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We present two data-driven procedures to estimate the transition density of an homogeneous Markov chain. The first yields a piecewise constant estimator on a suitable random partition. By using an Hellinger-type loss, we establish non-asymptotic risk bounds for our estimator when the square root of the transition density belongs to possibly inhomogeneous Besov spaces with possibly small regularity index. Some simulations are also provided. The second procedure is of theoretical interest and leads...
The MINQUE of the linear function of the unknown variance-components parameter in mixed linear model under linear restrictions of the type is defined and derived. As an illustration of this estimator the example of the one-way classification model with the restrictions , where , is given.
The paper concerns with a heteroscedastic random coefficient autoregressive model (RCA) of the form . Two different procedures for estimating or , respectively, are described under the special seasonal behaviour of . For both types of estimators strong consistency and asymptotic normality are proved.
A complete and sufficient statistic is found for stationary marked Poisson processes with a parametric distribution of marks. Then this statistic is used to derive the uniformly best unbiased estimator for the length density of a Poisson or Cox segment process with a parametric primary grain distribution. It is the number of segments with reference point within the sampling window divided by the window volume and multiplied by the uniformly best unbiased estimator of the mean segment length.
An estimation of the linear function of elements of unknown matrices in the covariance components model is presented.
We consider the problem of estimating the mean of a Gaussian vector with independent components of common unknown variance . Our estimation procedure is based on estimator selection. More precisely, we start with an arbitrary and possibly infinite collection of estimators of based on and, with the same data , aim at selecting an estimator among with the smallest Euclidean risk. No assumptions on the estimators are made and their dependencies with respect to may be unknown. We establish...
Explicit expressions of UMVUE for variance components are obtained for a class of models that include balanced cross nested random models. These estimators are used to derive tests for the nullity of variance components. Besides the usual F tests, generalized F tests will be introduced. The separation between both types of tests will be based on a general theorem that holds even for mixed models. It is shown how to estimate the p-value of generalized F tests.
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