S. Zacks

Bio: S. Zacks is an academic researcher. The author has contributed to research in topics: Normal distribution & Estimator. The author has an hindex of 1, co-authored 1 publications receiving 539 citations.

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)

Techniques for Testing the Constancy of Regression Relationships Over Time

Abstract: Methods for studying the stability over time of regression relationships are considered. Recursive residuals, defined to be uncorrelated with zero means and constant variance, are introduced and tests based on the cusum and cusum of squares of recursive residuals are developed. Further techniques based on moving regressions, in which the regression model is fitted from a segment of data which is moved along the series, and on regression models whose coefficients are polynomials in time are studied. The Quandt log-likelihood ratio statistic is considered. Emphasis is placed on the use of graphical methods. The techniques proposed have been embodied in a comprehensive computer program, TIMVAR. Use of the techniques is illustrated by applying them to three sets of data.

Optimal Tests When a Nuisance Parameter is Present Only under the Alternative

Abstract: This paper derives asymptotically optimal tests for testing problems in which a nuisance parameter exists under the alternative hypothesis but not under the null. For example, the results apply to tests of structural change with unknown changepoint. The testing problem considered is nonstandard and the classical asymptotic optimality results for the Lagrange multiplier, Wald, and likelihood ratio do not apply. A weighted average power criterion is used here to generate optimal tests. This criterion is similar to that used by A. Wald (1943) to obtain the classical asymptotic optimality properties of Wald tests in 'regular' testing problems. Copyright 1994 by The Econometric Society.

Procedures for reacting to a change in distribution

Abstract: A problem of optimal stopping is formulated and simple rules are proposed which are asymptotically optimal in an appropriate sense. The problem is of central importance in quality control and also has applications in reliability theory and other areas.

Dealing with Structural Breaks

Abstract: This chapter is concerned with methodological issues related to estimation, testing and computation in the context of structural changes in the linear models. A central theme of the review is the interplay between structural change and unit root and on methods to distinguish between the two. The topics covered are: methods related to estimation and inference about break dates for single equations with or without restrictions, with extensions to multi-equations systems where allowance is also made for changes in the variability of the shocks; tests for structural changes including tests for a single or multiple changes and tests valid with unit root or trending regressors, and tests for changes in the trend function of a series that can be integrated or trendstationary; testing for a unit root versus trend-stationarity in the presence of structural changes in the trend function; testing for cointegration in the presence of structural changes; and issues related to long memory and level shifts. Our focus is on the conceptual issues about the frameworks adopted and the assumptions imposed as they relate to potential applicability. We also highlight the potential problems that can occur with methods that are commonly used and recent work that has been done to overcome them.