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In this paper we introduce two methods for the construction of asymmetric multivariate copulas. The …rst is connected with products of copulas. The second approach generalises the Archimedean copulas. The resulting copulas are asymmetric and may have more than two parameters in contrast to most of the parametric families of copulas described in the… (More)

In this paper we derive rates of strong convergence for the kernel density estimator and for the Nadaraya-Watson estimator under the-mixing condition and under the condition of absolute regularity. A combination of an inequality of Bernstein type (Rio 1995) and an exponential inequality (cf. Fuk/Nagaev 1971) is the crucial tool for the proofs. Moreover, we… (More)

We consider a (nonlinear) autoregressive model with unknown parameters (vector). The aim is to estimate the density of the residuals by a kernel esti-mator. Since the residuals are not observed, the usual procedure for estimating the density of the residuals is the following: rst, compute an estimator ^ for ; second, calculate the residuals by use of the… (More)

This paper is devoted to convergence problems of the Gasser-MMller estima-tor for the regression function in a xed-design regression model. We prove the asymptotic normality and rates of uniform strong convergence for this type of estimators under the-mixing condition on the residuals. The proof of strong convergence is based on a Bernstein-type inequality… (More)

In this paper we prove the asymptotic normality and rates of strong convergence of some types of estimators for the regression function in a xed-design regression model. We consider the Gasser-MMller estimator and the Priestley-Chao estimator (univariate and multivariate). The proofs of asymptotic normality are based on a central limit theorem from an… (More)

In this paper we prove rates of uniform strong convergence, convergence rates of the mean square error and the asymptotic normality of the kernel estimator for the transition density of a geometrically ergodic Markov chain. The assumptions on the Markov chain are closely related to absolute regularity. We allow the initial distribution of the Markov chain… (More)

In this paper we consider a linear regression model with fixed design. A new rule for the selection of a relevant sub-model is introduced on the basis of parameter tests. One particular feature of the rule is that subjective grading of the model complexity can be incorporated. We provide bounds for the mis-selection error. Simulations show that by using the… (More)

- Eckhard Liebscher
- Kybernetika
- 2009

- Eckhard Liebscher, Meelis Käärik
- 2016

Scatter plots of multivariate data sets motivate modeling of star-shaped distributions beyond elliptically contoured ones. We study properties of estimators for the density generator function, the star-generalized radius distribution and the density in a star-shaped distribution model. For the generator function and the star-generalized radius density, we… (More)

In the paper we prove rates of strong convergence of M-estimators for the parameters in a general nonlinear autoregressive model. In the proofs we utilize a variational principle from stochastic optimization theory which was proved by Shapiro (1991). The results allow applications to least squares estimators as well as to some classes of robust estimators.… (More)