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Random weighting method for density kernel estimates. (Chinese. English summary) Zbl 0969.62026

Summary: The random weighting statistics is designed for the kernel estimator of density functions. Under suitable conditions, it is proved that the random weighting approximation can attain the accuracy of \[ o\left(n^{-{\lambda \over 2(\lambda+1)}} (\log n)^{{2\lambda+ 1\over 4(\lambda+1)}} C_n \right), \] where \(\lambda>0\), \(0<C_n\to\infty\). Lastly we study the large sample properties of random weighting estimators.

MSC:

62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
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