The minimum variance unbiased estimator of the intensity of intersections is found for stationary Poisson process of segments with parameterized distribution of primary grain with known and unknown parameters. The minimum variance unbiased estimators are compared with commonly used estimators.
An iterative method based on a fixed-point property is proposed for finding maximum likelihood estimators for parameters in a model of network reliability with spatial dependence. The method is shown to converge at a geometric rate under natural conditions on data.
An iterative method based on a fixed-point property is proposed for finding maximum likelihood estimators for parameters in a model of network reliability with spatial dependence. The method is shown to converge at a geometric rate under natural conditions on data.
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.
The paper deals with sufficient conditions for the existence of general approximate minimum distance estimator (AMDE) of a probability density function on the real line. It shows that the AMDE always exists when the bounded -divergence, Kolmogorov, Lévy, Cramér, or discrepancy distance is used. Consequently, consistency rate in any bounded -divergence is established for Kolmogorov, Lévy, and discrepancy estimators under the condition that the degree of variations of the corresponding family...
In this paper we introduce extensions of the so-called Frisch-Waugh-Lovell Theorem. This is done by employing the close relationship between the concept of linear sufficiency and the appropriate reduction of linear models. Some specific reduced models which demonstrate alternatives to the Frisch-Waugh-Lovell procedure are discussed.