Breast cancer and quality of life: medical information extraction from health forums

International audienceInternet health forums are a rich textual resource with content generated through free exchanges among patients and, in certain cases, health professionals. We tackle the problem of retrieving clinically relevant information from such forums, with relevant topics being defined from clinical auto-questionnaires. Texts in forums are largely unstructured and noisy, calling for adapted preprocessing and query methods. We minimize the number of false negatives in queries by using a synonym tool to achieve query expansion of initial topic keywords. To avoid false positives, we propose a new measure based on a statistical comparison of frequent co-occurrences in a large reference corpus (Web) to keep only relevant expansions. Our work is motivated by a study of breast cancer patients' health-related quality of life (QoL). We consider topics defined from a breast-cancer specific QoL-questionnaire. We quantify and structure occurrences in posts of a specialized French forum and outline important future developments

Large deviations for M-estimators

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Large deviations for M-estimators

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Applications of large deviations to optimal experimental designs

International audienceWe give a large deviations principle for the least-squares estimator in a linear model. Next, we apply the large deviations result to find optimal experimental designs

Strong large deviations for arbitrary sequences of random variables

International audienceWe establish a large deviation approximation for the density function of an arbitrary sequence of random variables. The results are analogous to those obtained by Chaganty and Sethuraman (1985). We apply our theorems to the sample variance and the Mann–Whitney two-sample statistic

Sharp large deviations in nonparametric estimation

International audienceLarge deviation results for the kernel density estimator and the kernel regression estimator have been given by Louani [Louani, D., 1998, Large deviations limit theorems for the kernel density estimator. Scandinavian Journal of Statistics, 25, 243–253; Louani, D., 1999, Some large deviations limit theorems in conditional nonparametric statistics. Statistics, 33, 171–196]. We complete these works by establishing sharp large deviation results for the two estimators. This means that we study precisely the tail probabilities of the estimators. We distinguish two cases depending on the support of the kernel. To prove the results, we need an Edgeworth expansion obtained from a version of Cramer’s condition

Asymptotic approximation for the probability density function of an arbitrary sequence of random variables

International audienceWe establish a large deviation approximation for the density function of an arbitrary sequence of random variables. The results are analogous to those obtained by Chaganty and Sethuraman (1985). We apply our theorems to the sample variance and the Mann–Whitney two-sample statistic

Multidimensional strong large deviation results

International audienceWe establish strong large deviation results for an arbitrary sequence of randomvectors under some assumptions on the normalized cumulant generating function.In other words, we give asymptotic approximations for a multivariate tail probabilityof the same kind as the one obtained by Bahadur and Rao (Ann Math Stat 31:1015–1027, 1960) for the sample mean (in the one-dimensional case).The proof of our resultsfollows the same lines as in Chaganty and Sethuraman (J Stat Plan Inference, 55:265–280, 1996). We also present three statistical applications to illustrate our results, thefirst one dealing with a vector of independent sample variances, the second one witha Gaussian multiple linear regression model and the third one with the multivariateNadaraya–Watson estimator. Some numerical results are also presented for the firsttwo applications

Large deviation approximations for the Mann–Whitney statistic and the Jonckheere–Terpstra statistic

International audienceWe establish strong large deviation results for the Mann–Whitney statistic and the Jonckheere–Terpstra statistic, that is, asymptotic expansions of large deviation type for the tail probabilities.We then carry out some numerical comparisons with the exact upper tail probabilities for theWilcoxon–Mann–Whitney test and the Jonckheere–Terpstra test

Sharp large deviation principle for the conditional empirical process

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