Gutti Jogesh Babu

Statistical Challenges in Modern Astronomy

Despite centuries of close association, statistics and astronomy are surprisingly distant today. Most observational astronomical research relies on an inadequate toolbox of methodological tools. Yet the needs are substantial: astronomy encounters sophisticated problems involving sampling theory, survival analysis, multivariate classification and analysis, time series analysis, wavelet analysis, spatial point processes, nonlinear regression, bootstrap resampling and model selection. We review the recent resurgence of astrostatistical research, and outline new challenges raised by the emerging Virtual Observatory. Our essay ends with a list of research challenges and infrastructure for astrostatistics in the coming decade.

On deviations between empirical and quantile processes for mixing random variables

Let {Xn} be a strictly stationary [phi]-mixing process with [Sigma]j=1[infinity] [phi]1/2(j)

Sign test for ranked-set sampling

The exact null distribution of the ranked-set sample (RSS) sign test statistic is computed. The power of this test is compared with the simple random sample (SRS) sign test for some continuous symmetric distributions. The problem of imperfect judgement is discussed. The superiority of RSS over SRS is demonstrated.

Strong representations for LAD estimators in linear models

SummaryConsider the standard linear modelyi=ziβ+ei,i=1, 2,...,n, where zi denotes theith row of ann x p design matrix,β∈ℝp is an unknown parameter to be estimated andei are independent random variables with a common distribution functionF. The least absolute deviation (LAD) estimate

A note on bootstrapping the variance of sample quantile

\tilde \beta

Limit Processes with Independent Increments for the Ewens Sampling Formula

of β is defined as any solution of the minimization problem

Expansions for statistics involving the mean absolute deviations

\sum\limits_{i = 1}^n { \left| {y_i - z_i \tilde \beta } \right| = \inf \left\{ {\sum\limits_{i = 1}^n { \left| {y_i - z_i \beta } \right|:\beta \in \mathbb{R}^p } } \right\}} .