常態隨誤差假設下尋根隨機近似過程之模擬比較

A Simulation Comparison for the Root Finding Stochastic Approximation Procedures under Normal Random Error Assumption

費吳琛(Wu-Chen Fei) ； 劉劭愷(Shao-Kai Liu)

《國防管理學報》 14卷2期 (1993/07) Pp. 21-36

https://doi.org/10.29496/JNDM.199307.0003

摘要

Robbins典Monro在1951年首先提出以隨機近似過程來估計遞增型迴歸函數之根。在此之後，Anbar、Wu、Fei均曾提出不同之方法。為了進一步了解常態隨機誤差項之假設對隨機近似過程之影響，本文將對前述四位學者之方法在不同大小之樣本、邊界值、及起始點條件下，進行模擬比較。模擬結果顯示，Wu之方法在大多數之情況下表現較佳。

關鍵字

隨機近似 ； 模擬 ； Robbins-Montro

並列摘要

In 1951, Robbins and Monro introduced a stochastic procedure for finding the root of an increasing regression function. Thereafter, Anbar, Wu, and Fei also proposed different algorithms. For further understanding the effect of the assumption of normal random error, a simulation comparison among the procedures of Robbins-Monro, Anbar, Wu, and Fei is undertaken with different sample sizes, bounded values, and starting points. The result shows that the Wu's procedure performs best in most conditions.

並列關鍵字

Stochastic Approximation ； Simulation ； Robbins-Monro