 Facts and figures about UK taxes, benefits and public spending.
Income distribution, poverty and inequality.
Analysing government fiscal forecasts and tax and spending.
Analysis of the fiscal choices an independent Scotland would face.
Case studies that give a flavour of the areas where IFS research has an impact on society.
Reforming the tax system for the 21st century.
A peer-reviewed quarterly journal publishing articles by academics and practitioners.
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In this note we consider several versions of the bootstrap and argue that it is helpful in explaining and thinking about such procedures to use an explicit representation of the random resampling process. To illustrate the point we give such explicit representations and use them to produce some results about bootstrapping linear models that are, apparently, not widely known. Among these are a demonstration of the equivalence, to order n-1 of the covariance matrix of the bootstrap distribution of the least squares estimator and the Eicker(1967)/White(1980) heteroscedasticity robust covariance matrix estimate. And we examine the precise relations between an Efron(1979) bootstrap procedure and the Bayesian bootstrap of Rubin(1981) and show that their covariance matrices are identical to O(1/n). Search |
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