Monitoring Structural Changes in Generalized Linear Models

Abstract

In this article, we introduce two monitoring schemes to (sequentially) detect structural changes in generalized linear models and develop asymptotic theories for them. The first method is based on cumulative sums (CUSUM) of weighted residuals, in which the unknown in-control parameters have been replaced by its maximum likelihood (ML) estimate from the training sample, whereas the second scheme makes use of moving sums (MOSUM) of weighted residuals. We characterize the limit distribution of the test statistic and show that these tests are consistent. Moreover, we also obtain and tabulate the asymptotic critical values of the tests. Finally, we study the speed of detection under different conditions. The methods are illustrated and compared in several simulations.

Two tests for sequential detection of a change-point in a nonlinear model

“…By the asymptotic properties of a nonlinear regression, we have that the variance error estimatorσ 2 m is strongly converging to σ 2 , |σ m − σ| = o I P (1). The assertion (i) follows by the last relation together the relations (16), (17), (18)- (19).…”

One dimensional scan statistics generated by some dependent stationary sequences

“…Such approximations have several applications in probability and statistics (Bauer and Hackl, 1978;Chan, 2009;Chu et al, 1995;Glaz and Johnson, 1988;Lai, 1974;Xia et al, 2009). In this section, we compare values of P(S n ≤ s) generated by our 1-dependent Gaussian sequence with corresponding values obtained in Glaz et al (2012) for i.i.d.…”

Sequential change-point detection in a multinomial logistic regression model

“…The above study of detection of change is retrospective change-point detection, in regard to sequential change-point detection (on-line monitoring, sequential test or priori test) whereby data are not observed at once, but arrive in a sequential mannerone by one, Xia et al [20] introduced two procedures to sequentially detect structural change in generalized linear models with assuming independence. Höhle [21] proposed a CUSUM control chart method based on the generalized likelihood ratio statistic for sequential change-point detection in regression models for categorical time series.…”