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Optimal asymptotic quadratic error of nonparametric regression function estimates for a continuous-time process from sampled-data

 

作者: Denis Bosq,   Nathalie Cheze-payaud,  

 

期刊: Statistics  （Taylor Available online 1999）
卷期: Volume 32, issue 3  

页码: 229-247

 

ISSN:0233-1888

 

年代: 1999

 

DOI:10.1080/02331889908802665

 

出版商: Taylor & Francis Group

 

关键词: 62G05;62G07;62J02;62M09;62M10;Nonparametric regression estimation;sampled data;mixing continuous-parameter processes;quadratic-mean convergence;choice of bandwidth

 

数据来源: Taylor

 

摘要:

For different classes of deterministic and random sampling (tk), we establish the asymptotic expressions for the bias and the variance of the estimatern(x) based on sampled datafor the regression functionr(x) =E(YtXt=x) of unbounded continuous-time processes(not necessarily stationary). Under mild mixing conditions, we show thatrn(x) has exactly the same asymptotic quadratic error as in the i.i.d. case. In order to prove this result, we use some large deviations inequalities for mixing processes.

 

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