PHIL 6334 – “Probability/Statistics Lecture Notes 3 for 2/20/14: Estimation (Point and Interval)”:(Prof. Spanos)*
*This is Day #5 on the Syllabus, as Day #4 had to be made up (Feb 24, 2014) due to snow. Slides for Day #4 will go up Feb. 26, 2014. (See the revised Syllabus Second Installment.)
Experts convene to explore new philosophy of statistics field
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Error Statistics Philosophy
Inconsistent jargon alert! On page 25, precision and accuracy are equated. In the science jargon I was taught in both high school and university, the term “accuracy” is scientist jargon for what a statistician would call lack of bias and the term “precision” is scientist jargon for what a statistician would call low variance. So a measurement might any of the four possible combinations of high/low accuracy, high/low precision. (A low accuracy, high precision measurement indicates “systematic error”, that is, it’s tantamount to a poorly calibrated instrument.)
Corey: on page 25 there is no mention of “accuracy”. What is mentioned on that page is “reliability and precision” which refer to very different notions.
Sorry, it’s on page 20, not page 25. (I attribute this sloppiness to the fact that I’m getting sick.)
It’s kind of retro to read that unbiasedness is a desirable or “optimal” property, especially coming from a time series guy. (I assume that all econometricians are time series experts, right?)
When I was young and unformed (i.e., before I learned of the Bayesian approach) I was taking this course. The Robert E. Kearney who teaches it is a time series expert (and was also my graduate thesis advisor). He was teaching us about autocorrelation estimators, and he mentioned that the biased one was generally preferred over the unbiased one. I asked why anyone would ever prefer a biased estimator when an unbiased one was available; his answer, which I didn’t understand at the time, can be boiled down to “mean-sqaured-error bias-variance tradeoff”. I later saw the logic for myself when I tried both the biased and unbiased estimators on simulated data for a class assignment.
Darn it, should have read that last slide before commenting.