Journal ArticleDOI
Change-point problem and bootstrap
TLDR
In this paper, a class of simple estimators of the change-point m in a sequence of n independent random variables X1,X n satisfying E(X i ) = θ 0 for i = 1,…,m and E( X i ) was shown to be asymptotically valid.Abstract:
We consider a class of simple estimators of the change-point m in a sequence of n independent random variables X1…,X n satisfying E(X i ) = θ0 for i = 1,…,m and E(X i ) = θ0+δ n for i = m +1,…n. (θ0 and δ n are unknown). We obtain rates of consistency for the estimator, derive its limiting distribution and show that the bootstrap approximation is asymptotically valid. The results are illustrated by some simulations.read more
Citations
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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.
Journal ArticleDOI
Structural threshold regression
TL;DR: In this article, a concentrated least squares estimator of the threshold parameter based on an inverse Mills ratio bias correction is proposed, which is consistent and has shown good performance in Monte Carlo simulations.
Journal ArticleDOI
Effect of dependence on statistics for determination of change
TL;DR: In this article, a number of test statistics and estimators for detection of a change in the mean of a series of independent observations were proposed and studied, and the purpose of this paper is to examine the behaviour of these statistics if the observations are dependent, particularly, if they form a linear process.
Journal ArticleDOI
The effect of long-range dependence on change-point estimators
Lajos Horváth,Piotr Kokoszka +1 more
TL;DR: In this article, the authors study the asymptotic behavior of a class of estimators of the time of change in the mean of Gaussian observations having long-range dependence and prove that after a suitable normalization the estimators converge in distribution to functionals of fractional Brownian motion.
Journal ArticleDOI
On the detection of changes in autoregressive time series, II. Resampling procedures
TL;DR: In this article, the authors study an autoregressive time series model with a possible change in the regression parameters and obtain approximate estimates to the critical values for change-point tests through various bootstrapping methods.
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.
Journal ArticleDOI
Inference about the change-point in a sequence of binomial variables
TL;DR: In this paper, the problem of making inference about the point in a sequence of zero-one variables at which the binomial parameter changes is discussed, and the asymptotic distribution of the maximum likelihood estimate of the change-point is derived in computable form using random walk results.
Journal ArticleDOI
The problem of the Nile: Conditional solution to a changepoint problem
TL;DR: In this paper, an approximation to the conditional distribution of the maximum likelihood estimator of the change point given the ancillary values of observations adjacent to the estimated changepoint is derived and shown to be numerically equal to a Bayesian posterior distribution for the changepoint.
Journal ArticleDOI
Confidence regions and tests for a change-point in a sequence of exponential family random variables
TL;DR: In this article, maximum likelihood methods are used to test for a change in a sequence of independent exponential family random variables, with particular emphasis on the exponential distribution, and the confidence regions for the change point cover historical events that may have caused the changes.