Bodhisattva Sen

Velocity dispersion profiles of seven dwarf spheroidal galaxies

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 kinematic samples, which include more than 5500 dSph members. All the measured dSphs have stellar velocity dispersion of order 10 km s-1 that remains approximately constant with distance from the dSph center, out to and in some cases beyond the radius at which the mean surface brightness falls to the background level. Assuming dSphs reside within dark matter halos characterized by the NFW density profile, we obtain reasonable fits to the empirical velocity dispersion profiles. These fits imply that, among the seven dSphs, Mvir ~ 108-109 M☉. The mass enclosed at a radius of 600 pc, the region common to all data sets, lies in the range (2-7) × 107 M☉.

CLEAN KINEMATIC SAMPLES IN DWARF SPHEROIDALS: AN ALGORITHM FOR EVALUATING MEMBERSHIP AND ESTIMATING DISTRIBUTION PARAMETERS WHEN CONTAMINATION IS PRESENT

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 update parameter estimates for member and contaminant distributions. The EM approach has wide applicability to the analysis of astronomical data. Here we tailor an EM algorithm to operate on spectroscopic samples obtained with the Michigan-MIKE Fiber System (MMFS) as part of our Magellan survey of stellar radial velocities in nearby dwarf spheroidal (dSph) galaxies. These samples, to be presented in a companion paper, contain discrete measurements of line-of-sight velocity, projected position, and pseudo-equivalent width of the Mg-triplet feature, for ~1000-2500 stars per dSph, including some fraction of contamination by foreground Milky Way stars. The EM algorithm uses all of the available data to quantify dSph and contaminant distributions. For distributions (e.g., velocity and Mg-index of dSph stars) assumed to be Gaussian, the EM algorithm returns maximum-likelihood estimates of the mean and variance, as well as the probability that each star is a dSph member. These probabilities can serve as weights in subsequent analyses. Applied to our MMFS data, the EM algorithm identifies more than 5000 stars as probable dSph members. We test the performance of the EM algorithm on simulated data sets that represent a range of sample size, level of contamination, and amount of overlap between dSph and contaminant velocity distributions. The simulations establish that for samples ranging from large (N ~ 3000, characteristic of the MMFS samples) to small (N ~ 30), resembling new samples for extremely faint dSphs), the EM algorithm distinguishes members from contaminants and returns accurate parameter estimates much more reliably than conventional methods of contaminant removal (e.g., sigma clipping).

Nonparametric least squares estimation of a multivariate convex regression function

This paper deals with the consistency of the least squares estimator of a convex regression function when the predictor is multidimensional. We characterize and discuss the computation of such an estimator via the solution of certain quadratic and linear programs. Mild sufficient conditions for the consistency of this estimator and its subdifferentials in fixed and stochastic design regression settings are provided. We also consider a regression function which is known to be convex and componentwise nonincreasing and discuss the characterization, computation and consistency of its least squares estimator.

Inconsistency of bootstrap: The Grenander estimator

In this paper, we investigate the (in)-consistency of different bootstrap methods for constructing confidence intervals in the class of estimators that converge at rate

On Kinematic Substructure in the Sextans Dwarf Spheroidal Galaxy

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On risk bounds in isotonic and other shape restricted regression problems

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THE MICHIGAN/MIKE FIBER SYSTEM SURVEY OF STELLAR RADIAL VELOCITIES IN DWARF SPHEROIDAL GALAXIES: ACQUISITION AND REDUCTION OF DATA ∗

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A continuous mapping theorem for the smallest argmax functional

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Change-point in stochastic design regression and the bootstrap

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A Computational Framework for Multivariate Convex Regression and Its Variants

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