Maximum Score Estimation of Preference Parameters for a Binary Choice Model under Uncertainty

This paper develops maximum score estimation of preference parameters in the binary choice model under uncertainty in which the decision rule is affected by conditional expectations. The preference parameters are estimated in two stages: we estimate conditional expectations nonparametrically in the first stage and then the preference parameters in the second stage based on Manski (1975, 1985)'s maximum score estimator using the choice data and first stage estimates. The paper establishes consistency and derives rate of convergence of the two-stage maximum score estimator. Moreover, the paper also provides sufficient conditions under which the two-stage estimator is asymptotically equivalent in distribution to the corresponding single-stage estimator that assumes the first stage input is known. These results are of independent interest for maximum score estimation with nonparametrically generated regressors. The paper also presents some Monte Carlo simulation results for finite-sample behavior of the two-stage estimator

The Carnegie-Chicago Hubble Program: Discovery of the Most Distant Ultra-faint Dwarf Galaxy in the Local Universe

Ultra-faint dwarf galaxies (UFDs) are the faintest known galaxies and due to their incredibly low surface brightness, it is difficult to find them beyond the Local Group. We report a serendipitous discovery of an UFD, Fornax UFD1, in the outskirts of NGC 1316, a giant galaxy in the Fornax cluster. The new galaxy is located at a projected radius of 55 kpc in the south-east of NGC 1316. This UFD is found as a small group of resolved stars in the Hubble Space Telescope images of a halo field of NGC 1316, obtained as part of the Carnegie-Chicago Hubble Program. Resolved stars in this galaxy are consistent with being mostly metal-poor red giant branch (RGB) stars. Applying the tip of the RGB method to the mean magnitude of the two brightest RGB stars, we estimate the distance to this galaxy, 19.0 +- 1.3 Mpc. Fornax UFD1 is probably a member of the Fornax cluster. The color-magnitude diagram of these stars is matched by a 12 Gyr isochrone with low metallicity ([Fe/H] ~ -2.4). Total magnitude and effective radius of Fornax UFD1 are Mv ~ -7.6 +- 0.2 mag and r_eff = 146 +- 9 pc, which are similar to those of Virgo UFD1 that was discovered recently in the intracluster field of Virgo by Jang & Lee (2014).Fornax UFD1 is the most distant known UFD that is confirmed by resolved stars. This indicates that UFDs are ubiquitous and that more UFDs remain to be discovered in the Fornax cluster.Comment: 6 pages, 4 figures, 1 table, accepted for publication in ApJ Letter

Stellar Contents and Globular Cluster Candidates in the Sculptor Group Galaxy NGC 300

We present UBVI CCD photometry of the stellar contents and globular cluster(GC) candidates in the spiral galaxy NGC 300 in the Sculptor group. Color-magnitude diagrams for 18 OB associations having more than 30 member stars are presented. The slope of the initial mass function for the bright stars in NGC 300 is estimated to be Gamma = -2.6 +/- 0.3. Assuming the distance to NGC 300 of (m-M)_0 = 26.53 +/- 0.07, the mean absolute magnitude of three brightest blue stars is obtained to be = -8.95 mag. We have performed search for GCs in NGC 300 and have found 17 GC candidates in this galaxy. Some characteristics of these GC candidates are discussed.Comment: 24 pages(AASLaTeX), 14 Postscript figures, Accepted for publication in the Journal of the Korean Astronomical Society, 2002 March issue, Typos Correcte