We discuss the prediction of the sample variance of marks of a marked spatial point process on a continuous space by the threshold method. The threshold method is a statistical prediction using only the number of points with marks exceeding a given threshold value. Mase (1996) considered the method in the framework of spatial point processes on a discrete space and Sakaguchi and Mase (2003) extended the results of Mase (1996) to a continuous space. They considered the prediction of the sum of marks. In the present paper, it is shown that the sample variance of marks can be also predicted well if a point process is non-ergodic and marks satisfy some mixing-type condition. A simulation study is given to confirm the theoretical result.
In this article we study the simultaneous estimation of the Poisson means in J-way multiplicative models and a decomposable model for three-way layouts. The estimators which improve on the maximum likelihood estimators under the normalized squared error losses are provided for each model. The proposed estimators correspond to the ones by Clevenson and Zidek (1975), Tsui and Press (1982) and Chou (1991).
We study a nonparametric estimation of Lévy measures for multidimensional jump-diffusion models from some discrete observations. We suppose that the jump term is driven by a Lévy process with finite Lévy measure, that is, a compound Poisson process. We construct a kernel-estimator of the Lévy density under a sampling scheme where the terminal time tends to infinity and at the same time the distance between the observations tends to zero fast enough, and show the L2-consistency and the optimal rate in the MSE sense. First, we consider the case where the observations are given continuously and then compare it to the discretely observed case.
A convex combination of one-sample U-statistics was introduced by Toda and Yamato (2001) and its Edgeworth expansion was derived by Yamato et al. (2003). We introduce a convex combination of two-sample U-statistics, which includes two-sample U-statistic, V-statistic and limit of Bayes estimate. Its Edgeworth expansion is derived with remainder term o(N−1/2), under the condition that the kernel is non-degenerate. We give some examples of the expansion for three statistics, two-sample U-statistic, V-statistic and limit of Bayes estimate, based on some distributions.
For square contingency tables with ordered categories, Tomizawa (1992) proposed three kinds of double symmetry models, whose each has a structure of both symmetry about the main diagonal and asymmetry about the reverse diagonal of the table. This paper proposes the extensions of those models and gives the decompositions for three kinds of double symmetry models into the extended quasi double symmetry models, the weighted marginal double symmetry models, and the balance models. Those decompositions are applied to two kinds of data on unaided distance vision.
The efficiencies of the ratio- type estimators have been increased by using linear transformation on auxiliary variable in the literature. But such type of estimators requires the additional knowledge of unknown population parameters, which restricts their applicability. Keeping in view such restrictions, we have proposed two unbiased estimators of population mean of study variable on applying linear transformation to auxiliary variable by using its extreme values in the population that are generally available in practice. The comparison of the proposed estimators with the existing ones have been done with respect to their variances. It has also been shown that the proposed estimators have greater applicability and are more efficient than the mean per unit estimator even when the existing estimators are less efficient. We have also shown that under some known conditions the choice of most efficient estimators among the considered ones can be made for a given population. The theoretical results obtained are shown diagrammatically and have been verified numerically by taking some empirical populations.