系统工程理论与实践
繫統工程理論與實踐
계통공정이론여실천
Systems Engineering—Theory & Practice
2014年
10期
2650~2655
,共null页
均值变点 监测 非参数回归模型 小波变换 Bootstrap
均值變點 鑑測 非參數迴歸模型 小波變換 Bootstrap
균치변점 감측 비삼수회귀모형 소파변환 Bootstrap
change point in mean; monitoring; nonparametric regression model; wavelet transformation Bootstrap
本文首次考虑非参数回归模型均值函数结构变点的在线监测问题．首先对回归函数的局部线性估计值进行小波变换，基于得到的小波系数构造监测统计量，并在原假设和备择假设下推导出监测统计量的渐近分布；为提高监测效果，进一步构造了Bootstrap在线监测方法，定义了停时；模拟结果和实例分析显示该方法可以很好地监测到变点，并具有较短的检测延迟．
本文首次攷慮非參數迴歸模型均值函數結構變點的在線鑑測問題．首先對迴歸函數的跼部線性估計值進行小波變換，基于得到的小波繫數構造鑑測統計量，併在原假設和備擇假設下推導齣鑑測統計量的漸近分佈；為提高鑑測效果，進一步構造瞭Bootstrap在線鑑測方法，定義瞭停時；模擬結果和實例分析顯示該方法可以很好地鑑測到變點，併具有較短的檢測延遲．
본문수차고필비삼수회귀모형균치함수결구변점적재선감측문제．수선대회귀함수적국부선성고계치진행소파변환，기우득도적소파계수구조감측통계량，병재원가설화비택가설하추도출감측통계량적점근분포；위제고감측효과，진일보구조료Bootstrap재선감측방법，정의료정시；모의결과화실례분석현시해방법가이흔호지감측도변점，병구유교단적검측연지．
This paper, for the first time, considered the monitoring for mean change of nonparametric regression models. Firstly, the local linear estimator of regression function is given and a new statistic is constructed based on wavelet coefficients of the estimator, and its limiting distributions under null hypothesis and alternative hypothesis are obtained. A Bootstrap monitoring procedure is proposed and the stopping time is defined. Simulations and the results of real data analysis indicates that our procedure have good power and short detection delay in the monitoring of structural change of nonparametric regression models.
