Optimal-order bounds on the rate of convergence to normality in the multivariate delta method

Pinelis, Iosif; Molzon, Raymond

doi:10.48550/arxiv.0906.0177

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An Example Of Non-normal Approximation1

Introduction1

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2020

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“…with λ = np replaced by its consistent estimator (the "two-sided" test); the "subasymptotic approach" suggests incorporating estimate (17).…”

Section: An Example Of Non-normal Approximationmentioning

confidence: 99%

“…in each row r.v.s has been described by Mason [9]. An estimate of the accuracy of normal approximation to the distribution of Student's statistic with explicit constants has been given by Novak [10,11] in the case of identically distributed r.v.s and by Shao [20] in the case of non-identically distributed r.v.s (see also [12,17] and references therein).…”

Section: Introductionmentioning

confidence: 99%

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On the T-test

Novak¹

2020

Preprint

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The T -test is probably the most popular statistical test; it is routinely recommended by the textbooks.The applicability of the test relies upon the validity of normal or Student's approximation to the distribution of Student's statistic t n . However, the latter assumption is not valid as often as assumed.We show that normal or Student's approximation to L(t n ) does not hold uniformly even in the class P n of samples from zero-mean unit-variance bounded distributions. We present lower bounds to the corresponding error.The fact that a non-parametric test is not applicable uniformly to samples from the class P n seems to be established for the first time. It means the T -test can be misleading, and should not be recommended in its present form.We suggest a generalisation of the test that allows for variability of possible limiting/approximating distributions to L(t n ).

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“…with λ = np replaced by its consistent estimator (the "two-sided" test); the "subasymptotic approach" suggests incorporating estimate (17).…”

Section: An Example Of Non-normal Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%