Adaptive Density Estimation on the Circle by Nearly-Tight Frames

This work is concerned with the study of asymptotic properties of nonparametric density estimates in the framework of circular data. The estimation procedure here applied is based on wavelet thresholding methods: the wavelets used are the so-called Mexican needlets, which describe a nearly-tight frame on the circle. We study the asymptotic behaviour of the $L^{2}$-risk function for these estimates, in particular its adaptivity, proving that its rate of convergence is nearly optimal.Comment: 30 pages, 3 figure

An excess of damped Lyman alpha galaxies near QSOs

We present a sample of 33 damped Lyman alpha systems (DLAs) discovered in the Sloan Digital Sky Survey (SDSS) whose absorption redshifts (z_abs) are within 6000 km/s of the QSO's systemic redshift (z_sys). Our sample is based on 731 2.5 < z_sys < 4.5 non-broad-absorption-line (non-BAL) QSOs from Data Release 3 (DR3) of the SDSS. We estimate that our search is ~100 % complete for absorbers with N(HI) >= 2e20 cm^-2. The derived number density of DLAs per unit redshift, n(z), within v < 6000 km/s is higher (3.5 sigma significance) by almost a factor of 2 than that of intervening absorbers observed in the SDSS DR3, i.e. there is evidence for an overdensity of galaxies near the QSOs. This provides a physical motivation for excluding DLAs at small velocity separations in surveys of intervening 'field' DLAs. In addition, we find that the overdensity of proximate DLAs is independent of the radio-loudness of the QSO, consistent with the environments of radio-loud and radio-quiet QSOs being similar.Comment: Accepted for publication in MNRAS (13 pages, 6 figures