Tied-Down Wiener Process Approximations for Aligned Rank Order Processes and Some Applications
TLDR
For independent random variables distributed symmetrically around an unknown location parameter, aligned rank order statistics are constructed by using an estimator of the location parameter based on suitable rank statistics as discussed by the authors.Abstract:
For independent random variables distributed symmetrically around an unknown location parameter, aligned rank order statistics are constructed by using an estimator of the location parameter based on suitable rank statistics. The sequence of these aligned rank order statistics is then incorporated in the construction of suitable stochastic processes which converge weakly to some Gaussian functions, and, in particular, to tied-down Wiener processes in the most typical cases. The results are extended for contiguous alternatives and then applied in two specific problems in nonparametric inference. First, the problem of testing for shift at an unknown time point is treated, and then, some sequential type asymptotic nonparametric tests for symmetry around an unknown origin are considered.read more
Citations
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Convergence of Probability Measures
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Journal ArticleDOI
Nonparametric statistical procedures for the changepoint problem
Douglas A. Wolfe,Edna Schechtman +1 more
TL;DR: In this paper, a general review of nonparametric approaches for making inferences about r and Δ is presented, where the unknown parameter Δ represents the magnitude of the change and r is called the changepoint.
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Invariance Principles for Recursive Residuals
TL;DR: In this article, a general class of recursive residuals is defined by means of lower-triangular, orthonormal transformations, and some weak invariance principles are established under appropriate regularity conditions.
Journal ArticleDOI
Asymptotic theory of some tests for a possible change in the regression slope occurring at an unknown time point
TL;DR: In this paper, some testing procedures for a possible change in the regression slope occurring at an unknown time point are considered, based on least squares estimators and aligned rank order statistics.
Journal ArticleDOI
Statistical Analysis of “Structural Change”: An Annotated Bibliography
Peter Hackl,Anders H. Westlund +1 more
TL;DR: The typical structural change situation is described in this paper as follows: to cope with a particular economic phenomenon a model is specified, and it is suspected that for different periods of time, or for different spatial regions, different sets of parameter values are needed in order to describe the reality adequately; the "change point" which separates these periods, or regions, is unknown.
References
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Book
Convergence of Probability Measures
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.
Journal ArticleDOI
Convergence of Probability Measures
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Book
Theory of rank tests
TL;DR: In this article, the authors present an elementary theory of rank tests and a set of properties of rank estimators, including asymptotic optimality and efficiency, as well as non-null distributions.
Journal ArticleDOI
Estimates of Location Based on Rank Tests
J. L. Hodges,Erich L. Lehmann +1 more
TL;DR: Rank tests such as the two Wilcoxon tests or the Kruskal-Wallis H-test have been shown to be more robust against gross errors than that of the t-and F-tests, even in the rare case in which the suspicion of the possibility of gross errors is unfounded.