一类乘法删失模型小波估计器的相合性
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摘要
在实际应用中,假定密度函数的光滑性并不合理,原因在于密度函数的光滑性往往是未知的.针对乘法删失混合模型的密度估计问题,在不假定密度函数光滑性的前提下研究线性小波估计器平均相合性.这一结果可以看作是对Chaubey、Chesneau与Doosti(2015)工作的补充.
It is not reasonable to assume the smoothness in practical applications,because the smoothness index of density function is unknown. A mixture model under multiplicative censoring was established in this paper. The mean consistency of linear wavelet estimator was investegated without the assumption of smoothness. The research can be seen as an extension of Chaubey,Chesneau and Doosti 's( 2015)work.
It is not reasonable to assume the smoothness in practical applications,because the smoothness index of density function is unknown. A mixture model under multiplicative censoring was established in this paper. The mean consistency of linear wavelet estimator was investegated without the assumption of smoothness. The research can be seen as an extension of Chaubey,Chesneau and Doosti 's( 2015)work.
引文
[1]CHAUBEY Y P,CHESNEAU C,DOOSTI H.Adaptive wavelet estimation of a density from mixtures under multiplicative censoring[J].Statistics,2015,49(3):638-659.
[2]LI R,LIU Y M.Wavelet optimal estimations for a density with some additive noises[J].Applied and Computational Harmonic Analysis,2014,36(3):416-433.
[3]ZENG X C.A note on wavelet deconvolution density estimation[J].International Journal of Wavelets,Multiresolution and Information Processing,2017,15(6):1750055.
[4]ABBASZADEH M,CHESNEAU C,DOOSTI H.Nonparametric estimation of a density under bias and multiplicative censoring via wavelet methods[J].Statistics and Probability Letters,2012,82(5):932-941.
[5]POKHYLKO D.Wavelet estimators of a density constructed from observations of a mixture[J].Theory of Probability and Mathematical Statistics,2005,70:135-145.
[6]PRAKASA RAO B L S.Wavelet linear estimation for derivatives of a density from observations of mixtures with varying mixing proportions[J].International Journal of Pure and Applied Mathematics,2010,41(1):275-291.
[7]CHAUBEY Y P,DOOSTI H,PRAKASEA RAO B L S.Wavelet based estimation of the derivatives of a density with associated variables[J].International Journal of Pure and Applied Mathematics,2006,27(1):97-106.
[8]HARDLE W,KERKYACHARIAN G,PICARD D.Wavelets approximation and statistical application[M].New York:Springer-Verlag,1998:2-96.
[9]MEYER Y.Wavelets and operators[M].Cambridge:Cambridge University Press,1992:1-120.
[10]DAUBECHIES I.Ten lecture on wavelets[M].Philadelphia:SIAM,1992:120-210.
[2]LI R,LIU Y M.Wavelet optimal estimations for a density with some additive noises[J].Applied and Computational Harmonic Analysis,2014,36(3):416-433.
[3]ZENG X C.A note on wavelet deconvolution density estimation[J].International Journal of Wavelets,Multiresolution and Information Processing,2017,15(6):1750055.
[4]ABBASZADEH M,CHESNEAU C,DOOSTI H.Nonparametric estimation of a density under bias and multiplicative censoring via wavelet methods[J].Statistics and Probability Letters,2012,82(5):932-941.
[5]POKHYLKO D.Wavelet estimators of a density constructed from observations of a mixture[J].Theory of Probability and Mathematical Statistics,2005,70:135-145.
[6]PRAKASA RAO B L S.Wavelet linear estimation for derivatives of a density from observations of mixtures with varying mixing proportions[J].International Journal of Pure and Applied Mathematics,2010,41(1):275-291.
[7]CHAUBEY Y P,DOOSTI H,PRAKASEA RAO B L S.Wavelet based estimation of the derivatives of a density with associated variables[J].International Journal of Pure and Applied Mathematics,2006,27(1):97-106.
[8]HARDLE W,KERKYACHARIAN G,PICARD D.Wavelets approximation and statistical application[M].New York:Springer-Verlag,1998:2-96.
[9]MEYER Y.Wavelets and operators[M].Cambridge:Cambridge University Press,1992:1-120.
[10]DAUBECHIES I.Ten lecture on wavelets[M].Philadelphia:SIAM,1992:120-210.