A New Wavelet Linear Survival Function Estimator
نویسنده
چکیده
Abstract: Let {Xn, n=1} be a sequences of i.i.d. random variables with survival function 1 F(x) P[X x] = > . A wavelet linear survival function n F(x) based on X1, X2,..., Xn is introduced as an estimator for n F(x) . We establish that the Lp’-loss (2=r=p′= ∞) of the linear wavelet survival function estimator for a stochastic processes convergence at the rate rs 2 s 1 n (s s 1 /p 1 / p ) ′ − ′+ ′ ′ = − + when the survival function, n F(x) belongs to the Besov space p,q B . Strong consistency and pointwise as well as uniform of n F(x) are discussed.
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