Data is reanalyzed from an important series of 19th century experiments conducted by C. S. Peirce and designed to study the plausibility of the Gaussian law of errors for astronomical observations. Contrary to the findings of Peirce, but in accordance with subsequent analysis by Fréchet 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...

The classical problem of the monopolist faced with an unknown demand curve is considered in a simple stochastic setting. Sequential pricing strategies designed to maximize discounted profits are shown to converge sufficiently rapidly that they leave the monopolist ignorant about all but the most...

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...

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...

Parametric copulas are shown to be attractive devices for specifying quantile autoregressive models for nonlinear time-series. Estimation of local, quantile-specific copula-based time series models offers some salient advantages over classical global parametric approaches. Consistency and...

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(α) tests, as in Neyman (1959), and shown...

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...