On the joint density of the sum and sum of squares of nonnegative random variables

Hillier, Grant (2007) On the joint density of the sum and sum of squares of nonnegative random variables. In, Phillips, Garry D.A. and Tzavalis, Elias (eds.) The Refinement of Econometric Estimation and Test Procedures. Cambridge, GB. Cambridge University Press, pp. 326-346.

Record type: Book Section

Abstract

The small sample properties of estimators and tests are frequently too complex to be useful or are unknown. Much econometric theory is therefore developed for very large or asymptotic samples where it is assumed that the behaviour of estimators and tests will adequately represent their properties in small samples. Refined asymptotic methods adopt an intermediate position by providing improved approximations to small sample behaviour using asymptotic expansions. Dedicated to the memory of Michael Magdalinos, whose work is a major contribution to this area, this book contains chapters directly concerned with refined asymptotic methods. In addition, there are chapters focussing on new asymptotic results; the exploration through simulation of the small sample behaviour of estimators and tests in panel data models; and improvements in methodology. With contributions from leading econometricians, this collection will be essential reading for researchers and graduate students concerned with the use of asymptotic methods in econometric analysis.

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