Estimating functions in indirect inference
Estimating functions in indirect inference
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DOI：
10.1111/j.1369-7412.2003.05341.x
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发表时间：
2004-01-01
影响因子：
5.8
通讯作者：
Frigessi, A
中科院分区：
文献类型：
--
作者：
Heggland, K;Frigessi, A
有些模型的可能性评估在实践中是不可行的。对于这些模型，无法轻松计算 Metropolis-Hastings 接受概率。例如，当仅观察 G/G/1 队列的出发时间并且需要推断到达和服务分布时，就是这种情况。间接推断是一种估计模型中参数 θ 的方法，其似然函数不具有解析封闭形式，但可以从中抽取随机样本以获得固定的 θ 值。首先选择一个可以直接估计参数theta的辅助模型。接下来，根据原始数据估计辅助模型中的参数，从而得出估计值（β）上限。参数 beta 也是通过使用几个采样数据集来估计的，这些数据集是根据原始模型针对原始参数 beta 的不同值进行模拟的。最后，选择导致最佳匹配的参数β作为间接推断估计。我们分析辅助模型应该具有哪些属性才能给出令人满意的间接推理。我们研究这样的情况：数据被汇总在向量统计量 T 中，并且选择辅助模型，以便仅从 T 得出对 beta 的推论。在适当的假设下，间接估计器的渐近协方差矩阵与 T 的渐近协方差矩阵成正比，并且与 T 的期望值相对于 theta 的导数的平方成反比。我们讨论如何使用这些结果来选择良好的估计函数。我们将我们的发现应用于排队问题。
There are models for which the evaluation of the likelihood is infeasible in practice. For these models the Metropolis-Hastings acceptance probability cannot be easily computed. This is the case, for instance, when only departure times from a G/G/1 queue are observed and inference on the arrival and service distributions are required. Indirect inference is a method to estimate a parameter theta in models whose likelihood function does not have an analytical closed form, but from which random samples can be drawn for fixed values of theta. First an auxiliary model is chosen whose parameter theta can be directly estimated. Next, the parameters in the auxiliary model are estimated for the original data, leading to an estimate (beta) over cap. The parameter beta is also estimated by using several sampled data sets, simulated from the original model for different values of the original parameter beta. Finally, the parameter beta which leads to the best match to is chosen as the indirect inference estimate. We analyse which properties an auxiliary model should have to give satisfactory indirect inference. We look at the situation where the data are summarized in a vector statistic T, and the auxiliary model is chosen so that inference on beta is drawn from T only. Under appropriate assumptions the asymptotic covariance matrix of the indirect estimators is proportional to the asymptotic covariance matrix of T and componentwise inversely proportional to the square of the derivative, with respect to theta, of the expected value of T. We discuss how these results can be used in selecting good estimating functions. We apply our findings to the queuing problem.