Methods of evaluating and comparing the performance of diagnostic tests are of increasing importance as new tests are developed and marketed. When a test is based on an observed variable that lies on a continuous or graded scale, an assessment of the overall value of the test can be made through the use of a receiver operating characteristic (ROC) curve. The curve is constructed by varying the cutpoint used to determine which values of the observed variable will be considered abnormal and then plotting the resulting sensitivities against the corresponding false positive rates. When two or more empirical curves are constructed based on tests performed on the same individuals, statistical analysis on differences between curves must take into account the correlated nature of the data. This paper presents a nonparametric approach to the analysis of areas under correlated ROC curves, by using the theory on generalized U-statistics to generate an estimated covariance matrix.

Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach.

THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data The text begins with a revision of estimation and hypothesis testing methods, covering both classical and Bayesian philosophies, before advancing to the analysis of linear and generalized linear models Topics covered include linear and logistic regression, simple and complex ANOVA models (for factorial, nested, block, split-plot and repeated measures and covariance designs), and log-linear models Multivariate techniques, including classification and ordination, are then introduced Special emphasis is placed on checking assumptions, exploratory data analysis and presentation of results The main analyses are illustrated with many examples from published papers and there is an extensive reference list to both the statistical and biological literature The book is supported by a website that provides all data sets, questions for each chapter and links to software

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Experimental Design and Data Analysis for Biologists

Benjamini and Hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems. A simple procedure was given there as an FDR controlling procedure for independent test statistics and was shown to be much more powerful than comparable procedures which control the traditional familywise error rate. We prove that this same procedure also controls the false discovery rate when the test statistics have positive regression dependency on each of the test statistics corresponding to the true null hypotheses. This condition for positive dependency is general enough to cover many problems of practical interest, including the comparisons of many treatments with a single control, multivariate normal test statistics with positive correlation matrix and multivariate $t$. Furthermore, the test statistics may be discrete, and the tested hypotheses composite without posing special difficulties. For all other forms of dependency, a simple conservative modification of the procedure controls the false discovery rate. Thus the range of problems for which a procedure with proven FDR control can be offered is greatly increased.

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The control of the false discovery rate in multiple testing under dependency

The least squares estimator of a regression coefficient β is vulnerable to gross errors and the associated confidence interval is, in addition, sensitive to non-normality of the parent distribution. In this paper, a simple and robust (point as well as interval) estimator of β based on Kendall's [6] rank correlation tau is studied. The point estimator is the median of the set of slopes (Yj - Yi )/(tj-ti ) joining pairs of points with ti ≠ ti , and is unbiased. The confidence interval is also determined by two order statistics of this set of slopes. Various properties of these estimators are studied and compared with those of the least squares and some other nonparametric estimators.

Estimates of the Regression Coefficient Based on Kendall's Tau

We propose a rank-test of the null hypothesis of short memory stationarity possibly after linear detrending. For the level-stationarity hypothesis, the test statistic we propose is a modied version of the popular KPSS statistic, in which ranks substitute the original observations. We prove that the rank KPSS statistic shares the same limiting distribution as the standard KPSS statistic under the null and diverges under I(1) alternatives. For the trend-stationarity hypothesis, we apply the same rank KPSS statistic to the residual of a Theil-Sen regression on a linear trend. We derive the asymptotic distribution of the Theil-Sen estimator under short memory errors and prove that the Theil-Sen detrended rank KPSS statistic shares the same weak limit as the least-squares detrended KPSS. We study the asymptotic relative eciency

http://www.statistica.unimib.it/utenti/WorkingPapers/WorkingPapers/20110201.pdf

A KPSS better than KPSS Rank tests for short memory stationarity

This paper proposes a test of the null hypothesis of stationarity that is robust to the presence of fat-tailed errors The test statistic is a modified version of the KPSS statistic, in which ranks substitute the original observations The rank KPSS statistic has the same limiting distribution as the standard KPSS statistic under the null and diverges under I(1) alternatives It features good power both under thin-tailed and fat-tailed distributions and it turns out to be a valid alternative to the original KPSS and the recently proposed Index KPSS (de Jong et al 2007)

A robust version of the KPSS test based on ranks

We consider multi-center experiments (for determining a consensus value) conducted in possibly heterogeneous set-ups leading to unbalanced heteroscedastic one-way random effects models. When normality of both the random components and their homoscedasticity are in doubt, standard statistical methods may not be valid. Two robust R-estimators (for the common location parameter), based on signed-rank statistics, are proposed and their properties studied. When large heteroscedasticity is present or the distribution of random effect is abnormal, the proposed estimators perform better than the classical weighted least squares and selected estimators. This feature is illustrated with an arsenic in oyster tissue problem, along with some other simulation studies.

Robust R-Estimation of a Consensus Value from Multi-Center Studies

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Notes: Correction to "The Invariance Principle for One-Sample Rank-Order Statistics"

Analogous to the usual stopping time for fixed-width confidence interval estimation of a real-valued parameter θ(F), a stopping time for fixed-width confidence band estimation of, a statistical functional process RF is considered. Techniques for showing that the resulting sequential confidence region has the correct asymptotic coverage probability are illustrated in several examples. Sufficient conditions for asymptotic efficiency and normality of the stopping time are given. Some implications of using the stopping time in conjunction with a bootstrap confidence band procedure are investigated in the context of estimating a dstribution function.

Pranab Kumar Sen

Papers

A KPSS better than KPSS Rank tests for short memory stationarity

A robust version of the KPSS test based on ranks

Robust R-Estimation of a Consensus Value from Multi-Center Studies

Notes: Correction to "The Invariance Principle for One-Sample Rank-Order Statistics"

On stopping times for fixed-width confidence regions