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Additionally, for 6.1.3, let 0MLE denote your MLE of 0, and show that (a) MLE is a consistent estimator of 0, i.e., LE 0, as n →x. [Hints will be given in class on this.] (b) Consider the MLE given by MLE distribution of Zn. = = Yn − ½ and put Zn = n(0 – ÔMLE). Find the limiting

Additionally, for 6.1.3, let 0MLE denote your MLE of 0, and show that (a) MLE is a consistent estimator of 0, i.e., LE 0, as n →x. [Hints will be given in class on this.] (b) Consider the MLE given by MLE distribution of Zn. = = Yn − ½ and put Zn = n(0 – ÔMLE). Find the limiting

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 5E
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Additionally, for 6.1.3, let AMLE denote your MLE of 0, and show that (a) MLE is a consistent estimator of 0, i.e., ÔMLE ² 0, as n → ∞. [Hints will be given in class on this.] (b) Consider the MLE given by ÎMLE = Y₂ −/ and put Zn = n(0-MLE). Find the limiting distribution of Zn.
Transcribed Image Text:Additionally, for 6.1.3, let AMLE denote your MLE of 0, and show that (a) MLE is a consistent estimator of 0, i.e., ÔMLE ² 0, as n → ∞. [Hints will be given in class on this.] (b) Consider the MLE given by ÎMLE = Y₂ −/ and put Zn = n(0-MLE). Find the limiting distribution of Zn.
6.1.3. Let Y₁ < Y₂ < · · < Yn be the order statistics of a random sample from a distribution with pdf f(x; 0) = 1, 0 – 21/12 ≤ x ≤ 0 + 1/2, -∞ <<∞, zero elsewhere. This is a nonregular case. Show that every statistic u(X₁, X2, ..., Xn) such that Yn ≤u(X₁, X2, ..., Xn) ≤ Y₁ + 1/2 6.1. Maximum Likelihood Estimation 361 is a mle of 0. In particular, (4Y₁ + 2Yn +1)/6, (Y₁ + Yn)/2, and (2Y₁ +4Yn − 1)/6 are three such statistics. Thus, uniqueness is not, in general, a property of mles.
Transcribed Image Text:6.1.3. Let Y₁ < Y₂ < · · < Yn be the order statistics of a random sample from a distribution with pdf f(x; 0) = 1, 0 – 21/12 ≤ x ≤ 0 + 1/2, -∞ <<∞, zero elsewhere. This is a nonregular case. Show that every statistic u(X₁, X2, ..., Xn) such that Yn ≤u(X₁, X2, ..., Xn) ≤ Y₁ + 1/2 6.1. Maximum Likelihood Estimation 361 is a mle of 0. In particular, (4Y₁ + 2Yn +1)/6, (Y₁ + Yn)/2, and (2Y₁ +4Yn − 1)/6 are three such statistics. Thus, uniqueness is not, in general, a property of mles.
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