@article{oai:ynu.repo.nii.ac.jp:00006868,
 author = {Takahata, Hiroshi},
 issue = {2},
 journal = {Yokohama Mathematical Journal = 横濱市立大學紀要. D部門, 数学},
 month = {},
 note = {application/pdf, Let ＄￥{X_{z} : z￥in R^{a}￥}＄ be a strictly stationary real-valued random field and ＄￥{N(A) : A￥subset R^{d}￥}＄ a Poisson random measure which is independent of ＄X＄ . Assume that the distribution of ＄X_{z}＄ has a density function ＄f(x)＄ . Fix an observation-domain ＄V￥subset R^{d}＄ . Suppose that we are to estimate the value ＄f(x)＄ using the data observed on V. lf the data are given as observations at counting points of ＄N(dz)＄ , then the following kernel density estimator is natural: ＄f_{V}(x)=(N(V)h_{N(V)})^{-1}￥int_{V}K((x-X_{z})/h_{N(V)})N(dz)＄ where ＄h_{n}＄ is a band-width parameter. In this paper we discuss the central limit theorem and the convergence rate of the bias and the mean square error for ＄f_{V}(x)＄ as the volume ＄|V|＄ tends to ＄￥infty＄ . In addition, we shall refer to the estimations of joint probability density functions.},
 pages = {127--152},
 title = {NONPARAMETRIC DENSITY ESTIMATIONS FOR A CLASS OF MARKED POINT PROCESSES},
 volume = {41},
 year = {1994}
}