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We consider the problem of nonparametric estimation of a convex regression function φ 0. We study the risk of the least squares estimator (LSE) under the natural squared error loss. We show that the risk is always bounded from above by n −4/5 (up to logarithmic factors) while being much smaller when φ 0 is well-approximable by a piecewise affine convex(More)
—In this paper, we study the covering numbers of the space of convex and uniformly bounded functions in multidimen-sion. We find optimal upper and lower bounds for the-covering number of , in the-metric, , in terms of the relevant constants, where , , , and denotes the set of all convex functions on that are uniformly bounded by. We summarize previously(More)
We present stellar velocity dispersion profiles for seven Milky Way dwarf spheroidal (dSph) satellite galaxies. We have measured 8394 line-of-sight velocities (±2.5 km s −1) for 6804 stars from high-resolution spectra obtained at the Magellan and MMT telescopes. We combine these new data with previously published velocities to obtain the largest available(More)
In this paper we investigate the (in)-consistency of different boot-strap methods for constructing confidence bands in the class of esti-mators that converge at rate cube-root n. The Grenander estimator (see Grenander (1956)), the nonparametric maximum likelihood esti-mator of an unknown non-increasing density function f on [0, ∞), is a prototypical(More)
SUMMARY We introduce a method based on a pseudolikelihood ratio for estimating the distribution function of the survival time in a mixed–case interval censoring model. In a mixed case model, an individual is observed a random number of times, and at each time it is recorded whether an event has happened or not. One seeks to estimate the distribution of time(More)
In this paper we consider the problem of constructing confidence intervals in the presence of nuisance parameters. We discuss a generalization of the unified method of Feldman and Cousins (1998) with nuisance parameters. We demonstrate our method with several examples that arise frequently in High Energy Physics and Astronomy. We also discuss the hybrid(More)
This paper develops a point impact linear regression model in which the trajectory of a continuous stochastic process, when evaluated at a "sensitive time point", is associated with a scalar response. The proposed model complements and is more interpretable than the functional linear regression approach that has become popular in recent years. The(More)
We develop an algorithm for estimating parameters of a distribution sampled with contamination. We employ a statistical technique known as " expectation maximization " (EM). Given models for both member and contaminant populations, the EM algorithm iteratively evaluates the membership probability of each discrete data point, then uses those probabilities to(More)
We consider a two-component mixture model with one known component. We develop methods for estimating the mixing proportion and the other unknown distribution given i.i.d. data from the mixture model. We use ideas from shape restricted function estimation and develop " tuning parameter free " estimators that are easily implementable and have good finite(More)