The Drunken Man and Goodness-of-fit


  • Prof. Michael Stephens – Department of Statistics and Actuarial Science – Simon Fraser University – Canada
  • FCUL (DEIO) Campo Grande – Bloco C6 Piso 4 – Sala 6.4.31 – 14:30h
  • Sexta-feira, 9 de Julho de 2010
 Abstract: In 1905, Karl Pearson asked for the distribution of the distance from the start, of a man who takes N steps of unit length in random directions. The problem has arisen again in recent work on testing fit to a distribution given a minimal sufficient statistic, and using the Rao-Blackwell distribution of the test statistic. When the test of fit is made, there is a remarkable correlation of the p-value with that given by the parametric bootstrap. The talk will begin with a discussion of Pearson’s problem, which has a fascinating history in its own right. In the goodness-of-fit problem, illustrated by testing the von Mises distribution, the Rao-Blackwell distribution will be estimated using the Gibbs sampler; mathematical details will be kept to a minimum and references given. Finally, the comparison with the bootstrap results will be shown, and some conclusions drawn.