisson Process

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