Since Quetelet's work in the 19th century social science has iconi fied "the average man", that hypothetical man without qualities who is comfortable with his head in the oven, and his feet in a bucket of ice. Conventional statistical methods, since Quetelet, have sought to estimate the effects...

Models of unobserved heterogeneity, or frailty as it is commonly known in survival analysis, can often be formulated as semiparametric mixture models and estimated by maximum likelihood as proposed by Robbins (1950) and elaborated by Kiefer and Wolfowitz (1956). Recent developments in convex...

Nonparametric maximum likelihood estimation of general mixture models pioneered by the work of Kiefer and Wolfowitz (1956) has been recently reformulated as an exponential family regression spline problem in Efron (2016). Both approaches yield a low dimensional estimate of the mixing...

Statistical models of unobserved heterogeneity are typically formalized as mixtures of simple parametric models and interest naturally focuses on testing for homogeneity versus general mixture alternatives. Many tests of this type can be interpreted as C(») tests, as in Neyman (1959), and shown...

Shape constraints play an increasingly prominent role in nonparametric function estimation. While considerable recent attention has been focused on log concavity as a regularizing device in nonparametric density estimation, weaker forms of concavity constraints encompassing larger classes of...

Single index linear models for binary response with random coefficients have been extensively employed in many econometric settings under various parametric specifications of the distribution of the random coefficients. Nonparametric maximum likelihood estimation (NPMLE) as proposed by Cosslett...

Empirical Bayes methods for Gaussian compound decision problems involving longitudinal data are considered. The new convex optimization formulation of the nonparametric (Kiefer-Wolfowitz) maximum likelihood estimator for mixture models is employed to construct nonparametric Bayes rules for...

Recent developments in the theory of choice under uncertainty and risk yield a pessimistic decision theory that replaces the classical expected utility criterion with a Choquet expectation that accentuates the likelihood of the least favorable outcomes. A parallel theory has recently emerged in...

Statistical models of unobserved heterogeneity are typically formalized as mix- tures of simple parametric models and interest naturally focuses on testing for homogeneity versus general mixture alternatives. Many tests of this type can be interpreted as C(») tests, as in Neyman (1959), and...

Additive models for conditional quantile functions provide an attractive framework for nonparametric regression applications focused on features of the response beyond its central tendency. Total variation roughness penalities can be used to control the smoothness of the additive components much...