Name
Title | ||
|---|---|---|
Bayesian Minimax Estimation of the Normal Model With Incomplete Prior Covariance Matrix Specification |
Abstract | ||
|---|---|---|
This work addresses the issue of Bayesian robustness in the multivariate normal model when the prior covariance matrix is not completely specified, but rather is described in terms of positive semi-definite bounds. This occurs in situations where, for example, the only prior information available is the bound on the diagonal of the covariance matrix derived from some physical constraints, and that the covariance matrix is positive semi-definite, but otherwise arbitrary. Under the conditional Gamma-minimax principle, previous work by DasGupta and Studden shows that an analytically exact solution is readily available for a special case where the bound difference is a scaled identity. The goal in this work is to consider this problem for general positive definite matrices. The contribution in this paper is a theoretical study of the geometry of the minimax problem. Extension of previous results to a more general case is shown and a practical algorithm that relies on semi-definite programming and the convexity of the minimax formulation is derived. Although the algorithm is numerically exact for up to the bivariate case, its exactness for other cases remains open. Numerical studies demonstrate the accuracy of the proposed algorithm and the robustness of the minimax solution relative to standard and recently proposed methods. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1109/TIT.2010.2080612 | IEEE Transactions on Information Theory |
Keywords | Field | DocType |
shrinkage method,positive semi-definite,semi-definite programming,practical algorithm,multivariate normal model,bayesian robustness,bayes methods,bivariate case,covariance matrices,incomplete prior covariance matrix,conditional gamma-minimax principle,general positive definite matrix,general case,minimax techniques,normal model,incomplete prior covariance matrix specification,minimax estimator,robust bayesian analysis,bayesian point estimate,prior uncertainty,bayesian minimax estimation,gamma-minimax,minimax formulation,positive semi-definite bound,minimax solution,covariance matrix,minimax problem,uncertainty,robustness,positive semi definite,bayesian analysis,exact solution,semi definite programming,estimation,bayesian methods,point estimation,algorithm design and analysis,multivariate normal | Robust Bayesian analysis,Applied mathematics,Discrete mathematics,Mathematical optimization,Minimax,Estimation of covariance matrices,Matrix (mathematics),Positive-definite matrix,Multivariate normal distribution,Covariance matrix,Mathematics,Covariance | Journal |
Volume | Issue | ISSN |
56 | 12 | 0018-9448 |
Citations | PageRank | References |
1 | 0.35 | 11 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Duc-Son Pham | 1 | 273 | 18.57 |
| Hung Hai Bui | 2 | 1188 | 112.37 |
| Svetha Venkatesh | 3 | 4190 | 425.27 |