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

Junlian XU

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PDF(162 KB)
Front. Math. China ›› 2014, Vol. 9 ›› Issue (3) : 623-640. DOI: 10.1007/s11464-014-0353-y
RESEARCH ARTICLE
RESEARCH ARTICLE

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

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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.

Keywords

Wavelet estimator / density derivative / weight function / negatively associated / Besov space

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Junlian XU. Wavelet linear estimations of density derivatives from a negatively associated stratified size-biased sample. Front. Math. China, 2014, 9(3): 623‒640 https://doi.org/10.1007/s11464-014-0353-y

References

[1]
AlamK, SaxenaK M L. Positive dependence in multivariate distribution. Comm Statist-Theory Methods A, 1981, 10: 1183-1196
CrossRef Google scholar
[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
CrossRef Google scholar
[3]
ChesneauC. Wavelet block thresholding for density estimation in the presence of bias. J Korean Statist Soc, 2010, 39: 43-53
CrossRef Google scholar
[4]
ChesneauC, DewanI, DoostiH. Wavelet linear density estimation for associated stratified size-biased sample. J Nonparametr Stat, 2012, 2: 429-445
CrossRef Google scholar
[5]
DaubechiesI. Ten Lectures on Wavelets. Philadelphia: SIAM, 1992
CrossRef Google scholar
[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
CrossRef Google scholar
[8]
Joag-DevK, ProschanF. Negative association of random variables with application. Ann Statist, 1983, 11: 286-295
CrossRef Google scholar
[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
CrossRef Google scholar
[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
CrossRef Google scholar
[14]
ShaoQ M. A comparison theorem on moment inequalities between negatively associated and independent random variables. J Theoret Probab, 2000, 13: 343-356
CrossRef Google scholar
[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
CrossRef Google scholar

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