Inference about the change-point in a sequence of binomial variables

Tests for Parameter Instability and Structural Change with Unknown Change Point.

Abstract: This paper considers tests for parameter instability and structural change with unknown change point. The results apply to a wide class of parametric models that are suitable for estimation by generalized method of moments procedures. The asymptotic distributions of the test statistics considered here are nonstandard because the change point parameter only appears under the alternative hypothesis and not under the null. The tests considered here are shown to have nontrivial asymptotic local power against all alternatives for which the parameters are nonconstant. The tests are found to perform quite well in a Monte Carlo experiment reported elsewhere. Copyright 1993 by The Econometric Society.

Detection of abrupt changes: theory and application

Abstract: This book is downloadable from http://www.irisa.fr/sisthem/kniga/. Many monitoring problems can be stated as the problem of detecting a change in the parameters of a static or dynamic stochastic system. The main goal of this book is to describe a unified framework for the design and the performance analysis of the algorithms for solving these change detection problems. Also the book contains the key mathematical background necessary for this purpose. Finally links with the analytical redundancy approach to fault detection in linear systems are established. We call abrupt change any change in the parameters of the system that occurs either instantaneously or at least very fast with respect to the sampling period of the measurements. Abrupt changes by no means refer to changes with large magnitude; on the contrary, in most applications the main problem is to detect small changes. Moreover, in some applications, the early warning of small - and not necessarily fast - changes is of crucial interest in order to avoid the economic or even catastrophic consequences that can result from an accumulation of such small changes. For example, small faults arising in the sensors of a navigation system can result, through the underlying integration, in serious errors in the estimated position of the plane. Another example is the early warning of small deviations from the normal operating conditions of an industrial process. The early detection of slight changes in the state of the process allows to plan in a more adequate manner the periods during which the process should be inspected and possibly repaired, and thus to reduce the exploitation costs.

Hypothesis testing when a nuisance parameter is present only under the alternative

Abstract: SUMMARY We wish to test a simple hypothesis against a family of alternatives indexed by a one-dimensional parameter, 0. We use a test derived from the corresponding family of test statistics appropriate for the case when 0 is given. Davies (1977) introduced this problem when these test statistics had normal distributions. The present paper considers the case when their distribution is chi-squared. The results are applied to the detection of a discrete frequency component of unknown frequency in a time series. In addition quick methods for finding approximate significance probabilities are given for both the normal and chi-squared cases and applied to the two-phase regression problem in the normal case.

Local Regression and Likelihood

Abstract: The Origins of Local Regression.- Local Regression Methods.- Fitting with LOCFIT.- Local Likelihood Estimation.- Density Estimation.- Flexible Local Regression.- Survival and Failure Time Analysis.- Discrimination and Classification.- Variance Estimation and Goodness of Fit.- Bandwidth Selection.- Adaptive Parameter Choice.- Computational Methods.- Optimizing Local Regression.

changepoint: An R Package for Changepoint Analysis

Abstract: One of the key challenges in changepoint analysis is the ability to detect multiple changes within a given time series or sequence. The changepoint package has been developed to provide users with a choice of multiple changepoint search methods to use in conjunction with a given changepoint method and in particular provides an implementation of the recently proposed PELT algorithm. This article describes the search methods which are implemented in the package as well as some of the available test statistics whilst highlighting their application with simulated and practical examples. Particular emphasis is placed on the PELT algorithm and how results differ from the binary segmentation approach.

Estimating the current mean of a normal distribution which is subjected to changes in time

Abstract: : A tracking problem is considered. Observations are taken on the successive positions of an object traveling on a path, and it is desired to estimate its current position. The objective is to arrive at a simple formula which implicitly accounts for possible changes in direction and discounts observations taken before the latest change. To develop a reasonable procedure, a simpler problem is studied. Successive observations are taken on n independently and normally distributed random variables X sub 1, X sub 2, ..., X sub n with means mu sub 1, mu sub 2, ..., mu sub n and variance 1. Each mean mu sub i is equal to the preceding mean mu sub (i-1) except when an occasional change takes place. The object is to estimate the current mean mu sub n. This problem is studied from a Bayesian point of view. An 'ad hoc' estimator is described, which applies a combination of the A.M.O.C. Bayes estimator and a sequence of tests designed to locate the last time point of change. The various estimators are then compared by a Monte Carlo study of samples of size 9. This Bayesian approach seems to be more appropriate for the related problem of testing whether a change in mean has occurred. This test procedure is simpler than that used by Page. The power functions of the two procedures are compared. (Author)