On the estimation of correlation in a binary sequence model

Haolei Weng, Yang Feng

Research output: Contribution to journalArticle

Abstract

We consider a binary sequence generated by thresholding a hidden continuous sequence. The hidden variables are assumed to have a compound symmetry covariance structure with a single parameter characterizing the common correlation. We study the parameter estimation problem under such one-parameter models. We demonstrate that maximizing the likelihood function does not yield consistent estimates for the correlation. We then formally prove the nonestimability of the parameter by deriving a non-vanishing minimax lower bound. This counter-intuitive phenomenon provides an interesting insight that one-bit information of each latent variable is not sufficient to consistently recover their common correlation. On the other hand, we further show that trinary data generated from the hidden variables can consistently estimate the correlation with parametric convergence rate. Thus we reveal a phase transition phenomenon regarding the discretization of latent continuous variables while preserving the estimability of the correlation. Numerical experiments are performed to validate the conclusions.

Original languageEnglish (US)
Pages (from-to)123-137
Number of pages15
JournalJournal of Statistical Planning and Inference
Volume207
DOIs
StateAccepted/In press - Jan 1 2019

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Keywords

  • Binary data
  • Maximum likelihood estimate
  • Minimax lower bound
  • Phase transition
  • Thresholding
  • Trinary data

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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