Tze Leung Lai

Information bounds and quick detection of parameter changes in stochastic systems

By using information-theoretic bounds and sequential hypothesis testing theory, this paper provides a new approach to optimal detection of abrupt changes in stochastic systems. This approach not only generalizes previous work in the literature on optimal detection far beyond the relatively simple models treated but also suggests alternative performance criteria which are more tractable and more appropriate for general stochastic systems. In addition, it leads to detection rules which have manageable computational complexity for on-line implementation and yet are nearly optimal under the different performance criteria considered.

Strong consistency of least squares estimates in multiple regression II

The strong consistency of least squares estimates in multiple regression models with independent errors is obtained under minimal assumptions on the design and weak moment conditions on the errors.

Asymptotic properties of general autoregressive models and strong consistency of least-squares estimates of their parameters

This paper establishes several almost sure asymptotic properties of general autoregressive processes. By making use of these properties, we obtain a proof of the strong consistency of the least-squares estimates of the parameters of the process without any assumption on the roots of the characteristic polynomial.

Efficient recursive algorithms for detection of abrupt changes in signals and control systems

This paper addresses a number of open problems concerning the generalized likelihood ratio (GLR) rules for online detection of faults and parameter changes in control systems. It is shown that with an appropriate choice of the threshold and window size, these GLR rules are asymptotically optimal. The rules are also extended to non-likelihood statistics that are widely used in monitoring adaptive algorithms for system identification and control by establishing Gaussian approximations to these statistics when the window size is chosen suitably. Recursive algorithms are developed for practical implementation of the procedure, and importance sampling techniques are introduced for determining the threshold of the rule to satisfy prescribed bounds on the false alarm rate.

Heart rate and heart rate variability during sleep in aborted sudden infant death syndrome

Heart rate and heart rate variability were studied during sleep at monthly intervals in 18 normal infants and 12 infants with aborted sudden infant death syndrome during the first four months of life. At each age studied and in both REM and quiet sleep, the aborted SIDS infants had a 5 to 10% faster heart rate. Moreover, the aborted SIDS infants had a 10 to 45% smaller beat-to-beat and overall heart rate variability. Although the differences in overall variability persisted after normalization by the absolute heart rate, the differences in the beat-to-beat variability narrowed. These findings, when taken in conjunction with our previous observation that aborted SIDS infants have a smaller QT index than normal infants, suggest that infants with aborted SIDS have an increase in sympathetic activity or in circulating levels of catecholamines.

Nonparametric Estimation and Regression Analysis with Left-Truncated and Right-Censored Data

Abstract In many prospective and retrospective studies, survival data are subject to left truncation in addition to the usual right censoring. For left-truncated data without covariates, only the conditional distribution of the survival time Y given Y ≥ τ can be estimated nonparametrically, where τ is the lower boundary of the support of the left-truncation variable T. If the data are also right censored, then the conditional distribution can be consistently estimated only at points not larger than τ*, where τ* is the upper boundary of the support of the right-censoring variable C. In this article we first consider nonparametric estimation of trimmed functionals of the conditional distribution of Y, with the trimming inside the observable range between τ and τ*. We then extend the approach to regression analysis and curve fitting in the presence of left truncation and right censoring on the response variable Y. Asymptotic normality of M estimators of the regression parameters derived from this approach is...

Consistency and asymptotic efficiency of slope estimates in stochastic approximation schemes

Adaptive stochastic approximation schemes for choosing the levels of x at which y is to be observed are useful in applications of the following nature. Suppose that in (1.1) x~ is the dosage level of a drug given to the i-th patient who turns up for treatment and that Yi is the response of the patient. Suppose also that an optimal response value y* is desired. Without loss of generality, we shall (replacing y~ by y~-y* if necessary) assume that y*=0. If 0 were known, then the dosage levels should all be set at 0. Since 0 is usually unknown, how can the dosage levels xi be chosen so as to approach the

Asymptotic properties of projections with applications to stochastic regression problems

Almost sure convergence properties of least-squares estimates in stochastic regression models and an asymptotic theory of related Euclidean projections are developed herein. Applications to autoregressive processes and to dynamic input-output systems are also discussed.

Linear rank statistics in regression analysis with censored or truncated data

A class of generalized linear rank statistics is introduced for regression analysis in the presence of truncation or censoring on the response variable. Applications of these statistics to hypothesis testing and estimation are discussed. Martingale theory and stochastic integrals of multiparameter empirical processes are applied to analyze the test statistics and the rank estimates.

Stochastic integrals of empirical-type processes with applications to censored regression

Motivated by the analysis of linear rank estimators and the Buckley-James nonparametric EM estimator in censored regression models, we study herein the asymptotic properties of stochastic integrals of certain two-parameter empirical processes. Applications of these results on empirical processes and their stochastic integrals to the asymptotic analysis of censored regression estimators are also given.