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

Hiroshi Shiraishi, Masanobu Taniguchi, Takashi Yamashita

Research output: Contribution to journalArticle

Abstract

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
Volume166
DOIs
Publication statusPublished - 2018 Jul 1

Fingerprint

Shrinkage Estimation
Higher-order Asymptotics
Shrinkage Estimator
Asymptotic Theory
Maximum Likelihood Estimator
Statistical Model
Maximum likelihood
Multivariate Regression
Multivariate Models
Mean Squared Error
Identically distributed
Numerical Study
Regression Model
Model
Dependent
Sufficient Conditions
Coefficient
Shrinkage estimation
Maximum likelihood estimator
Asymptotic theory

Keywords

  • 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

Cite this

Higher-order asymptotic theory of shrinkage estimation for general statistical models. / Shiraishi, Hiroshi; Taniguchi, Masanobu; Yamashita, Takashi.

In: Journal of Multivariate Analysis, Vol. 166, 01.07.2018, p. 198-211.

Research output: Contribution to journalArticle

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