应用Fiducial方法推断Logistic模型下的响应刺激量

基于Logistic响应模型,在二元响应数据下,将待估计的响应刺激量变换为模型的一个参数,应用鞍点逼近方法给出了该响应刺激量估计条件分布的高阶近似公式.在此基础上,引入Fiducial模型,并应用Fiducial模型给出了响应刺激量的区间估计,通过蒙特卡罗数值模拟表明,在样本量较小时,给合Fiducial模型,应用鞍点逼近方法,能够较好地估计响应刺激量.

Fiducial Method for Inference about Response Probabilities under the Logistic Response Model

This paper studies the lower confidence limits or confidence interval of interested parameter based on binary response data under the logistic response model.The saddlepoint approximations to the distribution of the estimator for an interested parameter and then the lower confidence limits or confidence limits or confidence interval of intersted parameter are derived.On this base,the Fiducial model is given,and using the Fuducial model the inference about response probalilities is given.Numerical results show that the saddlepoint approximations which conbine Fuducial model are much more accurate than the saddlepoint approximations and asymptotic normality,especially for the cases of small sample sizes.