TY - JOUR

T1 - Nonparametric estimation of a multivariate probability density for mixing sequences by the method of wavelets

AU - Hosseinioun, Narges

AU - Doosti, Hassan

AU - Niroumand, Hossein Ali

PY - 2011/7

Y1 - 2011/7

N2 - The mathematical theory of wavelet and their applications in statistics have become a well-known technique for non-parametric curve estimation: see e.g. Meyer (1990), Daubachies (1992), Chui (1992), Donoho and Johnstone (1995) and Vidakovic (1999). We Consider the problem of estimation of the partial derivatives of a multi- variate probability density f of mixing sequences, using wavelet-based method. Many stochastic processes and time series are known to be mixing. Under certain weak as- sumptions autoregressive and more generally bilinear time series models are strongly mixing with exponential mixing coefficients. The problem of density estimation from dependent samples is often considered. For instance quadratic losses were considered by Ango Nze and Doukhan (1993). Bosq (1995) and Doukhan and Loen (1990). We inves- tigate the variance and the rate of the almost convergence of wavelet-based estimators. Rate of convergence of estimators when f belongs to the Besov space is also established.

AB - The mathematical theory of wavelet and their applications in statistics have become a well-known technique for non-parametric curve estimation: see e.g. Meyer (1990), Daubachies (1992), Chui (1992), Donoho and Johnstone (1995) and Vidakovic (1999). We Consider the problem of estimation of the partial derivatives of a multi- variate probability density f of mixing sequences, using wavelet-based method. Many stochastic processes and time series are known to be mixing. Under certain weak as- sumptions autoregressive and more generally bilinear time series models are strongly mixing with exponential mixing coefficients. The problem of density estimation from dependent samples is often considered. For instance quadratic losses were considered by Ango Nze and Doukhan (1993). Bosq (1995) and Doukhan and Loen (1990). We inves- tigate the variance and the rate of the almost convergence of wavelet-based estimators. Rate of convergence of estimators when f belongs to the Besov space is also established.

KW - Mixing process

KW - Multivariate density

KW - Nonparametric estimation of partial derivatives

KW - Wavelet

UR - http://www.scopus.com/inward/record.url?scp=84863886841&partnerID=8YFLogxK

UR - http://ijpam.uniud.it/journal/onl_2011-28.htm

M3 - Article

AN - SCOPUS:84863886841

SP - 31

EP - 40

JO - Italian Journal of Pure and Applied Mathematics

JF - Italian Journal of Pure and Applied Mathematics

SN - 1126-8042

IS - 28

ER -