**Date & Time:** 19th April, 2013; 14.00-14.30

**Venue:** Ramanujan Hall

**Title:** Some new techniques of inference from time series and high dimensional data

**Speaker:**Dr. Radhendushka Srivastava

**Abstract:** A practical constraint that comes in the way of spectrum estimation of a continuous time stationary stochastic process is that of a minimum separation between successively observed samples of the process. When the underlying process is not band-limited, sampling at any uniform rate leads to the problem of non-identifiability (aliasing), while certain stochastic sampling schemes, including Poisson process sampling, are rendered infeasible by the constraint of minimum separation. We show that, subject to this constraint, no point process sampling scheme is alias-free for the class of all spectra. Subsequently, we restrict our attention to the class of band-limited spectra and show that certain point process sampling schemes under this constraint can be alias- free. We propose a new spectrum estimator which is consistent under the said constraint. In high dimension, the classical Hotelling's $T^2$ test tends to have small power or becomes undefined due to the singularity of the sample covariance matrix. We propose to overcome this problem by projecting the data matrix to lower dimensions through multiplication with a random matrix. A bootstrap test for equality of means of two normal populations is proposed on the basis of the projected lower dimensional data. The proposed test does not require any constraint on the dimension of the data and sample size. A simulation study indicates that the power of this test is larger than those of competing tests in high dimension.