Catherine Huber

Estimation des densités: risque minimax

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Covariate-Matched One-Sided Tests for the Difference between Functional Means

Abstract When testing hypotheses about the effects of different treatments, variation among covariates can become confounded with that between treatments unless the treatments are applied using paired covariates. In the context of unpaired covariates, we propose implicit covariate-matching methods for testing the hypothesis that one treatment effect is greater than another. The methods are founded on the assumption that the mean treatment effect, conditional on the covariate, is a smooth function of the covariate. They are implemented using new interpolation techniques for nonparametric curve estimation. Bootstrap arguments are used to construct critical points. We show that even when the covariate distributions are identical for both treatments, covariate matching of the type that we propose produces tests of greater power than methods that do not attempt matching. Our techniques have application to two-sided hypothesis testing.

Lower Bounds for Function Estimation

Over the last thirty years, it has been recognized that a common abstract framework underlies many basic problems of nonparametric estimation. In that framework, f is an unknown function to be estimated, known to belong to a class.P of smooth functions, and an observation X is available in order to perform the estimation. The X has its values in a measurable space (E,13) and obeys a probability law indexed by f and denoted Pf. The set of all probabilities P 9 where g varies in.P is denoted P.

Mathematical Methods in Survival Analysis, Reliability and Quality of Life

Part 1: Survival Analysis. Chapter 1. Model selection for additive regression (E. Brunel and F. Comte). Chapter 2. Nonparametric estimation of conditional probabilities, means and quantiles (O. Pons). Chapter 3. Inference in transformation models for arbitrarily censored and truncated data (F. Vonta, C. Huber). Chapter 4. Within-area distribution (L. Fortunato et al). Chapter 5. Semi-Markov models in medicine (E. Mathieu-Dupas, C. Gras-Aygon, J-P. Daures). Chapter 6. Bivariate Cox models (M. Broniatowski, A. Depire, Y. Ritov). Chapter 7. A nonparametric estimation of a class of survival functionals (B. Abdous). Chapter 8. Approximate likelihood (H. Lauter). Part 2: Reliability. Chapter 9. Cox regression with missing values of a non-proportional covariate (J-F. Dupuy, E. Leconte). Chapter 10. Bayesian sampling plan for type-I censored exponential data (C-T. Lin, Y-L. Huang, N. Balakrishnan). Chapter 11. Reliability of stochastic dynamical systems applied to fatigue crack growth (J. Chiquet and N. Limnios). Chapter 12. Statistical analysis of a redundant system with one stand-by unit (V. Bagdonavicius and I. Masiulaityte, M. Nikulin). Chapter 13. A modified test for the three-parameter Weibull distribution (V. Voinov, R. Alloyarova and N. Pya). Chapter 14. Accelerated life testing when the hazard rate function has cup shape (V. Bagdonavicius, L. Clerjaud, M. Nikulin). Chapter 15. Software reliability (J. Ledoux). Part 3: Quality of Life. Chapter 16. Latent Markov Rasch model (F. Bartolucci, F. Pennoni, M. Lupparelli). Chapter 17. Selection of items fitting a Rasch model (J-B. Hardouin, M. Mesbah). Chapter 18. Longitudinal latent regression modeling (S. Bacci). Chapter 19. Empirical validation of a quality of life instrument (J. Chwalow et al). Part 4: Related Topics. Chapter 20. Deterministic modeling of the size of the HIV/AIDS epidemic in Cuba (R. Lounes, H. de Arazoza, Y. H.Hsieh, J. Joanes). Chapter 21. Some probabilistic models useful in sport sciences (L. Gerville-Reache, M. Nikulin, S. Orazio, N. Paris, V. Rosa). List of Authors. Index.

The Choice of Loglinear Models in Contingency Tables when the Variables of Interest Are Not Jointly Observed

The problem of estimating the relationship between two variables when their cross-classification is not directly observed is usually resolved by modelling the incomplete data by loglinear models. Some models are invalid, in the sense that they are incompatible with the observations, and the maximum likelihood method fails to give solutions. This paper gives simple rules to exclude these invalid models and presents a discussion about the choice among valid models.

Hierarchical Dependency Models for Multivariate Survival Data with Censoring

A familyof partial likelihood logistic models is proposed for clusteredsurvival data that are reported in discrete time and that maybe censored. The possible dependence of individual survival timeswithin clusters is modeled, while distinct clusters are assumedto be independent. Two types of clusters are considered. First,all clusters have the same size and are identically distributed.Second, the clusters may vary in size. In both cases our asymptoticresults apply to a large number of small independent clusters.