Non-parametric maximum likelihood estimation of interval-censored failure time data subject to misclassification

The paper considers non-parametric maximum likelihood estimation of the failure time distribution for interval censored data subject to misclassification. Such data can arise from two types of observation scheme; either where observations continue until the first positive test result or where tests continue regardless of the test results. In the former case, the misclassification probabilities must be known, whereas in the latter case joint estimation of the event-time distribution and misclassification probabilities is possible. The regions for which the maximum likelihood estimate can only have support are derived. Algorithms for computing the maximum likelihood estimate are investigated and it is shown that algorithms appropriate for computing non-parametric mixing distributions perform better than an iterative convex minorant algorithm in terms of time to absolute convergence. A profile likelihood approach is proposed for joint estimation. The methods are illustrated on a data set relating to the onset of cardiac allograft vasculopathy in post-heart-transplantation patients

Hidden semi-Markov-switching quantile regression for time series

A hidden semi-Markov-switching quantile regression model is introduced as an extension of the hidden Markov-switching one. The proposed model allows for arbitrary sojourn-time distributions in the states of the Markov-switching chain. Parameters estimation is carried out via maximum likelihood estimation method using the Asymmetric Laplace distribution. As a by product of the model specification, the formulae and methods for forecasting, the state prediction, decoding and model checking that exist for ordinary hidden Markov-switching models can be applied to the proposed model. A simulation study to investigate the behaviour of the proposed model is performed covering several experimental settings. The empirical analysis studies the relationship between the stock index from the emerging market of China and those from the advanced markets, and investigates the determinants of high levels of pollution in an Italian small city.publishedVersio

Distribution-free analysis of homogeneity

In this dissertation three problems strongly connected to the topic of homogeneity are considered. For each of them a distribution-free approach is investigated using simulated as well as real data. The first procedure proposed is motivated by the fact that a mere rejection of homogeneity is unsatisfactory in many applications, because it is often not clear which discrepancies of the samples case the rejection. To capture the dissimilarities our method combines a fairly general mixture model with the classical nonparametric two-sample Kolmogorov-Smirnov test. In case of a rejection by this test, the proposed algorithm quantifies the discrepancies between the corresponding samples. These dissimilarities are represented by the so called shrinkage factor and the correction distribution. The former measures the degree of discrepancy between the two samples. The latter contains information with regard to the over- and undersampled regions when comparing one sample to the other in the Kolmogorov-Smirnov sense. We prove the correctness of the algorithm as well as its linear running time when applied to sorted samples. As illustrated in various data settings, the fast method leads to adequate and intuitive results. The second topic investigated is a new class of two-sample homogeneity tests based on the concept of f-divergences. These distance like measures for pairs of distributions are defined via the corresponding probability density functions. Thus, homogeneity tests relying on f-divergences are not limited to discrepancies in location or scale, but can detect arbitrary types of alternatives. We propose a distribution-free estimation procedure for this class of measures based on kernel density estimation and spline smoothing. As shown in extensive simulations, the new method performs stable and quite well in comparison to several existing non- and semiparametric divergence estimators. Furthermore, we construct distribution-free two-sample homogeneity tests relying on various divergence estimators using the permutation principle. The tests are compared to an asymptotic divergence procedure as well as to several traditional parametric and nonparametric tests on data from different distributions under the null hypothesis and several alternatives. The results suggest that divergence-based methods have considerably higher power than traditional methods if the distributions do not predominantly differ in location. Therefore, it is advisable to use such tests if changes in scale, skewness, kurtosis or the distribution type are possible while the means of the samples are of comparable size. The methods are thus of great value in many applications as illustrated on ion mobility spectrometry data. The last topic we deal with is the detection of structural breaks in time series. The method introduced is motivated by characteristic functions and Fourier-type transforms. It is highly flexible in several ways: firstly, it allows to test for the constancy of an arbitrary feature of a time series such as location, scale or skewness. It is thus applicable in various problems. Secondly, the method makes use of arbitrary estimators of the feature under investigation. Hence, a robustification of the approach or other modifications are straightforward. We demonstrate the testing procedure focussing on volatility as well as on kurtosis. In both cases our approach leads to reasonable rejection rates for symmetric distributions in comparison to several test derived from the literature. In particular, the test shines in presence of multiple structural breaks, because its test statistic is constructed in a blockwise manner. The position and number of the presumable change points located by the new procedure also correspond to the true ones quite well. The method is thus well suited for many applications as illustrated on exchange rate data