Local Asymptotics for Linear Rank Statistics with Estimated Score Functions

Neuhaus, Georg

doi:10.1214/aos/1176350357

Cited by 22 publications

(16 citation statements)

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“…V = π d/2 (d/2+1). Together with (26)(27)(28) this shows that for any sequence of admissible alternatives…”

Section: Proof Of(ii)mentioning

confidence: 76%

Optimal calibration for multiple testing against local inhomogeneity in higher dimension

Rohde

2010

Probab. Theory Relat. Fields

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Based on two independent samples X 1 , . . . , X m and X m+1 , . . . , X n drawn from multivariate distributions with unknown Lebesgue densities p and q respectively, we propose an exact multiple test in order to identify simultaneously regions of significant deviations between p and q. The construction is built from randomized nearest-neighbor statistics. It does not require any preliminary information about the multivariate densities such as compact support, strict positivity or smoothness and shape properties. The properly adjusted multiple testing procedure is shown to be sharp-optimal for typical arrangements of the observation values which appear with probability close to one. The proof relies on a new coupling Bernstein type exponential inequality, reflecting the non-subgaussian tail behavior of a combinatorial process. For power investigation of the proposed method a reparametrized minimax set-up is introduced, reducing the composite hypothesis " p = q" to a simple one with the multivariate mixed density (m/n) p + (1 − m/n)q as infinite dimensional nuisance parameter. Within this framework, the test is shown to be spatially and sharply asymptotically adaptive with respect to uniform loss on isotropic Hölder classes. The exact minimax risk asymptotics are obtained in terms of solutions of the optimal recovery.

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“…V = π d/2 (d/2+1). Together with (26)(27)(28) this shows that for any sequence of admissible alternatives…”

Section: Proof Of(ii)mentioning

confidence: 76%

Optimal calibration for multiple testing against local inhomogeneity in higher dimension

Rohde

2010

Probab. Theory Relat. Fields

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“…Especially for the order selection tests, the all subsets version is definitely preferred to the nested sequence. The last two settings are taken from Ledwina (1994) where the score-based BIC test is found to be superior to a variety of other classical tests for uniformity, such as Anderson & Darling's statistic and tests by Stephens (1974) and Neuhaus (1987Neuhaus ( , 1988.…”

Section: Testing Uniformitymentioning

confidence: 99%

Goodness of Fit via Non‐parametric Likelihood Ratios

Claeskens

Hjort

2004

Scandinavian J Statistics

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To test if a density "f" is equal to a specified "f" 0, one knows by the Neyman-Pearson lemma the form of the optimal test at a specified alternative "f" 1. Any non-parametric density estimation scheme allows an estimate of "f". This leads to estimated likelihood ratios. Properties are studied of tests which for the density estimation ingredient use log-linear expansions. Such expansions are either coupled with subset selectors like the Akaike information criterion and the Bayesian information criterion regimes, or use order growing with sample size. Our tests are generalized to testing the adequacy of general parametric models, and to work also in higher dimensions. The tests are related to, but are different from, the 'smooth tests' that go back to Neyman [Skandinavisk Aktuarietidsskrift 20(1937) 149] and that have been studied extensively in recent literature. Our tests are large-sample equivalent to such smooth tests under local alternative conditions, but different from the smooth tests and often better under non-local conditions. Copyright 2004 Board of the Foundation of the Scandinavian Journal of Statistics..

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“…There have been several attempts to extend the range of sensitivity of linear rank tests to larger classes of alternatives (cf. Randles & Hogg, 1973;Neuhaus, 1987;Behnen & Neuhaus, 1989;Bajorski, 1992;Fan, 1996). For a profound analysis of the weakness of classical approach and a novel way to overcome them we refer to Neuhaus (1987) and Behnen & Neuhaus (1989).…”

Section: Introductionmentioning

confidence: 99%

“…On the one hand, our solution exploits the core of Neuhaus' (1987) approach to the two-sample problem. On the other hand, in contrast to Neuhaus (1987), we are not using the kernel estimate to approximate the unknown non-parametric score function but we follow an idea introduced in Kallenberg & Ledwina (1997a) and developed in Inglot et al (1997). These papers have given a nice solution to the classical goodness-of-®t problem when R q valued, say, nuisance parameter is present.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Data Driven Rank Test for Two‐Sample Problem

Janic‐Wró¹,

Ledwina²

2000

Scandinavian J Statistics

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Traditional linear rank tests are known to possess low power for large spectrum of alternatives. In this paper we introduce a new rank test possessing a considerably larger range of sensitivity than linear rank tests. The new test statistic is a sum of squares of some linear rank statistics while the number of summands is chosen via a databased selection rule. Simulations show that the new test possesses high and stable power in situations when linear rank tests completely break down, while simultaneously it has almost the same power under alternatives which can be detected by standard linear rank tests. Our approach is illustrated by some practical examples. Theoretical support is given by deriving asymptotic null distribution of the test statistic and proving consistency of the new test under essentially any alternative.

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Local Asymptotics for Linear Rank Statistics with Estimated Score Functions

Cited by 22 publications

References 0 publications

Optimal calibration for multiple testing against local inhomogeneity in higher dimension

Optimal calibration for multiple testing against local inhomogeneity in higher dimension

Goodness of Fit via Non‐parametric Likelihood Ratios

Data Driven Rank Test for Two‐Sample Problem

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