
Estimating the Mean and Variance of a Highdimensional Normal Distribution Using a Mixture Prior
This paper provides a framework for estimating the mean and variance of ...
read it

Ridgetype Linear Shrinkage Estimation of the Matrix Mean of Highdimensional Normal Distribution
The estimation of the mean matrix of the multivariate normal distributio...
read it

Mean Test with Fewer Observation than Dimension and Ratio Unbiased Estimator for Correlation Matrix
Hotelling's Tsquared test is a classical tool to test if the normal mea...
read it

MultiTarget Shrinkage
Stein showed that the multivariate sample mean is outperformed by "shrin...
read it

Pathwise Derivatives for Multivariate Distributions
We exploit the link between the transport equation and derivatives of ex...
read it

Compound Poisson Processes, Latent Shrinkage Priors and Bayesian Nonconvex Penalization
In this paper we discuss Bayesian nonconvex penalization for sparse lear...
read it

Occam Factor for Gaussian Models With Unknown Variance Structure
We discuss model selection to determine whether the variancecovariance ...
read it
Mean Shrinkage Estimation for HighDimensional Diagonal Natural Exponential Families
Shrinkage estimators have been studied widely in statistics and have profound impact in many applications. In this paper, we study simultaneous estimation of the mean parameters of random observations from a diagonal multivariate natural exponential family. More broadly, we study distributions for which the diagonal entries of the covariance matrix are certain quadratic functions of the mean parameter. We propose two classes of semiparametric shrinkage estimators for the mean vector and construct unbiased estimators of the corresponding risk. Further, we establish the asymptotic consistency and convergence rates for these shrinkage estimators under squared error loss as both n, the sample size, and p, the dimension, tend to infinity. Finally, we consider the diagonal multivariate natural exponential families, which have been classified as consisting of the normal, Poisson, gamma, multinomial, negative multinomial, and hybrid classes of distributions. We deduce consistency of our estimators in the case of the normal, gamma, and negative multinomial distributions if p n^1/3log^4/3n→ 0 as n,p →∞, and for Poisson and multinomial distributions if pn^1/2→ 0 as n,p →∞.
READ FULL TEXT
Comments
There are no comments yet.