caa a22 4500 475826825 CHVBK 20180406123830.0 cr unu---uuuuu 170329e20001201xx s 000 0 eng 10.1023/A:1017504723799 doi (NATIONALLICENCE)springer-10.1023/A:1017504723799 Honda Toshio Institute of Social Sciences, University of Tsukuba Tsukuba, 305-8571, Ibaraki, JAPAN aut Nonparametric Density Estimation for a Long-Range Dependent Linear Process [Elektronische Daten] [Toshio Honda] We estimate the marginal density function of a long-range dependent linear process by the kernel estimator. We assume the innovations are i.i.d. Then it is known that the term of the sample mean is dominant in the MISE of the kernel density estimator when the dependence is beyond some level which depends on the bandwidth and that the MISE has asymptotically the same form as for i.i.d. observations when the dependence is below the level. We call the latter the case where the dependence is not very strong and focus on it in this paper. We show that the asymptotic distribution of the kernel density estimator is the same as for i.i.d. observations and the effect of long-range dependence does not appear. In addition we describe some results for weakly dependent linear processes. The Institute of Statistical Mathematics, 2000 Kernel density estimator nationallicence long-range dependence nationallicence linear process nationallicence bandwidth nationallicence asymptotic normality nationallicence Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/4(2000-12-01), 599-611 0020-3157 52:4<599 2000 52 10463 https://doi.org/10.1023/A:1017504723799 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1017504723799 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Honda Toshio Institute of Social Sciences, University of Tsukuba Tsukuba, 305-8571, Ibaraki, JAPAN aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/4(2000-12-01), 599-611 0020-3157 52:4<599 2000 52 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer