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Statistical inference of minimum BD estimators and classifiers for varying-dimensional models

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  • Zhang, Chunming

Abstract

Stochastic modeling for large-scale datasets usually involves a varying-dimensional model space. This paper investigates the asymptotic properties, when the number of parameters grows with the available sample size, of the minimum- estimators and classifiers under a broad and important class of Bregman divergence (), which encompasses nearly all of the commonly used loss functions in the regression analysis, classification procedures and machine learning literature. Unlike the maximum likelihood estimators which require the joint likelihood of observations, the minimum-BD estimators are useful for a range of models where the joint likelihood is unavailable or incomplete. Statistical inference tools developed for the class of large dimensional minimum- estimators and related classifiers are evaluated via simulation studies, and are illustrated by analysis of a real dataset.

Suggested Citation

  • Zhang, Chunming, 2010. "Statistical inference of minimum BD estimators and classifiers for varying-dimensional models," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1574-1593, August.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:7:p:1574-1593
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    1. Bradley Efron, 2004. "The Estimation of Prediction Error: Covariance Penalties and Cross-Validation," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 619-632, January.
    2. Zhang, Chunming & Lu, Yuefeng & Johnstone, Tom & Oakes, Terry & Davidson, Richard J., 2008. "Efficient modeling and inference for event-related fMRI data," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4859-4871, June.
    3. Harrison, David Jr. & Rubinfeld, Daniel L., 1978. "Hedonic housing prices and the demand for clean air," Journal of Environmental Economics and Management, Elsevier, vol. 5(1), pages 81-102, March.
    4. Bartlett, Peter L. & Jordan, Michael I. & McAuliffe, Jon D., 2006. "Convexity, Classification, and Risk Bounds," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 138-156, March.
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