Abstract:
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Fitting high-dimensional dependent data models is a challenging endeavor and typically requires some form of dimension reduction or stylized estimation algorithm. Particle swarm optimization (PSO) refers to a class of heuristic optimization algorithms that exploit analogies with animal flocking behavior in order obtain optima without strong conditions on the objective function. Bare bones PSO (BBPSO) is a particularly simple PSO algorithm that depends only the particle's personal best location, the particle's group best location, and Gaussian noise where "best'" is defined in terms of the objective function. We introduce a class of PSO algorithms based on BBPSO, termed adaptively tuned BBPSO (AT-BBPSO), by adding a scale parameter to the algorithm and which we dynamically tune using an analogy with random walk Metropolis. Our proposed algorithm is embedded within a Metropolis Hastings algorithm to provide an efficient proposal distribution and thus improves mixing and convergence. In order to illustrate this optimization method and compare it to alternatives, we provide a simulation study and apply it to a high-dimensional spatial problem arising from official statistics.
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