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This thesis can be divided into two parts. In the first part (Chapter 2) we apply Stein's method in the classical sense to the normal approximation of the posterior distribution in exponential families. In Bayesian statistics it is well known that the normalised posterior distribution approaches the standard normal distribution as the sample size grows. We work out bounds on the total variation and Wasserstein distance between the standardised posterior and the standard normal distribution in the case where likelihood of the data comes from an exponential family and apply these general bounds to several examples of exponential families. In the second part (Chapter 3 and Chapter 4) we leave classical Stein's method behind and use Stein operators together with a appropriate function classes for the purpose of parameter estimation. We develop a new class of moment-type point estimators for univariate ergodic and strictly stationary time series and establish consistency as well as asymptotic normality. Moreover, we obtain a two-step estimator which reaches asymptotic effciency. The new estimators are then compared to methods from the literature through simulation studies for several examples., Doctorat en Sciences, info:eu-repo/semantics/nonPublished

The asymptotic distribution of a wide class of V- and U-statistics with estimated parameters is derived in the case when the kernel is not necessarily differentiable along the parameter. The results have their application in goodness-of-fit problems.

The asymptotic distribution of a wide class of V- and U-statistics with estimated parameters is derived in the case when the kernel is not necessarily differentiable along the parameter. The results have their application in goodness-of-fit problems.

We propose specification tests for the innovation distribution in conditional duration models. The new tests are based either on the cumulative distribution function, or on exponential transforms such as the Laplace transform and the characteristic function, or on characterizations of the innovation-distribution under test. We study the finite-sample performance of the proposed procedures in comparison with alternative tests which employ nonparametric density estimates as well as with tests based on entropy. A bootstrap version of the tests is utilized in order to study the small sample behavior of the procedures. A real-data example illustrates the applicability of our method and confirms conclusions drawn by earlier authors

We propose specification tests for the innovation distribution in conditional duration models. The new tests are based either on the cumulative distribution function, or on exponential transforms such as the Laplace transform and the characteristic function, or on characterizations of the innovation-distribution under test. We study the finite-sample performance of the proposed procedures in comparison with alternative tests which employ nonparametric density estimates as well as with tests based on entropy. A bootstrap version of the tests is utilized in order to study the small sample behavior of the procedures. A real-data example illustrates the applicability of our method and confirms conclusions drawn by earlier authors

Тестови сагласности са расподелом и тестови симетрије заузимају значајно место у непараметарској статистици..., Goodness of t and symmetry tests occupy a signicant part of nonparametric statistic. Most of classical tests are based on the distance between the assumed distribution function and its consistent estimate, empirical distribution function. The symmetry tests are analogously constructed. A new approach that is especially attractive in recent years is making tests based on characterizations of dierent types. Those tests use U-empirical distribution functions (generalized empirical ones), U-empirical transforms (eg. Laplace transform, characteristic functions etc.) and U-empirical moments of distributions. The main advantage of these tests is that they are often free of some distribution parameters. Therefore they are suitable for testing composite hypothesis.