Stochastic domination in predictive density estimation for ordered normal means under α-divergence loss
نویسندگان
چکیده
منابع مشابه
Minimax Estimation of Discrete Distributions under $\ell_1$ Loss
We consider the problem of discrete distribution estimation under l1 loss. We provide tight upper and lower bounds on the maximum risk of the empirical distribution (the maximum likelihood estimator), and the minimax risk in regimes where the support size S may grow with the number of observations n. We show that among distributions with bounded entropy H , the asymptotic maximum risk for the e...
متن کامل2 01 2 on the within - Family Kullback - Leibler Risk in Gaussian Predictive Models
We consider estimating the predictive density under KullbackLeibler loss in a high-dimensional Gaussian model. Decision theoretic properties of the within-family prediction error – the minimal risk among estimates in the class G of all Gaussian densities are discussed. We show that in sparse models, the class G is minimax suboptimal. We produce asymptotically sharp upper and lower bounds on the...
متن کاملRobust Estimation in Linear Regression Model: the Density Power Divergence Approach
The minimum density power divergence method provides a robust estimate in the face of a situation where the dataset includes a number of outlier data. In this study, we introduce and use a robust minimum density power divergence estimator to estimate the parameters of the linear regression model and then with some numerical examples of linear regression model, we show the robustness of this est...
متن کاملAdmissible Predictive Density Estimation
Let X|μ ∼ Np(μ,vxI ) and Y |μ ∼ Np(μ,vyI ) be independent pdimensional multivariate normal vectors with common unknown mean μ. Based on observing X = x, we consider the problem of estimating the true predictive density p(y|μ) of Y under expected Kullback–Leibler loss. Our focus here is the characterization of admissible procedures for this problem. We show that the class of all generalized Baye...
متن کاملMinimax rate adaptive estimation over continuous hyper-parameters
|We study minimax-rate adaptive estimation for density classes indexed by continuous hyper-parameters. The classes are assumed to be partially ordered in terms of inclusion relationship. Under a mild condition on the minimax risks, we show that a minimax-rate adaptive estimator can be constructed for the classes. 1 Problem of interest This paper concerns adaptive density estimation. Information...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Multivariate Analysis
دوره 128 شماره
صفحات -
تاریخ انتشار 2014