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20 August 2019
19:54  Gradlevel Probability and Statistics Lecture Notes (diff  hist) . . (+409) . . Foojt (talk  contribs) 
N 19:52  Full Lecture 10 (diff  hist) . . (+179) . . Foojt (talk  contribs) (Created page with "= Lecture 10 = {{#lst:Lecture_10._A)_Finding_UMVU_Estimatorssection1}} {{#lst:Lecture_10._B)_Complete_Statisticsection1}} {{#lst:Lecture_10._C)_CramerRao_Lower_Boundsectio...") 
N 19:51  Full Lecture 9 (diff  hist) . . (+338) . . Foojt (talk  contribs) (Created page with "= Lecture 9 = {{#lst:Lecture_9._A)_Point_Estimation_(cont.)section1}} {{#lst:Lecture_9._B)_Evaluating_Estimatorssection1}} {{#lst:Lecture_9._C)_Minimum_Variance_Estimatorss...") 

N 19:50  Lecture 10. C) CramerRao Lower Bound (2 changes  history) . . (+4,328) . . [Foojt (2×)]  

19:50 (cur  prev) . . (+336) . . Foojt (talk  contribs)  
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19:39 (cur  prev) . . (+3,992) . . Foojt (talk  contribs) (Created page with "= CramérRao Lower Bound (CRLB) = It is possible to provide a meaningful lower bound to the variance of an estimator. (An example of a meaningless bound is zero.) Let <math...") 

N 19:50  Lecture 10. B) Complete Statistic (2 changes  history) . . (+8,839) . . [Foojt (2×)]  

19:50 (cur  prev) . . (+601) . . Foojt (talk  contribs)  
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19:36 (cur  prev) . . (+8,238) . . Foojt (talk  contribs) (Created page with "= Complete Statistic = A statistic <math display="inline">T</math> is '''complete''' for '''<math display="inline">\theta\in\Theta</math>''' if for any (measurable) function...") 

N 19:49  Lecture 10. A) Finding UMVU Estimators (2 changes  history) . . (+2,044) . . [Foojt (2×)]  

19:49 (cur  prev) . . (+398) . . Foojt (talk  contribs)  
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19:29 (cur  prev) . . (+1,646) . . Foojt (talk  contribs) (Created page with "= Finding UMVU estimators = In the previous lecture, we have introduced RaoBlackwell’s theorem, which can be used to reduce the variance of an existing estimator while pre...") 

N 19:47  Lecture 9. F) Factorization Theorem (3 changes  history) . . (+2,273) . . [Foojt (3×)]  

19:47 (cur  prev) . . (+328) . . Foojt (talk  contribs)  

19:27 (cur  prev) . . (+1) . . Foojt (talk  contribs)  
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19:27 (cur  prev) . . (+1,944) . . Foojt (talk  contribs) (Created page with "= Factorization Theorem = As we saw in the example of the Normal distribution, it can be tedious to find a sufficient statistic for a parameter. Luckily, there the factorizat...") 

N 19:46  Lecture 9. E) RaoBlackwell (2 changes  history) . . (+3,498) . . [Foojt (2×)]  

19:46 (cur  prev) . . (+585) . . Foojt (talk  contribs)  
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19:26 (cur  prev) . . (+2,913) . . Foojt (talk  contribs) (Created page with "= RaoBlackwell Theorem = The RaoBlackwell theorem allows us to take an existing estimator, and create a more efficient one. In order to do this, one requires a sufficient s...") 

N 19:45  Lecture 9. D) Sufficient Statistics (2 changes  history) . . (+5,901) . . [Foojt (2×)]  

19:45 (cur  prev) . . (+593) . . Foojt (talk  contribs)  
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19:25 (cur  prev) . . (+5,308) . . Foojt (talk  contribs) (Created page with "= Sufficient Statistics = Let <math display="inline">X_{1}..X_{n}</math> be a random sample from a distribution with pmf/pdf <math display="inline">f\left(\left.\cdot\right\...") 

N 19:44  Lecture 9. C) Minimum Variance Estimators (2 changes  history) . . (+2,100) . . [Foojt (2×)]  

19:44 (cur  prev) . . (+585) . . Foojt (talk  contribs)  
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19:20 (cur  prev) . . (+1,515) . . Foojt (talk  contribs) (Created page with "= Minimum Variance Estimators = We usually focus our attention on unbiased estimators. Those that, one average, produce the correct result. The collection of '''unbiased est...") 

N 19:43  Lecture 9. B) Evaluating Estimators (2 changes  history) . . (+5,427) . . [Foojt (2×)]  

19:43 (cur  prev) . . (+621) . . Foojt (talk  contribs)  
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19:19 (cur  prev) . . (+4,806) . . Foojt (talk  contribs) (Created page with "= Evaluating Estimators = A good estimator of <math display="inline">\theta</math> is close to <math display="inline">\theta</math> in some probabilistic sense. For reasons o...") 

N 19:42  Lecture 9. A) Point Estimation (cont.) (2 changes  history) . . (+2,909) . . [Foojt (2×)]  

19:42 (cur  prev) . . (+406) . . Foojt (talk  contribs)  
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19:15 (cur  prev) . . (+2,503) . . Foojt (talk  contribs) (Created page with "= Point Estimation (cont.) = == Example: Uniform == Suppose <math display="inline">X_{i}\overset{iid}{\sim}U\left(0,\theta\right)</math> where <math display="inline">\theta>...") 
19 August 2019

18:27  Gradlevel Probability and Statistics Lecture Notes (3 changes  history) . . (+387) . . [Foojt (3×)]  

18:27 (cur  prev) . . (+18) . . Foojt (talk  contribs)  

18:27 (cur  prev) . . (+37) . . Foojt (talk  contribs)  

18:07 (cur  prev) . . (+332) . . Foojt (talk  contribs) 
N 18:05  Full Lecture 8 (diff  hist) . . (+163) . . Foojt (talk  contribs) (Created page with "= Lecture 8 = {{#lst:Lecture_8._A)_Point_Estimationsection1}} {{#lst:Lecture_8._B)_Method_of_Momentssection1}} {{#lst:Lecture_8._C)_Maximum_Likelihoodsection1}}") 

N 18:04  Full Lecture 7 (2 changes  history) . . (+205) . . [Foojt (2×)]  

18:04 (cur  prev) . . (32) . . Foojt (talk  contribs)  
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18:03 (cur  prev) . . (+237) . . Foojt (talk  contribs) (Created page with "= Lecture 7 = {{#lst:Lecture Lecture_7._A)_Random_Samplesection1}} {{#lst:Lecture Lecture_7._B)_Statisticssection1}} {{#lst:Lecture Lecture_7._C)_Order_Statisticssection1}}...") 

N 18:01  Lecture 8. C) Maximum Likelihood (2 changes  history) . . (+5,304) . . [Foojt (2×)]  

18:01 (cur  prev) . . (+328) . . Foojt (talk  contribs)  
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17:52 (cur  prev) . . (+4,976) . . Foojt (talk  contribs) (Created page with "= Maximum Likelihood = Let <math display="inline">X_{1}..X_{N}</math> be a random sample from a distribution with pmf/pdf <math display="inline">f\left(\left\cdot\right.\the...") 

N 18:00  Lecture 8. B) Method of Moments (3 changes  history) . . (+9,474) . . [Foojt (3×)]  

18:00 (cur  prev) . . (+20) . . Foojt (talk  contribs)  

17:58 (cur  prev) . . (+533) . . Foojt (talk  contribs)  
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17:49 (cur  prev) . . (+8,921) . . Foojt (talk  contribs) (Created page with "= Method of Moments = == Example: Bernoulli == We start with an example. Suppose <math display="inline">X_{i}\sim Ber\left(p\right)</math>, where <math display="inline">p\in...") 

N 17:57  Lecture 8. A) Point Estimation (2 changes  history) . . (+1,362) . . [Foojt (2×)]  

17:57 (cur  prev) . . (+390) . . Foojt (talk  contribs)  
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17:42 (cur  prev) . . (+972) . . Foojt (talk  contribs) (Created page with "= Point Estimation = Let <math display="inline">X_{1}..X_{n}</math> be a random sample from a distribution with cdf <math display="inline">F\left(\left.\cdot\right\theta\rig...") 

N 17:56  Lecture 7. D) Statistical Inference (2 changes  history) . . (+1,818) . . [Foojt (2×)]  

17:56 (cur  prev) . . (+324) . . Foojt (talk  contribs)  
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17:40 (cur  prev) . . (+1,494) . . Foojt (talk  contribs) (Created page with "= Statistical Inference = This point marks the end of the introduction of the probability tools needed. Our goal now shifts, from situations where distributions are known and...") 

N 17:56  Lecture 7. C) Order Statistics (2 changes  history) . . (+2,742) . . [Foojt (2×)]  

17:56 (cur  prev) . . (+541) . . Foojt (talk  contribs)  
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17:40 (cur  prev) . . (+2,201) . . Foojt (talk  contribs) (Created page with "= Order Statistics = Let <math display="inline">X_{1}..X_{n}</math> be a random sample. The order statistics are the sample values placed in ascending order, i.e., <math dis...") 

N 17:55  Lecture 7. B) Statistics (2 changes  history) . . (+5,080) . . [Foojt (2×)]  

17:55 (cur  prev) . . (+533) . . Foojt (talk  contribs)  
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17:36 (cur  prev) . . (+4,547) . . Foojt (talk  contribs) (Created page with "= Statistics = Let <math display="inline">X_{1}..X_{n}</math> be a random sample and let <math display="inline">T:\mathbb{R}^{n}\rightarrow\mathbb{R}^{k}</math> be a function...") 

N 17:54  Lecture 7. A) Random Sample (2 changes  history) . . (+1,289) . . [Foojt (2×)]  

17:54 (cur  prev) . . (+362) . . Foojt (talk  contribs)  
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17:30 (cur  prev) . . (+927) . . Foojt (talk  contribs) (Created page with "= Random Sample = Let <math display="inline">X=\left(X_{1}..X_{n}\right)</math> be an ndimensional random vector. The random variables <math display="inline">X_{1}..X_{n}</ma...") 
18 August 2019
01:01  Gradlevel Probability and Statistics Lecture Notes (diff  hist) . . (+231) . . Foojt (talk  contribs) 

N 00:59  Full Lecture 6 (2 changes  history) . . (+415) . . [Foojt (2×)]  

00:59 (cur  prev) . . (56) . . Foojt (talk  contribs)  
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00:58 (cur  prev) . . (+471) . . Foojt (talk  contribs) (Created page with "= Lecture 6 = {{#lst:Lecture Lecture 6. A) Multiple Random Variables (cont.)section1}} {{#lst:Lecture Lecture 6. B) Conditional PMF/PDFsection1}} {{#lst:Lecture Lecture 6. C...") 
00:57  Lecture 6. G) Some Inequalities (diff  hist) . . (+364) . . Foojt (talk  contribs) 
00:55  Lecture 6. F) Covariance and Correlation (diff  hist) . . (+601) . . Foojt (talk  contribs) 
00:54  Lecture 6. E) Conditional Variance Identity (diff  hist) . . (+667) . . Foojt (talk  contribs) 
00:53  Lecture 6. D) Law of Iterated Expectations (diff  hist) . . (+609) . . Foojt (talk  contribs) 