Penalized spline estimation for varying-coefficient models. (English) Zbl 1143.62023
Summary: Varying-coefficient models are useful extensions of classical linear models. They arise from multivariate nonparametric regression, nonlinear time series modeling and forecasting, longitudinal data analysis, and others. This article proposes the penalized spline estimation for the varying-coefficient models. Assuming a fixed but potentially large number of knots, the penalized spline estimators are shown to be strongly consistent and asymptotically normal. A systematic optimization algorithm for the selection of multiple smoothing parameters is developed. One of the advantages of the penalized spline estimation is that it can accommodate varying degrees of smoothness among coefficient functions due to multiple smoothing parameters being used. Some simulation studies are presented to illustrate the proposed methods.
MSC:
62G08 | Nonparametric regression and quantile regression |
65C60 | Computational problems in statistics (MSC2010) |
62G20 | Asymptotic properties of nonparametric inference |
62G05 | Nonparametric estimation |
Keywords:
generalized cross validation (GCV); penalized spline; smoothing parameter estimation; varying-coefficient modelsReferences:
[1] | DOI: 10.2307/2669476 · Zbl 0996.62078 · doi:10.2307/2669476 |
[2] | DOI: 10.2307/2669472 · Zbl 0999.62052 · doi:10.2307/2669472 |
[3] | DOI: 10.2307/2290725 · Zbl 0776.62066 · doi:10.2307/2290725 |
[4] | DOI: 10.1198/016214501753168280 · Zbl 1018.62034 · doi:10.1198/016214501753168280 |
[5] | DOI: 10.1214/ss/1038425655 · Zbl 0955.62562 · doi:10.1214/ss/1038425655 |
[6] | DOI: 10.1214/aos/1017939139 · Zbl 0977.62039 · doi:10.1214/aos/1017939139 |
[7] | DOI: 10.3150/bj/1137421639 · Zbl 1098.62077 · doi:10.3150/bj/1137421639 |
[8] | DOI: 10.1137/0912021 · Zbl 0727.65009 · doi:10.1137/0912021 |
[9] | DOI: 10.1093/biomet/68.1.189 · Zbl 0462.62070 · doi:10.1093/biomet/68.1.189 |
[10] | Hastie T., J. Roy. Statist. Soc. Ser. B. 55 pp 757– (1993) |
[11] | DOI: 10.1093/biomet/85.4.809 · Zbl 0921.62045 · doi:10.1093/biomet/85.4.809 |
[12] | DOI: 10.1093/biomet/89.1.111 · Zbl 0998.62024 · doi:10.1093/biomet/89.1.111 |
[13] | DOI: 10.1081/STA-120029828 · Zbl 1114.62318 · doi:10.1081/STA-120029828 |
[14] | Parker R. L., J. Roy. Statist. Soc. B 47 pp 40– (1985) |
[15] | DOI: 10.1198/106186002853 · doi:10.1198/106186002853 |
[16] | Wahba G., Approximation Theory III pp 905– (1980) |
[17] | DOI: 10.1111/1467-9868.00240 · doi:10.1111/1467-9868.00240 |
[18] | DOI: 10.1198/016214504000000980 · Zbl 1117.62445 · doi:10.1198/016214504000000980 |
[19] | DOI: 10.2307/2670054 · Zbl 1064.62523 · doi:10.2307/2670054 |
[20] | DOI: 10.1198/016214502388618861 · Zbl 1045.62035 · doi:10.1198/016214502388618861 |
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.