Abstract
To define a likelihood we have to specify the form of distribution of the observations, but to define a quasi-likelihood function we need only specify a relation between the mean and variance of the observations and the quasi-likelihood can then be used for estimation. For a one-parameter exponential family the log likelihood is the same as the quasi-likelihood and it follows that assuming a one-parameter exponential family is the weakest sort of distributional assumption that can be made. The Gauss-Newton method for calculating nonlinear least squares estimates generalizes easily to deal with maximum quasi-likelihood estimates, and a rearrangement of this produces a generalization of the method described by Nelder & Wedderburn (1972).
Keywords
MathematicsExponential familyLikelihood functionApplied mathematicsGeneralizationExponential functionMaximum likelihoodMaximum likelihood sequence estimationExpectation–maximization algorithmRestricted maximum likelihoodEstimation theoryQuasi-likelihoodVariance functionGeneralized linear modelLikelihood-ratio testStatisticsMathematical analysisRegression analysis
Affiliated Institutions
Related Publications
Maximum Likelihood Estimation in Truncated Samples
In this paper we consider the problem of estimation of parameters from a sample in which only the first $r$ (of $n$) ordered observations are known. If $r = \\lbrack qn \\rbrack...
A Linear Spatial Correlation Model, with Applications to Positron Emission Tomography
Abstract A simple spatial-correlation model is presented for repeated measures data. Correlation between observations on the same subject is assumed to decay as a linear functio...
Maximum Likelihood from Incomplete Data Via the <i>EM</i> Algorithm
Summary A broadly applicable algorithm for computing maximum likelihood estimates from incomplete data is presented at various levels of generality. Theory showing the monotone ...
Estimating the Mean and Variance of Normal Populations from Singly Truncated and Doubly Truncated Samples
This paper is concerned with the problem of estimating the mean and variance of normal populations from singly and doubly truncated samples having known truncation points. Maxim...
Bootstrap Methods: Another Look at the Jackknife
We discuss the following problem: given a random sample $\\mathbf{X} = (X_1, X_2, \\cdots, X_n)$ from an unknown probability distribution $F$, estimate the sampling distribution...
Publication Info
- Year
- 1974
- Type
- article
- Volume
- 61
- Issue
- 3
- Pages
- 439-447
- Citations
- 1939
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
1939
OpenAlex
Cite This
R. W. M. Wedderburn
(1974).
Quasi-likelihood functions, generalized linear models, and the Gauss—Newton method.
Biometrika
, 61
(3)
, 439-447.
https://doi.org/10.1093/biomet/61.3.439
Identifiers
- DOI
- 10.1093/biomet/61.3.439