Two non parametric methods for change-point detection in distribution

The change-point detection problem is determining whether a change has taken place. Two non parametric methods based on empirical likelihood and the likelihood ratio are proposed for detecting a change-point problem in distributions for independent observations. Numerical studies are carried out to evaluate the performance of the proposed methods. The simulation results demonstrate that the proposed methods are robust, that is, they perform well regardless of whether the observations are from the same distribution family.     

Semiparametric Estimation of a Change-point for Recurrent Events Data

One particular recurrent events data scenario involves patients experiencing events according to a common intensity rate, and then a treatment may be applied. The treatment might be effective for a limited amount of time, so that the intensity rate would be expected to change abruptly when the effect of the treatment wears out. In particular, we allow models for the intensity rate, post-treatment, to be at first decreasing and then change to increasing (and vice versa). Two estimators of the location of this change are proposed.     

Nonparametric boundary detection

We propose a two-step nonparametric method for detecting the boundary curve of an object in an image. First we treat boundary points as change-points on lines across the image, and identify them by the one-sided kernel smoothing method. After obtaining potential boundary points, we use the principal curve method to smooth these points in order to obtain an estimate of smooth boundary curve, Computer simulations are provided to illustrate the effectiveness of the method.     

Nonparametric AMOC Changepoint Tests for Stochastically Ordered Alternatives

The problem considered is that of testing on the basis of a finite sequence of independent observations if all the observations have the same distribution versus the alternative that there is a unique change in the distribution and i.i.d. observations after the change are stochastically larger. The distributions before and after the possible change are continuous but not fully specified. We suggest a family of nonparametric tests based on ranks. Asymptotic approximations for the significance level of the test are obtained analytically. Monte Carlo experiments show that the rate of convergence of our asymptotics is fast.     

Application and Reliability of Change-Point Analyses for Detecting a Defective Stage in Integrated Circuit Manufacturing

ABSTRACT

This article presents a reliable method for highlighting a defective stage within a manufacturing process when the existence of a failure is only known at the end of the process. It was developed in the context of integrated circuit manufacturing, where low costs and high yields are indispensable if the manufacturer is to be competitive. Change detection methods were used to point out the defective stage. Two methods were compared and the best chosen. Thanks to this approach, it was possible to solve some yield problems for which the engineers' investigations were far from the real cause of failure. However, there is a strong requirement to assess the reliability of the suspicions cast on the incriminated stage, otherwise engineers could be made to do useless work and time could be wasted looking into events that are not the true cause of failure. Two complementary tools were implemented for this reliability assessment and their efficiency is illustrated by several examples.     

Change-Point Estimation in Long Memory Nonparametric Models with Applications

We consider the estimation of a change point or discontinuity in a regression function for random design model with long memory errors. We provide several change-point estimators and investigate the consistency of the estimators. Using the fractional ARIMA process as an example of long memory process, we report a small Monte Carlo experiment to compare the performance of the estimators in finite samples. We finish by applying the method to a climatological data example.     

Asymptotic Comparison Between Constant-stress Testing and Step-stress Testing for Type-I Censored Data from Exponential Distribution

By running the life tests at higher stress levels than normal operating conditions, accelerated life testing quickly yields information on the lifetime distribution of a test unit. The lifetime at the design stress is then estimated through extrapolation using a regression model. In constant-stress testing, a unit is tested at a fixed stress level until failure or the termination time point of the test, while step-stress testing allows the experimenter to gradually increase the stress levels at some pre-fixed time points during the test. In this article, the optimal k-level constant-stress and step-stress accelerated life tests are compared for the exponential failure data under Type-I censoring. The objective is to quantify the advantage of using the step-stress testing relative to the constant-stress one. A log-linear relationship between the mean lifetime parameter and stress level is assumed and the cumulative exposure model holds for the effect of changing stress in step-stress testing. The optimal design point is then determined under C-optimality, D-optimality, and A-optimality criteria. The efficiency of step-stress testing compared to constant-stress testing is discussed in terms of the ratio of optimal objective functions based on the information matrix.     

A power study of k-linear-r-ahead recursive residuals test for change-point in finite sequences

A change-point problem in finite sequences is considered along with, so-called, k-linear-r-ahead recursive residuals and a test procedure proposed by ?o?a¸d? et al. [?o?a¸d?, J.A., Szkutnik, Z., Majerczak, J. and Duda, K. 1998, Detection of change point in oxygen uptake during an incremental exercise test using recursive residuals: relationship to the plasma lactate accumulation and blood acid base balance. European Journal of Applied Physiology, 78, 369–377.]. Theoretical significance levels of that (conservative) test are compared with its simulated sizes. Numerical approximations to the powers against various alternatives are given. Properties of the k-linear-r-ahead recursive residuals are described and the consistency of the test is proved, when the noise level goes to zero.     

Tabulating weighted sup-norm functionals used in change-point analysis

We introduce a number of weighted partial sum processes of which certain sup-norm functionals may be used, for example, to detect changes in the mean of independent observations. Their limiting distributions are derived mathematically, simulated and then tabulated. With this information, a detailed numerical investigation of the power of these functionals is carried out.* ^*Research mainly done while at Carleton University, partially supported by an NSERC Canada Grant of Miklós Csörg? at Carleton University, Ottawa. Also supported by the Austrian Science Foundation (FWF) under grant SFB#010 (‘Adaptive Information Systems and Modelling in Economics and Management Science’) while at Technische Universität Wien. ? ^?Research partially supported by an NSERC Canada Grant of Miklós Csörg? at Carleton University, Ottawa.      

Multiple change-point estimation with U-statistics

We consider a multiple change-point problem: a finite sequence of independent random variables consists of segments given by a known number of the so-called change-points such that the underlying distribution differs from segment to segment. The task is to estimate these change-points under no further assumptions on the within-segment distributions. In this completely nonparametric framework the proposed estimator is defined as the maximizing point of weighted multivariate U-statistic processes. Under mild moment conditions we prove almost sure convergence and the rate of convergence.