Titlebook: Biased Sampling, Over-identified Parameter Problems and Beyond; Jing Qin Book 2017 Springer Nature Singapore Pte Ltd. 2017 Biased Sampling

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Brief Review of Parametric Likelihood Inferences,Maximum likelihood estimation (MLE) under regular conditions can be found in most statistical books. In non-regular cases, however, it involves all kinds of problems, such as solution on the boundary of parameter space, multiple roots, non-existence, inconsistency in the presence of many incidental parameters, etc.

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Empirical Likelihood with Applications,The maximum likelihood method for regular parametric models has many optimality properties. As a result, it is one of the most popular methods in statistical inference. However, model mis-specification is a big concern since a misspecified model may lead to bias results.

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,Kullback–Leibler Likelihood and Entropy Family,Besides empirical likelihood, the Kullback–Leibler likelihood is another popular method to calibrate auxiliary information. The entropy family has also been used extensively in information theory. We mainly focus on discussions for continuous random variable cases. The discrete cases can be treated similarly.

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Discrete Data Models,The logistic regression model has been widely used in statistical literature for analyzing categorical data. In this chapter we present many other useful discrete data models. If the data collection process is retrospective, then we end up with different biased sampling problems.

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