JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (4): 21-25.doi: 10.6040/j.issn.1671-9352.0.2016.329

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Convergence properties of the kernel-type density estimator under WOD dependent samples

HU Xue-ping, ZHANG Hong-mei   

  1. School of Mathematics and Computational Science, Anqing Normal University, Anqing 246133, Anhui, China
  • Received:2016-07-01 Online:2017-04-20 Published:2017-04-11

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Abstract: Let {Xn,n≥1} be an identically distributed WOD random sequence with a commen density functiong f(x). Based on the Rosenthal-type inequality and Bernstein-type inequality for WOD sequence, the kernel estimator for density function f(x)was investigated under suitable conditions, and the consistency in r order mean, the pointwise strong consistency and uniform consistency in L1 were obtained.

Key words: WOD samples, consistency in r order mean, kernel estimator, pointwise strong consistency

CLC Number: 

  • O212
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