Estimation of mean vector is a classical problem which includes Stein’s paradox. There are many approahces in estimating mean vecotr such as linear estimator and approximate Bayes estimator using nonparametric empirical Bayes or nonparametric maximum likelihood estimation. Efron (2014) categorized nonparametric empirical Bayes estimation by introducing f-modeling and g-modeling. Its application area is very broad including small area estimation and high dimensional classification.
*Park, H. and Park, J. (2021+) Poisson mean vector estimation with Nonparametric Maximum Likelihood Estimation and Application to Protein Domain Data. Submitted.
Park, J. (2018). Simultaneous Estimation based on Empirical Likelihood and Nonparametric Maximum Likelihood Estimation, Computational Statistics and Data Analysis, 117, 19-31. Article Link
Park, J. (2014). Shrinkage Estimator in Normal Mean Vector Estimation based on Conditional Maximum Likelihood, Statistics and Probability Letters, 93, 1-6.
Park, J. (2012). Nonparametric Empirical Bayes Estimator in Simultaneous Estimation of Poisson Means and Application to Mass Spectrometry Data, Journal of Nonparametric Statistics, 24, 245-265.
Park, J. and Davis, W. (2011). Estimating and testing conditional sums of means in high dimensional multivariate binary data, Journal of Statistical Planning and Inference, 141, 1021-1030.
Greenshtein, E., Park, J. and Ritov, Y. (2008). Estimating the mean of high valued observations in high dimensions, Journal of Statistical Theory and Practice, 2, 407-418.