We consider the one-armed bandit problem of Woodroofe [J. Amer. Statist. Assoc. 74 (1979) 799-806], which involves sequential sampling from two populations: one whose characteristics are known, and one which depends on an unknown parameter and incorporates a covariate. The goal is to maximize...

The problem of optimal prediction in the stochastic linear regression model with infinitely many parameters is considered. We suggest a prediction method that outperforms asymptotically the ordinary least squares predictor. Moreover, if the random errors are Gaussian, the method is...

We consider deconvolving bivariate irregular densities supported on the circumference of the unit circle. The errors are bivariate, and the observations are available on the plane. Assuming that the estimated density is smooth on the circle, we compute exact asymptotics of the minimax risks and...