×

Wavelets for nonparametric stochastic regression with mixing stochastic process. (English) Zbl 1318.62130

Summary: We propose a wavelet based stochastic regression function estimator for the estimation of the regression function for a sequence of mixing stochastic process with a common one-dimensional probability density function. Some asymptotic properties of the proposed estimator are investigated. It is found that the estimators have similar properties to their counterparts studied earlier in literature.

MSC:

62G08 Nonparametric regression and quantile regression
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
62G20 Asymptotic properties of nonparametric inference
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1017/CBO9780511543395 · doi:10.1017/CBO9780511543395
[2] Antoniadis A., Statistica Sinica 4 pp 651– (1994)
[3] Antoniadis , A. , Pham , D. T. ( 1995 ). Wavelet regression for random or irregular design. Technical Report RT 148, IMAG-LMC , University of Grenoble , France . · Zbl 1042.62534
[4] DOI: 10.1016/S0167-9473(98)90145-1 · Zbl 1042.62534 · doi:10.1016/S0167-9473(98)90145-1
[5] DOI: 10.1198/016214501753208942 · Zbl 1072.62561 · doi:10.1198/016214501753208942
[6] DOI: 10.2307/2290996 · Zbl 0815.62018 · doi:10.2307/2290996
[7] DOI: 10.1016/S0167-7152(97)00017-5 · Zbl 0889.62029 · doi:10.1016/S0167-7152(97)00017-5
[8] Daubechies , I. ( 1992 ).Ten Lectures on Wavelets. CBMS-NSF regional conferences series in applied mathematics . Philadelphia : SIAM .
[9] Delouille V., Sankhya, Ser. A 63 pp 328– (2001)
[10] DOI: 10.1198/016214504000000971 · Zbl 1117.62315 · doi:10.1198/016214504000000971
[11] DOI: 10.1006/jath.1996.3008 · Zbl 0862.42023 · doi:10.1006/jath.1996.3008
[12] Donoho D. L., J. Roy. Statist. Soc. Ser. B 57 pp 301– (1995)
[13] Donoho D. L., Ann. Statist. 2 pp 508– (1996)
[14] Doosti H., J. Indian Stat. Assoc. 44 pp 127– (2005)
[15] Doukhan P., C.R. Acad. Sci. Pairs 310 pp 425– (1990)
[16] Eubank R. L., Spline Smoothing and Nonparametric Regression (1988) · Zbl 0702.62036
[17] Härdle W., Wavelets: Approximation and Statistical Applications. (1998) · Zbl 0899.62002
[18] Huang S. Y., Statistica Sinica 9 pp 137– (1999)
[19] DOI: 10.1016/0167-7152(92)90231-S · Zbl 0749.62026 · doi:10.1016/0167-7152(92)90231-S
[20] DOI: 10.2307/2669536 · doi:10.2307/2669536
[21] DOI: 10.1016/0167-7152(95)00046-1 · Zbl 0845.62033 · doi:10.1016/0167-7152(95)00046-1
[22] Meyer Y., Ondelettes et Operateurs (1990)
[23] Müller H. G., Nonparametric Regression Analysis of Longitudinal Data 46 (1988) · Zbl 0664.62031
[24] DOI: 10.1023/A:1014640632666 · Zbl 1003.62037 · doi:10.1023/A:1014640632666
[25] Rosenblatt M., Stochastic Curve Estimation (1991) · Zbl 1163.62318
[26] DOI: 10.1023/A:1008818328241 · doi:10.1023/A:1008818328241
[27] DOI: 10.1007/978-3-0346-0419-2 · Zbl 1235.46003 · doi:10.1007/978-3-0346-0419-2
[28] DOI: 10.1111/j.1467-9574.1995.tb01454.x · Zbl 0830.62055 · doi:10.1111/j.1467-9574.1995.tb01454.x
[29] DOI: 10.1002/9780470317020 · doi:10.1002/9780470317020
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.