概率密度函数及其导数的估计

CONVERGENCE RATE OF ESTIMATES OF PROBABILITY DENSITY FUNCTION AND ITS DERIVATIVES

  • 摘要: 本文研究一个对概率密度函数f(x)及其导数的估计,它基于Fourier变换方法上,被称为Fourier变换估计.我们讨论了这估计的相合性及渐近正态性,并用这方法对众数也进行了估计.

     

    Abstract: In this paper, we obtain the strong uniform convergence rate δnr) of estimatis of probability density f(x) and its derivatives frx), here \begingathered\delta_n(r)=\sup _-\infty<\infty<\infty\left|\hatf_n^(r)(x)-f^(r)(x)\right|, \hatf_n^(r)(x)=\frac1n \pi \sum_k=1^n\left\frac\sin \left\left(x-\infty_k\right) \varphi(n)\rightx-x_k\right_0^(r), \\ (r=0,1,2, \cdots),\endgathered, xkk=1, 2,…, n) are i.i.d. samples drawn from a population with density fx), \varphi(n)>0, \lim _i \rightarrow \infty \varphi(n)=\infty,The asymptotic normalities are discussed.

     

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