Tweedie’s Formula and Selection Bias Bradley Efron ∗ Stanford University Abstract We suppose that the statistician observes some large number of estimates z i , each with its own unobserved expectation parameter µ i . The largest few of the z i ’s are likely to substantially overestimate...
The largest few of the zis are likely to substantially overestimate their corresponding is, this being an example of selection bias, or regression to the mean. Tweedies formula, first reported by Robbins in 1956, offers a simple empirical Bayes approach for correcting selection bias. This article...
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Substituting the MLEs μ ^ M and λ ^ M into formula (11), and maximizing this profile loglikelihood function or minimizing the negative profile log-likelihood function through one-dimensional search, then the MLE p ^ M can be obtained. In this paper, the MATLAB function “FMINSEARCH” is...
Substituting the MLEs μ ^ M and λ ^ M into formula (11), and maximizing this profile loglikelihood function or minimizing the negative profile log-likelihood function through one-dimensional search, then the MLE p ^ M can be obtained. In this paper, the MATLAB function “FMINSEARCH” is...