Frontiers of Mathematics in China >

2014 , Vol. 9 >Issue 3: 623 - 640

DOI: https://doi.org/10.1007/s11464-014-0353-y

RESEARCH ARTICLE

Wavelet linear estimations of density derivatives from a negatively associated stratified size-biased sample

  • Junlian XU , 1,2
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  • 1. Department of Applied Mathematics, Beijing University of Technology, Beijing 100124, China
  • 2. Department of Mathematics, Baoji University of Arts and Sciences, Baoji 721013, China

Received date: 16 May 2013

Accepted date: 03 Dec 2013

Published date: 24 Jun 2014

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

We define a wavelet linear estimator for density derivative in Besov space based on a negatively associated stratified size-biased random sample. We provide two upper bounds of wavelet estimations on Lp (1≤p<∞) risk.

Key words： Wavelet estimator; density derivative; weight function; negatively associated; Besov space

Cite this article

Junlian XU . Wavelet linear estimations of density derivatives from a negatively associated stratified size-biased sample[J]. Frontiers of Mathematics in China, 2014 , 9(3) : 623 -640 . DOI: 10.1007/s11464-014-0353-y

References

Publishing order | Descend order by publishing year | Descend order by cited within
1
AlamK, SaxenaK M L. Positive dependence in multivariate distribution. Comm Statist-Theory Methods A, 1981, 10: 1183-1196

DOI

2
ChaubeyY P, DoostiH, Prakasa RaoB L S. Wavelet based estimation of the derivatives of a density for a negatively associated process. J Stat Theory Pract, 2008, 2: 453-463

DOI

3
ChesneauC. Wavelet block thresholding for density estimation in the presence of bias. J Korean Statist Soc, 2010, 39: 43-53

DOI

4
ChesneauC, DewanI, DoostiH. Wavelet linear density estimation for associated stratified size-biased sample. J Nonparametr Stat, 2012, 2: 429-445

DOI

5
DaubechiesI. Ten Lectures on Wavelets. Philadelphia: SIAM, 1992

DOI

6
EfromovichS. Nonparametric Curve Estimation. Methods, Theory, and Applications. New York: Springer, 1999

7
HädleW, KerkyacharianG, PicardD, TsybakovA. Wavelets, Approximations, and Statistical Applications. Lecture Notes in Statistics, Vol 129. Berlin: Springer-Verlag, 1998

DOI

8
Joag-DevK, ProschanF. Negative association of random variables with application. Ann Statist, 1983, 11: 286-295

DOI

9
LiuY M, WangH Y. Wavelet estimations for density derivatives. Sci China Math, 2013, (3): 483-495

10
NewmanC M. Normal fluctuations and the KFG inequalities. Comm Math Phys, 1980, 74: 119-128

DOI

11
PatilG P, RaoC R. The Weighted Distributions: A Survey of Their Applications. Amsterdam: North-Holland, 1977

12
Prakasa RaoB L S. Nonparametric estimation of the derivatives of a density by the method of wavelets. Bull Inform Cybernet, 1996, 28: 91-100

13
RamirezP, VidakovicB. Wavelet density estimation for stratified size-biased sample. J Statist Plann Inference, 2010, 140: 419-432

DOI

14
ShaoQ M. A comparison theorem on moment inequalities between negatively associated and independent random variables. J Theoret Probab, 2000, 13: 343-356

DOI

15
SinghR S. Applications of estimators of a density and its derivatives to certain statistical problems. J Roy Statist Soc Ser B, 1977, 39: 357-363

16
SinghR S. Non-parametric estimation of derivatives of average of μ-densities with convergence rates and applications. SIAM J Appl Math, 1978, 35: 637-649

DOI

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