Higher-order asymptotic theory of shrinkage estimation for general statistical models

Hiroshi Shiraishi, Masanobu Taniguchi, Takashi Yamashita

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


In this study, we develop a higher-order asymptotic theory of shrinkage estimation for general statistical models, which includes dependent processes, multivariate models, and regression models (i.e., non-independent and identically distributed models). We introduce a shrinkage estimator of the maximum likelihood estimator (MLE) and compare it with the standard MLE by using the third-order mean squared error. A sufficient condition for the shrinkage estimator to improve the MLE is given in a general setting. Our model is described as a curved statistical model p(⋅;θ(u)), where θ is a parameter of the larger model and u is a parameter of interest with dimu<dimθ. This setting is especially suitable for estimating portfolio coefficients u based on the mean and variance parameters θ. We finally provide the results of our numerical study and discuss an interesting feature of the shrinkage estimator.

Original languageEnglish
Pages (from-to)198-211
Number of pages14
JournalJournal of Multivariate Analysis
Publication statusPublished - 2018 Jul


  • Curved statistical model
  • Dependent data
  • Higher-order asymptotic theory
  • Maximum likelihood estimation
  • Portfolio estimation
  • Regression model
  • Shrinkage estimator
  • Stationary process

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty


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