We develop an algorithm to overcome the curse of dimensionality in sequential Monte Carlo (SMC) for functional data. In the inner iterations of the algorithm for given parameter values, the conditional SMC is extended to obtain draws of the underlying state vectors. These draws in turn are used in the outer iterations to update the parameter values in the framework of stochastically approximated expectation-maximization to obtain maximum likelihood estimates of the parameters. Standard errors of the parameters are calculated using a stochastic approximation of Louis formula. Three numeric examples are used for illustration. They show that although the computational burden remains high, the algorithm produces reasonable results without exponentially increasing the particle numbers.

中文翻译：

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序列蒙特卡罗吉布斯与函数数据的随机近似期望最大化算法相结合

我们开发了一种算法来克服功能数据的顺序蒙特卡罗 (SMC) 中的维数灾难。在给定参数值的算法内部迭代中，条件 SMC 被扩展以获得底层状态向量的绘制。这些绘图依次用于外部迭代，以更新随机近似期望最大化框架中的参数值，以获得参数的最大似然估计。使用路易斯公式的随机近似计算参数的标准误差。三个数字示例用于说明。他们表明，尽管计算负担仍然很高，但该算法产生了合理的结果，而不会以指数方式增加粒子数。