The limit distribution of the maximum value test statistic in the general case

2016 ◽  
Author(s):  
Petr Philonenko ◽  
Sergey Postovalov ◽  
Artem Kovalevskii
Keyword(s):  
Limit Distribution ◽  
Test Statistic ◽  
Distribution Of The Maximum ◽  
Maximum Value

scholarly journals Testing in Nonparametric Accelerated Life Time Models

2016 ◽  
Vol 37 (1) ◽  
Author(s):  
Hannelore Liero
Keyword(s):  
Limit Distribution ◽  
Goodness Of Fit ◽  
Bootstrap Method ◽  
Life Time ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Time Model ◽  
Power Of The Test ◽  
Accelerated Life ◽  
Type Test

A goodness-of-fit test for testing the acceleration function in a nonparametric life time model is proposed. For this aim the limit distribution of an L2-type test statistic is derived. Furthermore, a bootstrap method is considered and the power of the test is studied.

The supersession of one rumour by another

1977 ◽  
Vol 14 (1) ◽  
pp. 127-134 ◽  
Author(s):  
G. K. Osei ◽  
J. W. Thompson
Keyword(s):  
Population Size ◽  
Finite Population ◽  
Closed Population ◽  
Asymptotic Case ◽  
Distribution Of The Maximum ◽  
Maximum Value

A model is considered for a situation in which one rumour suppresses another in a closed population. The distribution of the maximum value attained by the proportion spreading the weaker rumour is obtained in the asymptotic case, and this is compared with some actual distributions for finite population size. Closer approximations to the latter distributions are obtained.

ASYMPTOTIC SIZE AND A PROBLEM WITH SUBSAMPLING AND WITH THE m OUT OF n BOOTSTRAP

2009 ◽  
Vol 26 (2) ◽  
pp. 426-468 ◽  
Author(s):  
Donald W.K. Andrews ◽  
Patrik Guggenberger
Keyword(s):  
Limit Distribution ◽  
Test Statistic ◽  
Nominal Level ◽  
Asymptotic Size ◽  
Bootstrap Tests ◽  
Exact Size ◽  
High Level

This paper considers inference based on a test statistic that has a limit distribution that is discontinuous in a parameter. The paper shows that subsampling and m out of n bootstrap tests based on such a test statistic often have asymptotic size—defined as the limit of exact size—that is greater than the nominal level of the tests. This is due to a lack of uniformity in the pointwise asymptotics. We determine precisely the asymptotic size of such tests under a general set of high-level conditions that are relatively easy to verify. The results show that the asymptotic size of subsampling and m out of n bootstrap tests is distorted in some examples but not in others.

The limit distribution for maxima of ‘weighted' rth-nearest-neighbour distances

1982 ◽  
Vol 19 (02) ◽  
pp. 344-354
Author(s):  
Norbert Henze
Keyword(s):  
Limit Distribution ◽  
Goodness Of Fit ◽  
Continuity Condition ◽  
Weak Continuity ◽  
Nearest Neighbour ◽  
Multivariate Test ◽  
Maximum Value ◽  
Special Case ◽  
Distance To The Boundary ◽  
Independent Identically Distributed

Let X 1, X 2, · ··, Xn be independent identically distributed random points with common density f(x), taking values in a bounded region (p ≧ 1). We obtain the limit distribution, as n → ∞, for the maximum value of the suitably ‘weighted' (according to f(x)) rth-nearest-neighbour distances of Χ 1, · ··, Χ n (r ≧ 1 fixed) provided that f(x) is bounded from below by a positive constant and a weak continuity condition holds. This is achieved by refining an argument used by the author (Henze (1981)) to derive the limit distribution in the special case r = 1. Edge-effects are eliminated by defining, for each Xi , the distance to the boundary of G to be the ‘rth-nearest-neighbour distance' if it is smaller than the distance to the rth nearest neighbour among the remaining points. Applications to a multivariate test of goodness of fit are given.

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