Statistics for Spatial Data.

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

In the choice of an estimator for the spectrum of a stationary time series from a finite sample of the process, the problems of bias control and consistency, or "smoothing," are dominant. In this paper we present a new method based on a "local" eigenexpansion to estimate the spectrum in terms of the solution of an integral equation. Computationally this method is equivalent to using the weishted average of a series of direct-spectrum estimates based on orthogonal data windows (discrete prolate spheroidal sequences) to treat both the bias and smoothing problems. Some of the attractive features of this estimate are: there are no arbitrary windows; it is a small sample theory; it is consistent; it provides an analysis-of-variance test for line components; and it has high resolution. We also show relations of this estimate to maximum-likelihood estimates, show that the estimation capacity of the estimate is high, and show applications to coherence and polyspectrum estimates.

Spectrum estimation and harmonic analysis

Economic Control of Quality of Manufactured Product.

This paper derives asymptotically optimal tests for testing problems in which a nuisance parameter exists under the alternative hypothesis but not under the null. For example, the results apply to tests of structural change with unknown changepoint. The testing problem considered is nonstandard and the classical asymptotic optimality results for the Lagrange multiplier, Wald, and likelihood ratio do not apply. A weighted average power criterion is used here to generate optimal tests. This criterion is similar to that used by A. Wald (1943) to obtain the classical asymptotic optimality properties of Wald tests in 'regular' testing problems. Copyright 1994 by The Econometric Society.

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Optimal Tests When a Nuisance Parameter is Present Only under the Alternative

SUMMARY We propose an analytical and conceptual framework for a systematic and comprehensive assessment of disease seasonality to detect changes and to quantify and compare temporal patterns. To demonstrate the proposed technique, we examined seasonal patterns of six enterically transmitted reportable diseases (EDs) in Massachusetts collected over a 10-year period (1992-2001). We quantified the timing and intensity of seasonal peaks of ED incidence and examined the synchronization in timing of these peaks with respect to ambient temperature. All EDs, except hepatitis A, exhibited well-defined seasonal patterns which clustered into two groups. The peak in daily incidence of Campylobacter and Salmonella closely followed the peak in ambient temperature with the lag of 2-14 days. Cryptosporidium, Shigella, and Giardia exhibited significant delays relative to the peak in temperature (~ 40 days, P <002). The proposed approach provides a detailed quantification of seasonality that enabled us to detect significant differences in the seasonal peaks of enteric infections which would have been lost in an analysis using monthly or weekly cumulative information. This highly relevant to disease surveillance approach can be used to generate and test hypotheses related to disease

/pdf/seasonality-in-six-enterically-transmitted-diseases-and-4iy7eb1krc.pdf

Seasonality in six enterically transmitted diseases and ambient temperature

The article reviews methods of inference for single and multiple change-points in time series, when data are of retrospective (off-line) type. The inferential methods reviewed for a single change-point in time series include likelihood, Bayes, Bayes-type and some relevant non-parametric methods. Inference for multiple change-points requires methods that can handle large data sets and can be implemented efficiently for estimating the number of change-points as well as their locations. Our review in this important area focuses on some of the recent advances in this direction. Greater emphasis is placed on multivariate data while reviewing inferential methods for a single change-point in time series. Throughout the article, more attention is paid to estimation of unknown change-point(s) in time series, and this is especially true in the case of multiple change-points. Some specific data sets for which change-point modelling has been carried out in the literature are provided as illustrative examples under both single and multiple change-point scenarios.

Inference for single and multiple change-points in time series: SINGLE AND MULTIPLE CHANGE-POINTS IN TIME SERIES

Statistics are derived for tests of changes at unknown times in the parameters of a general linear regression model. Asymptotic distribution theory for the tests is discussed. Simulations are carried out to compare power of the statistics derived in this paper with that of other statistics. The derived statistics are shown to have good power properties as compared to other statistics, particularly for the difficult problem of detecting small changes. The change-point methodology is then applied to data on the incidence of AIDS in the United States.

Ian B. MacNeill

Papers

Seasonality in six enterically transmitted diseases and ambient temperature

Inference for single and multiple change-points in time series: SINGLE AND MULTIPLE CHANGE-POINTS IN TIME SERIES

Tests for parameter changes at unknown times in linear regression models

Tests for parameter changes at unknown times in linear regression models

Residual partial sum limit process for regression models with applications to detecting parameter changes at unknown times