Some principles for surveillance adopted for multivariate processes with a common change point

The surveillance of multivariate processes has received growing attention during the last decade. Several generalizations of well-known methods such as Shewhart, CUSUM and EWMA charts have been proposed. Many of these multivariate procedures are based on a univariate summarized statistic of the multivariate observations, usually the likelihood ratio statistic. In this paper we consider the surveillance of multivariate observation processes for a shift between two fully specified alternatives. The effect of the dimension reduction using likelihood ratio statistics are discussed in the context of sufficiency properties. Also, an example of the loss of efficiency when not using the univariate sufficient statistic is given. Furthermore, a likelihood ratio method, the LR method, for constructing surveillance procedures is suggested for multivariate surveillance situations. It is shown to produce univariate surveillance procedures based on the sufficient likelihood ratios. As the LR procedure has several optimality properties in the univariate, it is also used here as a benchmark for comparisons between multivariate surveillance procedures     

Test for Parameter Change in Linear Processes Based on Whittle's Estimator

In this article, we develop a cusum test for testing for parameter changes in linear processes based on Whittle's estimator. It is shown that under regularity conditions, the test statistic converges to the sup of a Brownian bridge. The result is particularly useful in handling the change point test in stationary ARMA processes. A simulation result is provided for illustration.     

Asymptotic distributions of quadratic forms occurring in changepoint problems

A stochastic-process approach is used to derive the asymptotic distributions of quadratic forms occurring in the analysis of changepoint data.     

Comment on “modeling asset returns with alternative stable distributions”

This paper considers a modified CUSUM test, suggested by Dufour (1982) for parameter instability and structural change with an unknown change point in a linear model with serially correlated disturbances, in which a preliminary estimate of the autoregressive coefficient for the error process is obtained, and used to transform the data. Then the standard CUSUM statistic is calculated on the transformed data. This paper derives the asymptotic distribution of the modified CUSUM test. We show that the modified CUSUM test retains its asymptotic significance level, i.e., the modified CUSUM test has the same asymptotic distribution as the CUSUM test with serially uncorrelated errors.     

IDENTIFYING THE OUT OF CONTROL VARIABLE IN A MULTIVARIATE CONTROL CHART

ABSTRACT

The identification of the out of control variable, or variables, after a multivariate control chart signals, is an appealing subject for many researchers in the last years. In this paper we propose a new method for approaching this problem based on principal components analysis. Theoretical control limits are derived and a detailed investigation of the properties and the limitations of the new method is given. A graphical technique which can be applied in some of these limiting situations is also provided.     

On the power of some tests for examining the stability of regression coefficients

The main objective of the study is to compare four different procedures to test for the stability of regression coefficients. The comparisons are based on a numerical study and are with respect to their abilities to detect various simple forms of parameter instabilities. Besides the power comparisons a special interest is directed towards the choice of “window length” in the tests based on moving sums of squared recursive and ordinary least-squares residuals.     

Testing Heterogeneity for Frailty Distribution in Shared Frailty Model

Abstract

The frailties, representing extra variations due to unobserved measurements, are often assumed to be iid in shared frailty models. In medical applications, however, a speculation can arise that a data set might violate the iid assumption. In this paper we investigate this conjecture through an analysis of the kidney infection data in McGilchrist and Aisbett (McGilchrist, C. A., Aisbett, C. W. (1991). Regression with frailty in survival analysis. Biometrics 47:461–466). As a test procedure, we consider the cusum of squares test which is frequently used for monitoring a variance change in statistical models. Our result strongly sustains the heterogeneity of the frailty distribution.     

Covariance changes detection in multivariate time series

This paper studies the detection of step changes in the variances and in the correlation structure of the components of a vector of time series. Two procedures based on the likelihood ratio test (LRT) statistic and on a cumulative sums (cusum) statistic are considered and compared in a simulation study. We conclude that for a single covariance change the cusum procedure is more powerful in small and medium samples, whereas the likelihood ratio test is more powerful in large samples. However, for several covariance changes the cusum procedure works clearly better. The procedures are illustrated in two real data examples.     

Finite sample distributions of statistics in change point analysis

This paper is concerned with derivation of finite sampling distributions of some statistics which appear frequently in change point analysis. The exact distribution of cusum test statistic is approximated by two methods. Approximations are presented and their accuracies are measured. We first consider the change point in mean problem and we study the exact distribution of change point estimator. Finally, we consider the change point in variance case.     

A CUSUM SCHEME BASED ON THE EXPONENTIAL DISTRIBUTION FOR SURVEDLLANCE OF RARE CONGENITAL MALFORMATIONS

A method of monitoring the incidence of malformations is described. It is suitable for systems where the number of births between successive malformations is known or can be estimated with reasonable accuracy. The method utilises a cusum technique based on the exponential distribution to detect an increase in the incidence of malformations above a baseline level. Adequate information to enable the implementation of the method is presented. The proposed method compares favourably with others such as the Poisson cusum and the modified sets technique.