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A note on estimation in a simple probit model under dependency. (arXiv:1712.09694v1 [math.ST])
来源于:arXiv
We consider a probit model without covariates, but the latent Gaussian
variables having compound symmetry covariance structure with a single parameter
characterizing the common correlation. We study the parameter estimation
problem under such one-parameter probit models. As a surprise, we demonstrate
that the likelihood function does not yield consistent estimates for the
correlation. We then formally prove the parameter's nonestimability by deriving
a non-vanishing minimax lower bound. This counter-intuitive phenomenon provides
an interesting insight that one bit information of the latent Gaussian
variables is not sufficient to consistently recover their correlation. On the
other hand, we further show that trinary data generated from the Gaussian
variables can consistently estimate the correlation with parametric convergence
rate. Hence we reveal a phase transition phenomenon regarding the
discretization of latent Gaussian variables while preserving the estimability
of the correlation 查看全文>>