Abstract
The difference between an estimate and an estimator is emphasised and some properties of the latter, such as unbiasedness, consistency and efficiency, are introduced. The concepts of confidence intervals for the mean and variance are developed and their interpretation discussed by way of an example using income inequality data. Hypothesis testing is then introduced, and procedures for testing hypotheses about the mean and variance are proposed. Further considerations concerning hypothesis testing, such as Type I and II errors, power and prob-values, are discussed. These concepts are used to develop methods for performing inference on correlation coefficients, with a test for zero correlation and a confidence interval for the correlation coefficient being constructed.
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Notes
A proof of this result is extremely complicated, and was first shown by Karl Pearson, ‘On the standard error of the median …’, Biometrika 23 (1931), 361–363.
A proof of this result, which is based on the Cramer-Rao inequality (or lower bound), is given in Paul G. Hoel, Introduction to Mathematical Statistics, 4th edition (Wiley, 1971), p. 365.
Hypothesis testing plays a central role in statistical inference and its compatriot, statistical significance, has been the subject of many philosophical and methodological debates since the development of the competing inferential frameworks of Sir Ronald Fisher and Jerzy Neyman and Egon Pearson in the 1920s and 1930s: see, for example, Johannes Lenhard, ‘Models and statistical inference: the controversy between Fisher and Neyman-Pearson’, British Journal of the Philosophy of Science 57 (2006), 69–91.
This debate has flared up again recently in economics: see Stephen T. Ziliak and Deirdre N. McCloskey, The Cult of Statistical Significance: How the Standard Error Costs Us Jobs, Justice and Lives (University of Michigan Press, 2008)
and Kevin D. Hoover and Mark V. Siegler, ‘Sound and fury: McCloskey and significance testing in economics’, Journal of Economic Methodology 15 (2008), 1–37
A framework that may have the potential of reconciling the various approaches to hypothesis testing is the severe testing methodology of Deborah G. Mayo and Aris Spanos, ‘Severe testing as a basic concept in a Neyman-Pearson philosophy of induction’, British Journal of the Philosophy of Science 57 (2006), 323–357
For more economic-centred discussion of this idea, see John DiNardo, ‘Interesting questions in Freakonomics’, Journal of Economic Perspectives 45 (2007), 973–1000,
and Terence C. Mills, ‘Severe hypothesis testing in economics’, Journal of Quantitative Economics 7 (2009), 1–19.
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© 2014 Terence C. Mills
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Mills, T.C. (2014). Estimation and Inference. In: Analysing Economic Data. Palgrave Texts in Econometrics. Palgrave Macmillan, London. https://doi.org/10.1057/9781137401908_11
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DOI: https://doi.org/10.1057/9781137401908_11
Publisher Name: Palgrave Macmillan, London
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