Abstract
The connection between quasi-likelihood functions, exponential family models and nonlinear weighted least squares is examined. Consistency and asymptotic normality of the parameter estimates are discussed under second moment assumptions. The parameter estimates are shown to satisfy a property of asymptotic optimality similar in spirit to, but more general than, the corresponding optimal property of Gauss-Markov estimators.
Keywords
MathematicsExponential familyEstimatorApplied mathematicsStrong consistencyAsymptotic distributionProperty (philosophy)Local asymptotic normalityMoment (physics)Consistency (knowledge bases)Markov chainMaximum likelihoodConnection (principal bundle)StatisticsDiscrete mathematics
Related Publications
Quasi-likelihood functions, generalized linear models, and the Gauss—Newton method
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 mea...
Large sample estimation and hypothesis testing
Asymptotic distribution theory is the primary method used to examine the properties of econometric estimators and tests. We present conditions for obtaining cosistency and asymp...
Nonconcave penalized likelihood with a diverging number of parameters
A class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed by Fan and Li to simultaneously estimate parameters and select im...
Robust Standard Errors and Chi-Squares for Interaction Models
Kenny and Judd (1984) formulated a model with interaction effects of two latent variables and suggested using product variables to estimate the model. Using one and four product...
Estimation of a Common Effect Parameter from Sparse Follow-Up Data
Breslow (1981, Biometrika 68, 73-84) has shown that the Mantel-Haenszel odds ratio is a consistent estimator of a common odds ratio in sparse stratifications. For cohort studies...
Publication Info
- Year
- 1983
- Type
- article
- Volume
- 11
- Issue
- 1
- Citations
- 769
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
769
OpenAlex
Cite This
Peter McCullagh
(1983).
Quasi-Likelihood Functions.
The Annals of Statistics
, 11
(1)
.
https://doi.org/10.1214/aos/1176346056
Identifiers
- DOI
- 10.1214/aos/1176346056