U-Statistics in Sequential Tests and Change Detection

Abstract

Research on U-statistics within the general framework of sequential and change-point literature is surveyed. Some recent developments are discussed and extended. New sequential testing strategies based on Wiener process approximations are proposed, and empirical studies explore the finite sample performance of these tests. It allows users to choose one that is appropriate for their application.     

Sequential Change-Point Detection and Estimation

Abstract

Two groups of sequential testing procedures are proposed to detect an abrupt change in the distribution of a sequence of observations: truncated and open ended. They are based on large sample strong approximations of the efficient score vector under the null hypothesis of no change and under the alternative hypothesis. An estimator of the time of change is proposed and its approximate bias is analyzed. The estimation of the new parameters that describe the changed distribution naturally follows.     

CONTINUITY BETWEEN DISORDER AND ORDER IN THE SEQUENTIAL DEPOSITION OF PARTICLES

In previous work we pointed out that clusters of particles built through sequential quenching show increasing degrees of order as the temperature is lowered. In the low-temperature limit, a two-dimensional model system with a nondegenerate ground state would result in a perfect crystal. The opposite, high-temperature, limit corresponds to the case of random sequential addition (RSA). In the present work we study the continuous evolution from disorder to order at intermediate states using a triangular well potential to represent particle interactions. We investigate radial and bond-orientation correlation functions and the bond order parameter as measures of the degree of crystallinity of the structures up to a reduced number density of 0.65, which is close to the jamming limit of RSA.     

An optimal curtailment of a randomized ump test for a proprtion

Consider a fixed sample size UMP test of H₀: p ≤ p₀ versus H₁: p > p₀, where p is a Bernoulli parameter. If the test is non-randomized the optimal curtailed version is well-known. If the test is randomized, the decision of a UMP test is not uniquely determined. This paper considers the problem of curtailing such tests so that the expected number of observations is minimized. A simple complete characterization of such tests is given.     

Design of Group Sequential Clinical Trials with Ordinal Categorical Data Based on the Mann–Whitney–Wilcoxon Test

Abstract

In this paper, methodology necessary do design group sequential trials based on ordinal categorical data based on the Mann–Whitney–Wilcoxon test is presented and illustrated in two practical examples. Curtailment for futility is an important component in improving the performance of the methods in terms of expected sample sizes under the null hypothesis. Simulation can also be employed to verify the asymptotic properties claimed by the method, and if necessary be used to tweak the design to better approximate the desired operating characteristics.     

Optimal two-sided group sequential tests

We derive two-sided group sequential tests for normal responses with known variance which minimise expected sample size; minimisation is at a single value of the normal mean or integrated with respect to a normal density. In deriving these tests we use a method analogous to that used by Eales and Jennison (1992) to compute optimal one-sided tests. We present a comparison of our optimal tests with existing tests.     

Effects of inter-group correlations on sequential electron transitions through redox-mediated two-center electrochemical bridged contact

A consistent method for the calculation of the electric current through a redox-mediated electrochemical tunnel contact with two redox groups in the bridge molecule is presented for the sequential mechanism of electron transfer in the limit of infinitely large Coulomb repulsion between the electrons located in the same redox group. It is shown that the kinetic inter-group correlation exists which results in general in the deviation of exact solution from the approximate “quasi-chemical approach” even in the absence of inter-group Coulomb repulsion. The increase of the latter leads to the appearance of the electron correlation effects which result, in particular, in the second maximum (Coulomb blockade peak) in the current/overvoltage dependence.     

Truncated SPRTs with application to multivariate normal data

We develop truncated sequential probability ratio test (SPRT) procedures for multivariate normal data. The framework includes a general cost structure and arbitrary mean and covariance structures. The truncated SPRT solutions have a practical and easy-to-use decision boundary representation. In the homogeneous case, a very fast recursive algorithm is presented for calculating the decision boundaries. Misclassification rates and expected sample size are investigated and the results are compared with a nonsequential procedure. A real-life data set on kidney dysfunction following heart surgery is used to illustrate the truncated SPRT procedure.     

Sequential analysis applied to circular data

Some applications of sequentialk procedures for circular data in different areas of interest are presented here. Problems associated with the analysis of angular data as well as some of the methods to overcome them are briefly discussed. Three sequential procedures for testing between mean direction for a von Mises' population are presented. The first one assumes that the concentration parameter k is known, and the test, its OC and ASN are all described. The other two tests relate to the case where k is unknown. Finally, some applications of these tests are given.     

Sequential procedures for monltoring the parameters of the autoregressive model relative to unspecified targets

Sequential procedures are developed for monitoring the parameters of a time dependent autoregressive model relative to unspecified targets. Such a problem arises when we need to monitor the parameters for changes from their unknown initial values (the unspecified targets), instead of from specified targets. For this purpose, scores type statistics are proposed which: (1) reflect changes in the parameters from their initial values without requiring any input about these values; and (2) are aimed at detecting arbitrary shifts in the parameters, instead of at restrictive "one point" shift alternatives. The procedures developed are capable of monitoring any one of, or any combination of, the mean, variance or correlation structure of an autoregressive sequence of known finite order. Their false signal rates are controlled, and their performance under local shift