Designed quadrature to approximate integrals in maximum simulated likelihood estimation
研究了设计求积法（DQ）在混合多项Logit模型最大模拟似然估计中近似多维积分的表现，发现DQ比准蒙特卡洛方法更高效、易实现且权重为正，有望成为新的主流方法。
Summary Maximum simulated likelihood estimation of mixed multinomial logit models requires evaluation of a multidimensional integral. Quasi-Monte Carlo (QMC) methods such as Halton sequences and modified Latin hypercube sampling are workhorse methods for integral approximation. Earlier studies explored the potential of sparse grid quadrature (SGQ), but SGQ suffers from negative weights. As an alternative to QMC and SGQ, we looked into the recently developed designed quadrature (DQ) method. DQ requires fewer nodes to get the same level of accuracy as QMC and SGQ, is as easy to implement, ensures positivity of weights, and can be created on any general polynomial space. We benchmarked DQ against QMC in a Monte Carlo and an empirical study. DQ outperformed QMC in all considered scenarios, is practice ready, and has potential to become the workhorse method for integral approximation.