caa a22 4500 475826809 CHVBK 20180406123830.0 cr unu---uuuuu 170329e20001201xx s 000 0 eng 10.1023/A:1017517124707 doi (NATIONALLICENCE)springer-10.1023/A:1017517124707 Laws of Iterated Logarithm and Related Asymptotics for Estimators of Conditional Density and Mode [Elektronische Daten] [K. Mehra, Y. Ramakrishnaiah, P. Sashikala] Let (X i , Y i ) be a sequence of i.i.d. random vectors in R with an absolutely continuous distribution function H and let g x (y), y∈ R denote the conditional density of Y given X = x∈Λ(F), the support of F, assuming that it exists. Also let M(x) be the (unique) conditional mode of Y given X = x defined by M(x) = arg max y (y)). In this paper new classes of smoothed rank nearest neighbor (RNN) estimators of g x (y), its derivatives and M(x) are proposed and the laws of iterated logarithm (pointwise), uniform a.s. convergence over −∞ < y < ∞ and x∈ a compact C⫅Λ(F) and the asymptotic normality for the proposed estimators are established. Our results and proofs also cover the Nadayara-Watson (NW) case. It is shown using the concept of the relative efficiency that the proposed RNN estimator is superior (asymtpotically) to the corresponding NW type estimator of M(x), considered earlier in literature. The Institute of Statistical Mathematics, 2000 Conditional density nationallicence conditional mode nationallicence smooth rank nearest neighbor estimators nationallicence law of iterated logarithm nationallicence uniform strong convergence nationallicence Mehra K. Department of Mathematical Sciences, University of Alberta, T6G 2G1, Edmonton, Canada aut Ramakrishnaiah Y. Department of Statistics, Osmania University, 500007, Hyderabad-, India aut Sashikala P. Department of Statistics, B.B.C.I.T. Kachiguda, 500027, Hyderabad-, India aut Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/4(2000-12-01), 630-645 0020-3157 52:4<630 2000 52 10463 https://doi.org/10.1023/A:1017517124707 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1017517124707 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Mehra K. Department of Mathematical Sciences, University of Alberta, T6G 2G1, Edmonton, Canada aut NATIONALLICENCE 700 1- Ramakrishnaiah Y. Department of Statistics, Osmania University, 500007, Hyderabad-, India aut NATIONALLICENCE 700 1- Sashikala P. Department of Statistics, B.B.C.I.T. Kachiguda, 500027, Hyderabad-, India aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/4(2000-12-01), 630-645 0020-3157 52:4<630 2000 52 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer