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Sufficient statistic - Wikipedia
https://en.wikipedia.org:443/wiki/Sufficient_statistic
WebIn statistics, a statistic is sufficient with respect to a statistical model and its associated unknown parameter if "no other statistic that can be calculated from the same sample provides any additional information as to the value of the parameter".
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Lesson 24: Sufficient Statistics | STAT 415
https://online.stat.psu.edu:443/stat415/lesson/24
WebUpon completion of this lesson, you should be able to: To learn a formal definition of sufficiency. To learn how to apply the Factorization Theorem to identify a sufficient statistic. To learn how to apply the Exponential Criterion to identify a sufficient statistic.
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Lesson 24: Sufficient Statistics
https://online.stat.psu.edu:443/stat415/book/export/html/844
WebTherefore, the Factorization Theorem tells us that \(Y = \bar{X}\) is also a sufficient statistic for \(\lambda\)! If you think about it, it makes sense that \(Y = \bar{X}\) and \(Y=\sum_{i=1}^{n}X_i\) are both sufficient statistics, because if we know \(Y = \bar{X}\), we can easily find \(Y=\sum_{i=1}^{n}X_i\).
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1 Sufficient statistics - University of Arizona
https://www.math.arizona.edu:443/~tgk/466/sufficient.pdf
WebA statistic T = r(X1, X2, · · · , Xn) is a sufficient statistic if for each t, the conditional distribution of X1, X2, · · · , Xn given T = t and θ does not depend on θ. To motivate the mathematical definition, we consider the following “ex-periment.”. Let T = r(X1, · · · , Xn) be a sufficient statistic.
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Sufficient Statistic & The Sufficiency Principle: Simple Definition
https://www.statisticshowto.com:443/sufficient-statistic/
WebA sufficient statistic summarizes all of the information in a sample about a chosen parameter. For example, the sample mean , x̄, estimates the population mean , μ. x̄ is a sufficient statistic if it retains all of the information about the population mean that was contained in the original data points.
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Mathematical Statistics, Lecture 6 Sufficiency - MIT …
https://ocw.mit.edu:443/courses/18-655-mathematical-statistics-spring-2016/bbbca14a2009e47add8c7ea2a49daa41_MIT18_655S16_LecNote6.pdf
WebSufficiency: Factorization Theorem. Theorem 1.5.1 (Factorization Theorem Due to Fisher and Neyman). In a regular model, a statistic T (X ) with range T is sufficient for θ ∈ Θ, iff there exists functions g(t, θ) : T × Θ → R and h : X → R, such that p(x | θ) = g(T (x), θ)h(x), for all x ∈ X and θ ∈ Θ.
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7.6: Sufficient, Complete and Ancillary Statistics
https://stats.libretexts.org:443/Bookshelves/Probability_Theory/Probability_Mathematical_Statistics_and_Stochastic_Processes_(Siegrist)/07%3A_Point_Estimation/7.06%3A_Sufficient_Complete_and_Ancillary_Statistics
WebApr 24, 2022 · A sufficient statistic contains all available information about the parameter; an ancillary statistic contains no information about the parameter. The following result, known as Basu's Theorem and named for Debabrata Basu, makes this point more precisely.
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Sufficient Statistics - University of Arizona
https://www.math.arizona.edu:443/~jwatkins/sufficiency.pdf
WebDefinition 1. For observations X1, . . . , Xn, the statistic T, is called a sufficient statistic if equation (1) is a function of the values, t, of the statistic and does not depend on the value of the parameter θ. Pθ{X1 = x1, . . . , Xn = xn} = P{X1 …
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Sufficient Statistics | SpringerLink
https://link.springer.com:443/referenceworkentry/10.1007/978-3-642-04898-2_581
WebJan 1, 2014 · A statistic T is called complete sufficient for θ if and only if (1) T is sufficient for θ and (2) T is complete. A complete sufficient statistic, if it exists, is also a minimal sufficient statistic. For example, let X 1, …, X n be iid Uniform(0, θ) where θ ∈ ℜ + is unknown.
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Sufficient statistic - Encyclopedia of Mathematics
https://encyclopediaofmath.org:443/wiki/Sufficient_statistic
WebJun 6, 2020 · A sufficient statistic is known as minimal or necessary if it is a function of any other sufficient statistic. A necessary sufficient statistic realizes the utmost possible reduction of a statistical problem. In the examples discussed above the obtained sufficient statistics are also necessary.
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