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On Profile Likelihood

Journal of the American Statistical Association, 2000
Abstract We show that semiparametric profile likelihoods, where the nuisance parameter has been profiled out, behave like ordinary likelihoods in that they have a quadratic expansion. In this expansion the score function and the Fisher information are replaced by the efficient score function and efficient Fisher information.
Murphy, S.A., van der Vaart, A.W.
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Adjustments to profile likelihood

Biometrika, 1989
Summary: Conditional and marginal likelihoods constructed from parameter-dependent functions of the data have an additional parameter dependence that changes with the choice of supporting metric for the corresponding densities. We consider constructing marginal and conditional likelihoods by using densities expressed in terms of an intrinsic choice of ...
Fraser, D. A. S., Reid, N.
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An explanation of generalized profile likelihoods

Statistics and Computing, 2001
Let X, T, Y be random vectors such that the distribution of Y conditional on covariates partitioned into the vectors X e x and T e t is given by f(ys x, p), where p e (t, η(t)). Here t is a parameter vector and η(t) is a smooth, real–valued function of t. The joint distribution of X and T is assumed to be independent of t and η.
Joan G. Staniswalis, Peter F. Thall
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