Chambers R.L., Steel D.G., Wang S., Welsh A.H. Maximum Likelihood Estimation for Sample Surveys

Chapman & Hall/CRC, 2012. — 356 p. — ISBN: 978-1584886327, e-ISBN: 978-1420011357.Sample surveys provide data used by researchers in a large range of disciplines to analyze important relationships using well-established and widely used likelihood methods. The methods used to select samples often result in the sample differing in important ways from the target population and standard application of likelihood methods can lead to biased and inefficient estimates.
Maximum Likelihood Estimation for Sample Surveys presents an overview of likelihood methods for the analysis of sample survey data that account for the selection methods used, and includes all necessary background material on likelihood inference. It covers a range of data types, including multilevel data, and is illustrated by many worked examples using tractable and widely used models. It also discusses more advanced topics, such as combining data, non-response, and informative sampling.
The book presents and develops a likelihood approach for fitting models to sample survey data. It explores and explains how the approach works in tractable though widely used models for which we can make considerable analytic progress. For less tractable models numerical methods are ultimately needed to compute the score and information functions and to compute the maximum likelihood estimates of the model parameters. For these models, the book shows what has to be done conceptually to develop analyses to the point that numerical methods can be applied.
Designed for statisticians who are interested in the general theory of statistics, Maximum Likelihood Estimation for Sample Surveys is also aimed at statisticians focused on fitting models to sample survey data, as well as researchers who study relationships among variables and whose sources of data include surveys.Nature and role of sample surveys, Sample designs; Survey data, estimation and analysis,
Why analysts of survey data should be interested in maximum likelihood estimation,
Why statisticians should be interested in the analysis of survey data, A sample survey example,
Maximum likelihood estimation for infinite populations:
Data, Statistical models, Likelihood, Score and information functions, Maximum likelihood estimation,
Hypothesis tests, Confidence intervals, Sufficient and ancillary statistics.
Maximum likelihood theory for sample surveys.
Maximum likelihood using survey data, Illustrative examples with complete response,
Dealing with nonresponse, Illustrative examples with nonresponse.
Alternative likelihood-based methods for sample survey data.
Pseudo-likelihood, Sample likelihood; Analytic comparisons of maximum likelihood, pseudolikelihood
and sample likelihood estimation,
The role of sample inclusion probabilities in analytic analysis, Bayesian analysis.
Populations with independent units.
The score and information functions for independent units, Bivariate Gaussian populations, Multivariate Gaussian populations,
Non-Gaussian auxiliary variables, Stratified populations,
Multinomial populations, Heterogeneous multinomial logistic populations.
Regression models.
A Gaussian example, Parameterization in the Gaussian model, Other methods of estimation,
Non-Gaussian models, Different auxiliary variable distributions, Generalized linear models, Semiparametric and nonparametric methods
Clustered populations.
A Gaussian group dependent model, A Gaussian group dependent regression model,
Extending the Gaussian group dependent regression model, Binary group dependent models, Grouping models.
Informative nonresponse.
Nonresponse in innovation surveys, Regression with item nonresponse,
Regression with arbitrary nonresponse, Imputation versus estimation.
Maximum likelihood in other complicated situations.
Likelihood analysis under informative selection, Secondary analysis of sample survey data,
Combining summary population information with likelihood analysis,
Likelihood analysis with probabilistically linked data.