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題 名 | Nonparametric Estimation of Ratios of Noise to Signal in Stochastic Regression |
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作 者 | Yao,Qiwei; Tong,Howell; | 書刊名 | Statistica Sinica |
卷 期 | 10:3 2000.07[民89.07] |
頁 次 | 頁751-770 |
分類號 | 319 |
關鍵詞 | Absolutely regular; Asymptotic normality; Local polynomial regression; Noise to signal ratio; |
語 文 | 英文(English) |
英文摘要 | In this paper, we study three different types of estimates for the noise-to-signal ratios in a general stochastic regression setup. The locally linear and locally quadratic regression estimators serve as the building blocks in our approach. Under the assumption that the observations are strictly stationary and absolutely regular, we establish the asymptotic normality of the estimates, which indicates that the residual-based estimates are to be preferred. Further, the locally quadratic regression reduces the bias when compared with the locally linear (or locally constant) regression without the concomitant increase in the asymptotic variance, if the same bandwidth is used. The asymptotic theory also paves the way for a fully data-driven undersmoothing scheme to reduce the biases in estimation. Numerical examples with both simulated and real data sets are used as illustration. |
本系統中英文摘要資訊取自各篇刊載內容。