Strong consistency of wavelet estimators for errors-in-variables regression model

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• 作者：Huijun Guo ; Youming Liu
• 关键词：Errors ; in ; variables ; Fourier ; oscillating noise ; Regression function ; Strong consistency ; Wavelets
• 刊名：Annals of the Institute of Statistical Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：69
• 期：1
• 页码：121-144
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics, general; Statistics for Business/Economics/Mathematical Finance/Insurance;
• 出版者：Springer Japan
• ISSN：1572-9052
• 卷排序：69

文摘

This paper studies the strong consistency of some estimators for an errors-in-variables regression model. We first provide an extension of Meister’s theorem. Then, the same problem is dealt with under the Fourier-oscillating noises. Finally, we prove two strong consistency theorems for wavelet estimators corresponding to non-oscillating and Fourier-oscillating noises.