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- W2356636877 abstract "Let(X,Y),(X_i,Y_i)i=1,2,… be i.i.d.R~p×R~q-valued random vectors with common joint distribution G(x,y) and joint density g(x,y).Let h(x) be the marginal density of X and let f(y|x)=g(x,y)/h(x) be the conditional density of Y on X.In this paper we propose the following type of conditional density estimators (calle double ernel estimators) f_n(y|x)=sum from i=1 to n K_1((x-X_i)/(a_n))K_2((y-Y_i)/(b_n))/{b_n~q sum from j=1 to n K_i((x-X_j)/(a_n))} where K_1 and K_2 are probability density functions on R~p and R~q respectively,and both a_n and are sequences of small positive numbers.Denote g_n(x,y)=(na_n~pb_n~q)~(-1)sum from i=1 to n K_1((x-X_i)/(a_n))K_2((y-Y_i)/(b_n)), h_x(x)=(na_n~p)~(-1)sum from i=1 to n K_1((x-X_i)/(a_n)) then f_n(y|x)=g_n(x,y)=g_n(x,y)/h_n(x).If a_n=b_n,g_n(x,y) is Rosenblatt estimator of joint density g(x,y).In the paper,we obtain both pointwise and uniform strong consistency of g_n(x, y) and f_n(y|x)." @default.
- W2356636877 created "2016-06-24" @default.
- W2356636877 creator A5006118312 @default.
- W2356636877 date "1985-01-01" @default.
- W2356636877 modified "2023-09-28" @default.
- W2356636877 title "DOUBLE KERNEL ESTIMATORS OF CONDITIONAL DENSITY" @default.
- W2356636877 hasPublicationYear "1985" @default.
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