应用概率统计
應用概率統計
응용개솔통계
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS
2006年
3期
237-244
,共8页
平稳信号%左删失%自相关%自回归%相合性
平穩信號%左刪失%自相關%自迴歸%相閤性
평은신호%좌산실%자상관%자회귀%상합성
Stationary signal process%left censoring%autocovariance and autocorrelation%AR(p) process%consistency
设平稳信号过程{Xt}被白噪声序列{Yt}干扰.只有Xt＞Yt时可以观测到信号过程Xt,否则只能观测到白噪声Yt.这种数据模型被称为左截断数据模型.本文在左截断数据模型下估计平稳信号过程的{Xt}均值,自协方差函数,和自相关系数.证明所给的估计量是强相合估计.当Xt是自回归序列时,本文给出自回归模型的强相合的参数估计.
設平穩信號過程{Xt}被白譟聲序列{Yt}榦擾.隻有Xt＞Yt時可以觀測到信號過程Xt,否則隻能觀測到白譟聲Yt.這種數據模型被稱為左截斷數據模型.本文在左截斷數據模型下估計平穩信號過程的{Xt}均值,自協方差函數,和自相關繫數.證明所給的估計量是彊相閤估計.噹Xt是自迴歸序列時,本文給齣自迴歸模型的彊相閤的參數估計.
설평은신호과정{Xt}피백조성서렬{Yt}간우.지유Xt＞Yt시가이관측도신호과정Xt,부칙지능관측도백조성Yt.저충수거모형피칭위좌절단수거모형.본문재좌절단수거모형하고계평은신호과정적{Xt}균치,자협방차함수,화자상관계수.증명소급적고계량시강상합고계.당Xt시자회귀서렬시,본문급출자회귀모형적강상합적삼수고계.
Let {Xt} be a stationary signal process interfered by an white noise {Yt}. The signal Xt is detected and observed only when Xt ＞ Yt, otherwise only the white noise Yt is observed. This model is called the left censored model and the observation is called the left censored observation. In this paper we use the nonparametric MLE of the marginal distributions of Xt and Yt to construct estimates of the mean, autocovariance and autocorrelation functions of the original signal process {Xt}. The strong consistency of the estimates is derived. When {Xt} is a caausal autoregression process, consistent estimates of the autoregression parameters are provided.
