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1982
Consider a parametric family β = {Pθ,n:(θ,n) ∈ Θ × H} with Θ ⊂IRp and H arbitrary. We are interested in estimating the (structural) parameter θ The value of the nuisance parameter n changes from observation to observation, being a random variable, distributed according to some p-measure Γ on (H ,ℬ), i.e., the observation xν is a realization governed by
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Consider a parametric family β = {Pθ,n:(θ,n) ∈ Θ × H} with Θ ⊂IRp and H arbitrary. We are interested in estimating the (structural) parameter θ The value of the nuisance parameter n changes from observation to observation, being a random variable, distributed according to some p-measure Γ on (H ,ℬ), i.e., the observation xν is a realization governed by
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Elimination of Nuisance Parameters with Reference Priors
Biometrika, 1993Summary: The problem of eliminating nuisance parameters is tackled from different points of view. Standard likelihood techniques, such as profile likelihood and its modifications, are compared with a Bayesian analysis based on reference priors. Examples are considered to illustrate what happens in multiparameter problems.
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Orthogonality of Estimating Functions and Nuisance Parameters
Biometrika, 1991SUMMARY Cox & Reid (1987) proposed the technique of orthogonalizing parameters, to deal with the general problem of nuisance parameters, within fully parametric models. They obtained a large-sample approximation to the conditional likelihood. Along the same lines Davison (1988) studied generalized linear models.
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Dealing with nuisance parameters
2001Abstract Nuisance parameters create most of the complications in likelihood theory. They appear on the scene as a natural consequence of our effort to use ‘bigger and better ‘ models: while some parameters are of interest, others are only required to complete the model. The issue is important since nuisance parameters can have a dramatic
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On the Approximate Elimination of Nuisance Parameters by Conditioning
Biometrika, 1994Summary: The general problem of inference about a scalar parameter of interest \(\theta\) in the presence of a nuisance parameter \(\lambda\) using conditional inference is considered. A condition is given under which inference based on the conditional distribution of \(\widehat{\theta}\), the maximum likelihood estimate of \(\theta\), given \(\widehat{
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On the identifiability problem in the presence of random nuisance parameters
Signal Processing, 2012This paper concerns with the identifiability of a vector of unknown deterministic parameters. In many practical applications, the data model is affected by additional random parameters whose estimation is not strictly required, the so-called nuisance parameters. In these cases, the classical definition of identifiability, which requires the calculation
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Elimination of Nuisance Parameters
1988The problem begins with an unknown state of nature represented by the parameter of interest θ . We have some information about θ to begin with — e.g., we know that θ is a member of some well-defined parameter space θ- but we are seeking more. Toward this end, a statistical experiment & is planned and performed and this generates the sample observation ...
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On Sufficiency and Ancillarity in the Presence of a Nuisance Parameter
Biometrika, 1980SUMMARY This paper discusses the definitions of ancillarity and sufficiency in the presence of a nuisance parameter given by Godambe (1976a). Illustrative examples are given and the relation to Fisher information discussed. In view of the properties of distribution functions which provide optimum estimating equations, Godambe (1976a) proposed ...
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On information and ancillarity in the presence of a nuisance parameter
Biometrika, 1983This paper discusses ancillarity, in the presence of a nuisance parameter. For exponential distribution families, some equivalent properties regarding ancillarity are found and discussed.
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Estimating a Signal with Noisy Nuisance Parameters
Biometrika, 1989We describe two models in which n records of a signal in white noise are taken. In the first model the signal parameters of interest do not change between records, but the amplitude varies in a random way. In the second model, the location is the random nuisance parameter. We describe an efficient estimator for the first model.
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