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Show new changes starting from 20:21, 21 August 2019
   
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20 August 2019

     19:54  Grad-level 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_Estimators|section1}} {{#lst:Lecture_10._B)_Complete_Statistic|section1}} {{#lst:Lecture_10._C)_Cramer-Rao_Lower_Bound|sectio...")
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_Estimators|section1}} {{#lst:Lecture_9._C)_Minimum_Variance_Estimators|s...")
N    19:50  Lecture 10. C) Cramer-Rao 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 "= Cramér-Rao 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 Rao-Blackwell’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) Rao-Blackwell‎‎ (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 "= Rao-Blackwell Theorem = The Rao-Blackwell 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  Grad-level 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_Estimation|section1}} {{#lst:Lecture_8._B)_Method_of_Moments|section1}} {{#lst:Lecture_8._C)_Maximum_Likelihood|section1}}")
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_Sample|section1}} {{#lst:Lecture Lecture_7._B)_Statistics|section1}} {{#lst:Lecture Lecture_7._C)_Order_Statistics|section1}}...")
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 n-dimensional random vector. The random variables <math display="inline">X_{1}..X_{n}</ma...")

18 August 2019

     01:01  Grad-level 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/PDF|section1}} {{#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)