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Member Research & Reports

Member Research & Reports

NYU: Estimation of Correlation in a Binary Sequence Model

A study co-authored by Dr. Yang Feng, associate professor of biostatistics at New York University School of Global Public Health, was published by the Journal of Statistical Planning and Inference titled “On the estimation of correlation in a binary sequence model.”

The study considers 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. The parameter estimation problem under such one-parameter models is analyzed, and it is demonstrated that maximizing the likelihood function does not yield consistent estimates for the correlation. Then, the non-estimability of the parameter is formally proved by deriving a non-vanishing minimax lower bound. This counterintuitive 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, it further shows that trinary data generated from the hidden variables can consistently estimate the correlation with parametric convergence rate. Thus a phase transition phenomenon regarding the discretization of latent continuous variables is revealed while preserving the estimability of the correlation. To validate the conclusions, numerical experiments were performed.

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