论文标题
用于估计依赖观测的混合分布的随机近似算法
Stochastic Approximation Algorithm for Estimating Mixing Distribution for Dependent Observations
论文作者
论文摘要
在统计文献中，估计混合物分布的混合密度仍然是一个有趣的问题。 Newton和Zhang（1999）使用随机近似方法，引入了一种快速递归算法，用于估计混合物的混合密度。在适当选择的权重下，随机近似估计值会收敛到真实溶液。在Tokdar等。 al。 （2009）建立了这种递归估计方法的一致性。但是，所得估计量的一致性证明在观测中使用独立性作为假设。在这里，我们将牛顿算法的性能的调查扩展到了几种相关场景。我们证明，即使观察结果是由弱依赖的固定过程与目标混合物作为边缘密度的弱依赖的固定过程，在某些条件下的原始算法仍然保持一致。当依赖性的特征是观测值类似的数量时，我们在观测值之间对观测值的依赖性显示一致性。
Estimating the mixing density of a mixture distribution remains an interesting problem in statistics literature. Using a stochastic approximation method, Newton and Zhang (1999) introduced a fast recursive algorithm for estimating the mixing density of a mixture. Under suitably chosen weights the stochastic approximation estimator converges to the true solution. In Tokdar et. al. (2009) the consistency of this recursive estimation method was established. However, the proof of consistency of the resulting estimator used independence among observations as an assumption. Here, we extend the investigation of performance of Newton's algorithm to several dependent scenarios. We prove that the original algorithm under certain conditions remains consistent even when the observations are arising from a weakly dependent stationary process with the target mixture as the marginal density. We show consistency under a decay condition on the dependence among observations when the dependence is characterized by a quantity similar to mutual information between the observations.
