(2008) 'Survival analysis: An Epidemiological hazard?'. (1998) Asymptotic Statistics Cambridge University Press. Probability and Statistics: The Science of Uncertainty. ^ 'Statistical inference - Encyclopedia of Mathematics'.(2008) Oxford Dictionary of Statistics, OUP. The heuristic application of limiting results to finite samples is common practice in many applications, especially with low-dimensional models with log-concavelikelihoods (such as with one-parameter exponential families). The magnitude of the difference between the limiting distribution and the true distribution (formally, the 'error' of the approximation) can be assessed using simulation. For example, limiting results are often invoked to justify the generalized method of moments and the use of generalized estimating equations, which are popular in econometrics and biostatistics. However, the asymptotic theory of limiting distributions is often invoked for work with finite samples. Limiting results are not statements about finite samples, and indeed are irrelevant to finite samples. With indefinitely large samples, limiting results like the central limit theorem describe the sample statistic's limiting distribution, if one exists.
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