ROHMER Tom

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Generalized Linear Models with categorical explanatory variables are considered and parameters of the model are estimated with an original exact maximum likelihood method. The existence of a sequence of maximum likelihood estimators is discussed and considerations on possible link functions are proposed. A focus is then given on two particular positive distributions: the Pareto 1 distribution and the shifted log-normal distributions. Finally, the approach is illustrated on a actuarial dataset to model insurance losses.

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Abstract A class of tests for change-point detection designed to be particularly sensitive to changes in the cross-sectional rank correlation of multivariate time series is proposed. The derived procedures are based on several multivariate extensions of Spearman’s rho. Two approaches to carry out the tests are studied: the first one is based on resampling and the second one consists of estimating the asymptotic null distribution. The asymptotic validity of both techniques is proved under the null for strongly mixing observations. A procedure for estimating a key bandwidth parameter involved in both approaches is proposed, making the derived tests parameter-free. Their finite-sample behavior is investigated through Monte Carlo experiments. Practical recommendations are made and an illustration on trivariate financial data is finally presented.

Classical and more recent tests for detecting distributional changes in multivariate time series often lack power against alternatives that involve changes in the cross-sectional dependence structure. To be able to detect such changes better, a test is introduced based on a recently studied variant of the sequential empirical copula process. In contrast to earlier attempts, ranks are computed with respect to relevant subsamples, with beneficial consequences for the sensitivity of the test. For the computation of p-values we propose a multiplier resampling scheme that takes the serial dependence into account. The large-sample theory for the test statistic and the resampling scheme is developed. The finite-sample performance of the procedure is assessed by Monte Carlo simulations. Two case studies involving time series of financial returns are presented as well.

It is well known that the marginal laws of a random vector are not sufficient to characterize its distribution. When the marginal laws of the random vector are continuous, Sklar's theorem guarantees the existence and uniqueness of a function called the copula, characterizing the dependence between the components of the vector. The law of the random vector is perfectly deniable by giving the marginal laws and the copula. In this thesis, we propose two non-parametric tests to detect breaks in the distribution of multivariate observations, particularly sensitive to changes in the copula of the observations. They both improve recent proposals and result in more powerful tests than their predecessors for relevant classes of alternatives. Monte Carlo simulations illustrate the performance of these tests on moderate sample sizes. The first test is based on a Cramér-von Mises statistic constructed from the sequential empirical copula process. A multiplier-based resampling procedure is proposed for the test statistic. Its asymptotic validity under the null hypothesis is demonstrated under strong mixing conditions on the data. The second test focuses on the detection of a change in the multivariate Spearman rho of the observations. Although less general, it presents better results in terms of power than the first test for alternatives characterized by a change in the Spearman rho. Two strategies for calculating the p-value are compared theoretically and empirically: one uses a resampling of the statistic, the other is based on an estimate of the limiting distribution of the test statistic.