Name
Abstract | ||
|---|---|---|
This paper treats the problem of estimating positive parameters restricted to a polyhedral convex cone which includes typical order restrictions, such as simple order, tree order and umbrella order restrictions. In this paper, two methods are used to show the improvement of order-preserving estimators over crude non-order-preserving estimators without any assumption on underlying distributions. One is to use Fenchel's duality theorem, and then the superiority of the isotonic regression estimator is established under the general restriction to polyhedral convex cones. The use of the Abel identity is the other method, and we can derive a class of improved estimators which includes order-statistics-based estimators in the typical order restrictions. When the underlying distributions are scale families, the unbiased estimators and their order-restricted estimators are shown to be minimax. The minimaxity of the restrictedly generalized Bayes estimator against the prior over the restricted space is also demonstrated in the two dimensional case. Finally, some examples and multivariate extensions are given. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.jmva.2010.08.011 | J. Multivariate Analysis |
Keywords | Field | DocType |
isotonic regression,typical order restriction,underlying distribution,umbrella ordering,improved estimator,simultaneous estimation,secondary,kullback–leibler loss,simple ordering,simple order,tree order,tree ordering,umbrella order restriction,primary,62c10,scale parameter,62f30,modifying estimator,isotonic regression estimator,decision theory,weighted stein loss,positive parameter,stein loss,convex cone,restricted maximum likelihood estimator,crude non-order-preserving estimator,62h12,minimaxity,fenchel’s duality theorem,62c20,bayes estimator,order-statistics-based estimator,unbiased estimator,restricted maximum likelihood,kullback leibler,fenchel s duality theorem,order statistic | Econometrics,Minimax,Extremum estimator,Fenchel's duality theorem,Multivariate normal distribution,Statistics,Bayes estimator,Mathematics,Scale parameter,Convex cone,Estimator | Journal |
Volume | Issue | ISSN |
102 | 1 | Journal of Multivariate Analysis |
Citations | PageRank | References |
1 | 0.43 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hisayuki Tsukuma | 1 | 8 | 4.66 |
| Tatsuya Kubokawa | 2 | 36 | 11.73 |