Duane模型的导数最小二乘估计

 针对传统最小二乘估计仅仅考虑回归模型曲线本身的试验样本，不能同时对曲线动态变化规律进行描述、未能充分利用模型与数据信息的问题，依据在一次观测中待定参数的取值应使得随机样本与模型各阶导函数在概率尺度下具有最小距离的原理，通过构造模型曲线导数意义下的损失函数，提出了一种能够综合利用模型与试验数据导数信息的导数最小乘方估计方法，推广了传统最小二乘估计的模型条件与使用范围。并结合复杂可修产品可靠性增长的Duane模型给出了参数的一般导数最小二乘估计与最佳导数最小二乘估计式，证明了模型参数的导数最小二乘估计较传统最小二乘估计具有更好的统计性质。为实际中确定模型曲线，进行工程预测提供了一条新的技术途径。

Method of Derivative Least Square Estimation for Duane Model

The least square estimation(LSE) has been widely used in both natural science and social science,which is a standard approach to parameter estimation and inference in statistics.Furthermore,many of the inference methods in statistics are developed based on LSE.But the traditional LSE can only make use of the information of model itself,and is helpless with the dynamic change of the curve.The formulas estimated by the least square method can only be used within the test section,and predicting outside the test section will usually cause a great error.In this article,based on the principle of minimizing the distance between random sample and curve's derivative function in scale of probability,the conception of derivative least square estimation(DLSE) is established,which can extend the condition and scope of the traditional one.Besides this,the ordinary and the optimal DLSE are given in detail combined with the reliability growth Duane model for complex repairable system.The statistical properties indicate that the parameter's DLSE has uniformly smaller variance than the traditional estimators.Finally,an example of contrastive analysis is given,which can illustrate the performance of the presented method in both estimation and prediction.