PMID: 9004398Jan 15, 1997Paper

Toward a curse of dimensionality appropriate (CODA) asymptotic theory for semi-parametric models

Statistics in Medicine
James M Robins, Y Ritov

Abstract

We argue, that due to the curse of dimensionality, there are major difficulties with any pure or smoothed likelihood-based method of inference in designed studies with randomly missing data when missingness depends on a high-dimensional vector of variables. We study in detail a semi-parametric superpopulation version of continuously stratified random sampling. We show that all estimators of the population mean that are uniformly consistent or that achieve an algebraic rate of convergence, no matter how slow, require the use of the selection (randomization) probabilities. We argue that, in contrast to likelihood methods which ignore these probabilities, inverse selection probability weighted estimators continue to perform well achieving uniform n 1/2-rates of convergence. We propose a curse of dimensionality appropriate (CODA) asymptotic theory for inference in non- and semi-parametric models in an attempt to formalize our arguments. We discuss whether our results constitute a fatal blow to the likelihood principle and study the attitude toward these that a committed subjective Bayesian would adopt. Finally, we apply our CODA theory to analyse the effect of the 'curse of dimensionality' in several interesting semi-parametric mod...Continue Reading

Citations

Dec 15, 2005·Developmental Psychology·Jennifer L HillWen-Jui Han
May 13, 2009·The Journals of Gerontology. Series B, Psychological Sciences and Social Sciences·Robert D Plotnick
Sep 8, 2009·Epidemiologic Perspectives & Innovations : EP+I·Sander Greenland, James M Robins
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