Fusion of Hard and Soft Information in Nonparametric Density Estimation
Royset, Johannes O.
Wets, Roger J-B
MetadataShow full item record
This article discusses univariate density estimation in situations when the sample (hard information) is supplemented by “soft” information about the random phenomenon. These situations arise broadly in operations research and management science where practical and computational reasons severely limit the sample size, but problem structure and past experiences could be brought in. In particular, density estimation is needed for generation of input densities to simulation and stochastic optimization models, in analysis of simulation output, and when instantiating probability models. We adopt a constrained maximum likelihood estimator that incorporates any, possibly random, soft information through an arbitrary collection of constraints. We illustrate the breadth of possibilities by discussing soft information about shape, support, continuity, smoothness, slope, location of modes, symmetry, density values, neighborhood of known density, moments, and distribution functions. The maximization takes place over spaces of extended real-valued semicontinuous functions and therefore allows us to consider essentially any conceivable density as well as convenient exponential transformations. The infinite dimensionality of the optimization problem is overcome by approximating splines tailored to these spaces. To facilitate the treatment of small samples, the construction of these splines is decoupled from the sample. We discuss existence and uniqueness of the estimator, examine consistency under increasing hard and soft information, and give rates of convergence. Numerical examples illustrate the value of soft information, the ability to generate a family of diverse densities, and the effect of misspecification of soft information.
Showing items related by title, author, creator and subject.
Singham, Dashi I.; Royset, Johannes O.; Wets, Roger J.-B. (IEEE, 2013);The density of stochastic simulation output provides more information on system performance than the mean alone. However, density estimation methods may require large sample sizes to achieve a certain accuracy or desired ...
Naval Postgraduate Schoo; Van Horn, Matthew (Monterey, California: Naval Postgraduate School, 2013-11-22);Mechanochromic molecules open new pathways for the study of micro-damage in polymers. Their application stress and temperature diagnostics, however, requires measurement techniques capable of detecting the activated force- ...
Sabol, John J., III (Monterey, California: Naval Postgraduate School, 2016-06);Analysts often concern themselves with the tail regions of distributions, sometimes called extreme events, in order to measure or predict risk. One risk metric, the superquantile, possesses several properties that make it ...