Abstract
In this paper, we consider pointwise estimation over l^{p}(1leq p<infty ) risk for a density function based on a negatively associated sample. We construct linear and nonlinear wavelet estimators and provide their convergence rates. It turns out that those wavelet estimators have the same convergence rate up to the lnn factor. Moreover, the nonlinear wavelet estimator is adaptive.
Highlights
In practical problems, due to the existence of noise, it is possible to obtain real measurement data only with bias
When the independence of data is relaxed to the strong mixing case, Kou and Guo [10] studied the L2 risk of linear and nonlinear wavelet estimators in the Besov space
There is a lack of theoretical results on pointwise wavelet estimation for this density estimation model (1)
Summary
Due to the existence of noise, it is possible to obtain real measurement data only with bias (noise). Ω is a known biasing function, f denotes the unknown density function of unobserved random variable X, and μ := E[ω(X)] < ∞ The aim of this model is to estimate the unknown density function f by the observed negatively associated data Y1, Y2, . When the independence of data is relaxed to the strong mixing case, Kou and Guo [10] studied the L2 risk of linear and nonlinear wavelet estimators in the Besov space. Note that all those studies all focus on the global error. There is a lack of theoretical results on pointwise wavelet estimation for this density estimation model (1)
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