Overview of basic concepts in Statistics and Probability - SAMSI
Overview of basic concepts in Statistics and Probability - SAMSI
Overview of basic concepts in Statistics and Probability - SAMSI
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Estimators are r<strong>and</strong>om variables!<br />
<strong>Overview</strong> <strong>of</strong><br />
<strong>basic</strong> <strong>concepts</strong><br />
<strong>in</strong> <strong>Statistics</strong><br />
<strong>and</strong><br />
<strong>Probability</strong><br />
Avanti<br />
Athreya<br />
Prelim<strong>in</strong>aries<br />
Important<br />
distributions,<br />
scal<strong>in</strong>g laws,<br />
<strong>and</strong> the CLT<br />
Parametric<br />
estimation <strong>and</strong><br />
hypothesis<br />
test<strong>in</strong>g<br />
Estimators are themselves r<strong>and</strong>om variables!<br />
Estimators are functions <strong>of</strong> the r<strong>and</strong>om sample, i.e. the data.<br />
ESTIMATORS ARE RANDOM VARIABLES!<br />
The sample mean ˆµ, for <strong>in</strong>stance, is r<strong>and</strong>om.<br />
One can describe:<br />
1 The distribution function <strong>of</strong> an estimator;<br />
2 Its mean, variance, <strong>and</strong> other moments;<br />
3 Its asymptotic behavior as the sample size n grows large.
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