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条件密度的强相合的双重核估计

DOUBLE KERNEL ESTIMATORS OF CONDITIONAL DENSITY

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【作者】 孙东初

【Author】 SUN DONGCHU (East China Normal University)

【机构】 华东师范大学

【摘要】 <正> 根据从总体抽取的一个样本去估计总体分布的密度函数,在实际应用中具有重要意义.然而在非参数回归、条件分布和条件分位数的估计时,经常要用到条件密度,为此,我们考虑条件密度如下形式的核估计.

【Abstract】 Let(X,Y),(Xi,Yi)i=1,2,… be i.i.d.Rp×Rq-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) fn(y|x)=sum from i=1 to n K1((x-Xi)/(an))K2((y-Yi)/(bn))/{bnq sum from j=1 to n Ki((x-Xj)/(an))} where K1 and K2 are probability density functions on Rp and Rq respectively,and both an and are sequences of small positive numbers.Denote gn(x,y)=(nanpbnq-1sum from i=1 to n K1((x-Xi)/(an))K2((y-Yi)/(bn)), hx(x)=(nanp-1sum from i=1 to n K1((x-Xi)/(an)) then fn(y|x)=gn(x,y)=gn(x,y)/hn(x).If an=bn,gn(x,y) is Rosenblatt estimator of joint density g(x,y).In the paper,we obtain both pointwise and uniform strong consistency of gn(x, y) and fn(y|x).

  • 【文献出处】 应用概率统计 ,Chinese Journal of Applied Probability and Statistics , 编辑部邮箱 ,1985年02期
  • 【被引频次】14
  • 【下载频次】75
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