7.1.7. Let X₁, X2,..., Xn denote a random sample from a distribution that isN(μ, 0), 0 < 0 <∞, where is unknown. Let Y = Σ₁(Xi − X)²/n and letL[0, 8(y)] = [0-8(y)]². If we consider decision functions of the form 8(y) = by, whereb does not depend upon y, show that R(0, 8) = (0²/n²) [(n²-1)b²-2n(n-1)b+n²].Show that b = n/(n+1) yields a minimum risk decision function of this form. Notethat nY/(n + 1) is not an unbiased estimator of 0. With 8(y) = ny/(n + 1) and0 < 0 <∞, determine max, R(0,8) if it exists

Answered: Image /qna-images/answer/ba3a0ce2-f592-41a9-acad-dabf2a7df24d.jpg

7.1.7. Let X₁, X2,..., Xn denote a random sample from a distribution that is N(μ,0), 0 < 0 < x, where is unknown. Let Y = E(X₁ - X)²2/n and let L[0, 8(y)] = [0-8(y)]². If we consider decision functions of the form 8(y) = by, where b does not depend upon y, show that R(0, 8) = (02/n²)[(n²-1)6²-2n(n-1)b+n²]. Show that b = n/(n+1) yields a minimum risk decision function of this form. Note that nY/(n + 1) is not an unbiased estimator of 0. With 8(y) = ny/(n + 1) and 0 <0<∞, determine maxe R(0,8) if it exists

7.1.7. Let X₁, X2,..., Xn denote a random sample from a distribution that is N(μ,0), 0 < 0 < x, where is unknown. Let Y = E(X₁ - X)²2/n and let L[0, 8(y)] = [0-8(y)]². If we consider decision functions of the form 8(y) = by, where b does not depend upon y, show that R(0, 8) = (02/n²)[(n²-1)6²-2n(n-1)b+n²]. Show that b = n/(n+1) yields a minimum risk decision function of this form. Note that nY/(n + 1) is not an unbiased estimator of 0. With 8(y) = ny/(n + 1) and 0 <0<∞, determine maxe R(0,8) if it exists

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.

Chapter2: Exponential, Logarithmic, And Trigonometric Functions

Section2.CR: Chapter 2 Review

Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...

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