Using R-based VOStat as a Low-Resolution Spectrum Analysis Tool

We describe here an online software suite VOStat written mainly for the Virtual Observatory, a novel structure in which astronomers share terabyte scale data. Written mostly in the public-domain statistical computing language and environment R, it can do a variety of statistical analysis on multidimensional, multi-epoch data with errors. Included are techniques which allow astronomers to start with multi-color data in the form of low-resolution spectra and select special kinds of sources in a variety of ways including color outliers. Here we describe the tool and demonstrate it with an example from Palomar-QUEST, a synoptic sky survey.

Some statistical and computational challenges, and opportunities in astronomy

The data complexity and volume of astronomical findings have increased in recent decades due to major technological improvements in instrumentation and data collection methods. The contemporary astronomer is flooded with terabytes of raw data that produce enormous multidimensional catalogs of objects (stars, galaxies, quasars, etc.) numbering in the billions, with hundreds of measured numbers for each object. The astronomical community thus faces a key task: to enable efficient and objective scientific exploitation of enormous multifaceted data sets and the complex links between data and astrophysical theory. In recognition of this task, the National Virtual Observatory (NVO) initiative recently emerged to federate numerous large digital sky archives, and to develop tools to explore and understand these vast volumes of data. The effective use of such integrated massive data sets presents a variety of new challenging statistical and algorithmic problems that require methodological advances. An interdisciplinary team of statisticians, astronomers and computer scientists from The Pennsylvania State University, California Institute of Technology and Carnegie Mellon University is developing statistical methodology for the NVO. A brief glimpse into the Virtual Observatory and the work of the Penn State-led team is provided here

Using R-based VOStat as a low resolution spectrum analysis tool

We describe here an online software suite VOStat written mainly for the Virtual Observatory, a novel structure in which astronomers share terabyte scale data. Written mostly in the public-domain statistical computing language and environment R, it can do a variety of statistical analysis on multidimensional, multi-epoch data with errors. Included are techniques which allow astronomers to start with multi-color data in the form of low-resolution spectra and select special kinds of sources in a variety of ways including color outliers. Here we describe the tool and demonstrate it with an example from Palomar-QUEST, a synoptic sky survey

Limit theorems for functions of marginal quantiles

Multivariate distributions are explored using the joint distributions of marginal sample quantiles. Limit theory for the mean of a function of order statistics is presented. The results include a multivariate central limit theorem and a strong law of large numbers. A result similar to Bahadur's representation of quantiles is established for the mean of a function of the marginal quantiles. In particular, it is shown that $$\sqrt{n}\Biggl(\frac{1}{n}\sum_{i=1}^n\phi\bigl(X_{n:i}^{(1)},...,X_{n:i}^{(d)}\bigr)-\bar{\gamma}\Biggr)=\frac{1}{\sqrt{n}}\sum_{i=1}^nZ_{n,i}+\mathrm{o}_P(1)$$ as $n\rightarrow\infty$, where $\bar{\gamma}$ is a constant and $Z_{n,i}$ are i.i.d. random variables for each $n$. This leads to the central limit theorem. Weak convergence to a Gaussian process using equicontinuity of functions is indicated. The results are established under very general conditions. These conditions are shown to be satisfied in many commonly occurring situations.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ287 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Goodness-of-fit tests when parameters are estimated

Several nonparametric goodness-of-fit tests are based on the empirical distribution function. In the presence of nuisance parameters, the tests are generally constructed by first estimating these nuisance parameters. In such a case, it is well known that critical values shift, and the asymptotic null distribution of the test statistic may depend in a complex way on the unknown parameters. In this paper we use bootstrap methods to estimate the null distribution. We shall consider both parametric and nonparametric bootstrap methods. We shall first demonstrate that, under very general conditions, the process obtained by subtracting the population distribution function with estimated parameters from the empirical distribution has the same weak limit as the corresponding bootstrap version. Of course in the nonparametric bootstrap case a bias correction is needed. This result is used to show that the bootstrap method consistently estimates the null distributions of various goodness-of-fit tests. These results hold not only in the univariate case but also in the multivariate setting

Lepton Flavor Violation in Supersymmetric SO(10) Grand Unified Models

The study for lepton flavor violation combined with the neutrino oscillation may provide more information about the lepton flavor structure of the grand unified theory. In this paper, we study two lepton flavor violation processes, $\tau\to \mu\gamma$ and $Z\to \tau\mu$, in the context of supersymmetric SO(10) grand unified models. We find the two processes are both of phenomenological interest. In particular the latter may be important in some supersymmetric parameter space where the former is suppressed. Thus, Z-dacay may offer another chance for looking for lepton flavor violation.Comment: 26 pages, 10 figure