摘要
设平稳信号过程{X_t}被白噪声序列{Y_t}干扰．只有X_t＞Y_t时可以观测到信号过程X_t,否则只能观测到白噪声Y_t．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{X_t}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X_t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．
Let {Xt} be a statiouary 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 dist,ibutions of Xt and Yt to construct estimates of the mean, autocovariance and autocorrelation fnnctions of the original signal process {Xt}. The strong consistency of the estimates is derived. When {Xt} is a causal autoregression process, consistent estimates of the antoregression paramcters are provided.
出处
《应用概率统计》
CSCD
北大核心
2006年第3期237-244,共8页
Chinese Journal of Applied Probability and Statistics
基金
Research supported by National Natural Science Foundation of China(10231030).
关键词
平稳信号
左删失
自相关
自回归
相合性
Stationary signal process, left censoring, autocovariance and
autocorrelation, AR（p） process, consistency.
