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Quantile Regression: v. 149 (Quantitative Applications in the Social Sciences) by Lingxin Hao (2007-06-13)

Book Quantile Regression: v. 149 (Quantitative Applications in the Social Sciences) by Lingxin Hao (2007-06-13)

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- Language: Unknown
- Format: PDF - Djvu
- Pages:Unknown
- Publisher: SAGE Publications, Inc (2007-06-13) (1656)
- Bestsellers rank: 6
- Category: Other books
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  • By wiredweird on June 29, 2013

    The non-specialist (e.g. me) who thinks of regression thinks immediately of linear (i.e least-squares) regression - and stops there. This bakes in more hidden assumptions about the data than I care to name. For one, it assumes outliers won't skew the result, or that they can be dropped without [much] changing the result. When the extrema are the subjects of greatest interest, this assumption clearly falls on its face. Another is that the central tendency is the statistic of interest and residuals have zero mean. In many cases, wrong and wrong. Asymmetric and fat-tailed distributions pop up like mushrooms after a rain. Likewise, changes in the tenth- or ninetieth-percentile mark could be the subject of interest, as in "How has the distribution of wealth changed over time?" Without ending the list of least-squares assumptions, another big one comes to mind: what I can compute easily with closed-form expressions. Given that you have more computing power in your cell phone than existed on earth sixty years ago, that borders on the sin of sloth.Quantile regressions pull the statistical workhorse of regression well in the non-parametric direction. Although somewhat dense, this provides a reasonably clear introduction to quantile regression, not "How does the mean value change with the input value?" but "How does the median change?" Then, from the median (50th percentile) it generalizes readily to the N-th percentile. Although the algorithm performs a startling geometric transformation before turning into linear programming, a bit of thought exposes the significance of the transformation and the logic of the minimization algorithm. Starting there, it moves smoothly forward into discussion of confidence intervals, a case study, and some executable code. The little-known language of the latter might block many readers from deriving its full value, and I never convinced myself of the non-parametric purity of the confidence intervals. (That's probably just me, though.)Unlike least-squares regression, quantile regression gives essentially unchanged results under any positively monotonic data transformation. For example, if regression of raw data gives absolute differences, then log-scaling gives percentage differences, with no qualms about what the regression did to the transformed data. Still, this comes down do a linear regression at bottom, y=mx+b with m and b to be inferred from the data. Like least-squares, it can not directly produce nonlinear relationships, and can't handle non-monoticity at all. No one should let the fact of a tool's limitations stop them from using it, though. Every tool has constraints, and the successful practitioner knows the assumptions that bound the useful range of each one. Quantile regression's range of value might overlap least-squares' in many areas (like, where mean, median, and mode coincide), but adds significant area of inquiry as well. When I compare the cost of this book to the price I would have paid in classroom time getting the same knowledge, this brief but informative text is a rock-bottom bargain. And, in truth, I might never have found the classroom where this would have been presented. A prepared and diligent reader will find huge value in this book - not just in its presentation of new ideas, but in its critique of what you might have thought familiar.-- wiredweird

  • By Joe on January 20, 2012

    Very pleased with the both the speed of the order and the subject presentation, I would highly recommend the seller

  • By andres on April 2, 2015

    By far the most accessible and well written introduction to quantile regressions that i have come across. Highly recomended.


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