Statistics Seminars: Non-linear transformations of random data: moment determinacy of their distributions
14 April 2010 11:00 in Department of Mathematical Sciences, Durham University
Functional transformations (Box-Cox) of random data are intensively studied and widely used in statistical practice. Data come from observations of random variables or of stochastic processes. Our goal is to analyse the distributions of the data, before and after transforming, and their properties expressed in terms of the moments. Some distributions are uniquely determined by their moments (M-determinate) while others are non-unique (M-indeterminate). The determinacy property of a distribution is essential in inference problem. We use classical and/or modern criteria to analyse specific stochastic models. General statements will be given and well-illustrated with popular distributions. Some of the reported facts are not so well-known, and even surprising. If time permits, a couple of open questions will be outlined.
An event within the Lecture Day with Prof. Balakrishnan, more info available at http://www.maths.dur.ac.uk/~dma0je/bala/