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| 摘要: |
| 本文在α混合样本下研究Gasser和Müller提出的一类积分权非参数核回归估计的大样本性质.利用α混合序列的概率指数不等式和矩不等式，在较弱的条件下获得了积分权回归函数估计的强相合性与一致强相合性，推广了独立样本下该回归函数估计的相合性结果. |
| 关键词: α混合样本 积分权回归估计 强相合性 一致强相合性 |
| DOI： |
| 分类号:O212.7;O211.4 |
| 基金项目:海南省自然科学基金资助 (117173); 国家自然科学基金资助 (11461009). |
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| STRONG CONSISTENCY OF INTERGRAL WEIGHT REGRESSION ESTIMATOR FOR α-MIXING SAMPLES |
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YANG Xiu-tao,YANG Shan-chao
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| Abstract: |
| This paper is to study the large sample properties of a class of integral weight nonparametric kernel regression estimators proposed by Gasser and Müller under α mixing samples. By using the probability exponential inequality and the moment inequality of α mixing sequences, the strong consistency and uniform strong consistency of the integral weight regression function estimator are obtained under weaker conditions, which extend the relevant conclusions of the regression function estimator under independent samples. |
| Key words: α-mixing samples integral weight regression estimator strong consistency uniformly strong consistency |
