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学者姓名：钟晨
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Abstract ：
A kernel distribution estimator (KDE) is proposed for the error distribution in the functional data, which is computed from the residuals of the B-spline trajectories over all the measurements. The maximal stochastic process between the KDE and the error distribution is shown to converge to a Gaussian process with mean zero and specified covariance function under some mild conditions. Thus, a simultaneous confidence band (SCB) is constructed for the error distribution based on the KDE in the dense functional data. The proposed SCB is applicable in not only the independent functional data but also the functional time series. In addition, the symmetric test is proposed for the error distribution, as well as a goodness-of-fit test for mean function by using the bootstrap method. Simulation studies examine the finite sample performance of the SCB and show the bootstrap method performs well in numerical studies. The proposed theory is illustrated by the electroencephalogram (EEG) functional data.
Keyword ：
Bootstrap Bootstrap B-spline B-spline Goodness-of-fit test Goodness-of-fit test Kernel distribution estimator Kernel distribution estimator Simultaneous confidence band Simultaneous confidence band
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| GB/T 7714 | Zhong, Chen . Statistical inference and goodness-of-fit test in functional data via error distribution function [J]. | STATISTICS AND COMPUTING , 2025 , 35 (2) . |
| MLA | Zhong, Chen . "Statistical inference and goodness-of-fit test in functional data via error distribution function" . | STATISTICS AND COMPUTING 35 . 2 (2025) . |
| APA | Zhong, Chen . Statistical inference and goodness-of-fit test in functional data via error distribution function . | STATISTICS AND COMPUTING , 2025 , 35 (2) . |
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Abstract ：
The analysis of nonlinearity in spatial and spatial-temporal data continues to be a challenging topic. This article introduces a two-step estimation procedure for modeling nonstationary spatial processes that comprise a smooth bivariate trend function and a spatial autoregressive and moving average (SRAMA) error term. To remove the bivariate trend from the observed process, we apply the cutting-edge bivariate penalized spline method. The modified maximum likelihood estimator based on the residuals, as suggested by Yao and Brockwell (2006), is shown to be consistent and oracle efficient, achieving the same efficiency asymptotically as if the true trend function were known and removed to obtain the SARMA errors. Furthermore, we establish the consistency of Bayesian information criteria for model selection concerning the residual sequence. The finite sample performance of the proposed approach is evaluated with simulations and real data.
Keyword ：
asymptotic results asymptotic results bivariate spline estimator bivariate spline estimator modified maximum likelihood estimator modified maximum likelihood estimator oracle efficiency oracle efficiency spatial ARMA spatial ARMA
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| GB/T 7714 | Zhang, Tong , Zhang, Yuanyuan , Zhong, Chen . Oracally Efficient Estimation and Consistent Model Selection for Spatial ARMA Process With Bivariate Trend [J]. | JOURNAL OF TIME SERIES ANALYSIS , 2025 . |
| MLA | Zhang, Tong 等. "Oracally Efficient Estimation and Consistent Model Selection for Spatial ARMA Process With Bivariate Trend" . | JOURNAL OF TIME SERIES ANALYSIS (2025) . |
| APA | Zhang, Tong , Zhang, Yuanyuan , Zhong, Chen . Oracally Efficient Estimation and Consistent Model Selection for Spatial ARMA Process With Bivariate Trend . | JOURNAL OF TIME SERIES ANALYSIS , 2025 . |
| Export to | NoteExpress RIS BibTex |
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