Homework Help is Here – Start Your Trial Now!
Math
Statistics
Consider the statistical linear model Y = A0+ € with m = 6 obser- vations, a parameter vector 0 = (01, 02, 03) with n = 3 components and €~ N(0; 200²16) having mean 0 and component variance 200². A realisation of this model for data Y and design matrix A is given by 580.8 -140.2 219.0 -64.5 73.4 403.8 = 87 1 2 3 1 734 635 2 15 573 0₁ 02 03 + €1 €3 EA €5 €6 (a) Find the Maximum Likelihood (ML) estimate of and the co- variance matrix Cov() of the ML estimate (b) If has prior distribution ~ N(0, 10213), then find the distribu- tion of posterior (0Y) using ridge regression. (c) Show that the component correlations Corr((0; Y), (0, Y)) of (0Y) are smaller than those of Corr(,) of the ML estimate for i ‡j.

Consider the statistical linear model Y = A0+ € with m = 6 obser- vations, a parameter vector 0 = (01, 02, 03) with n = 3 components and €~ N(0; 200²16) having mean 0 and component variance 200². A realisation of this model for data Y and design matrix A is given by 580.8 -140.2 219.0 -64.5 73.4 403.8 = 87 1 2 3 1 734 635 2 15 573 0₁ 02 03 + €1 €3 EA €5 €6 (a) Find the Maximum Likelihood (ML) estimate of and the co- variance matrix Cov() of the ML estimate (b) If has prior distribution ~ N(0, 10213), then find the distribu- tion of posterior (0Y) using ridge regression. (c) Show that the component correlations Corr((0; Y), (0, Y)) of (0Y) are smaller than those of Corr(,) of the ML estimate for i ‡j.

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 1E
See similar textbooks
icon
Related questions
Question
Consider the statistical linear model Y = A0 + e with m = vations, a parameter vector 0 = (61,02, 03)" with n = 3 components and e ~ N(0; 200² I6) having mean 0 and component variance 200². A realisation of this model for data Y and design matrix A is given by 8 7 1 6 obser- €1 580.8 -140.2 2 3 1 €2 219.0 7 3 4 €3 02 Өз -64.5 6 3 5 €4 73.4 2 1 5 E5 403.8 5 7 3 €6 (a) Find the Maximum Likelihood (ML) estimate 0 of 0 and the co- variance matrix Cov(@) of the ML estimate ở (b) If 0 has prior distribution 0 ~ N(0, 10²I3), then find the distribu- tion of posterior (0|Y) using ridge regression. (c) Show that the component correlations Corr(0;|Y), (0;|Y)) of (0|Y) are smaller than those of Corr(0;, 0;) of the ML estimate 0 for i + j.
Transcribed Image Text:Consider the statistical linear model Y = A0 + e with m = vations, a parameter vector 0 = (61,02, 03)" with n = 3 components and e ~ N(0; 200² I6) having mean 0 and component variance 200². A realisation of this model for data Y and design matrix A is given by 8 7 1 6 obser- €1 580.8 -140.2 2 3 1 €2 219.0 7 3 4 €3 02 Өз -64.5 6 3 5 €4 73.4 2 1 5 E5 403.8 5 7 3 €6 (a) Find the Maximum Likelihood (ML) estimate 0 of 0 and the co- variance matrix Cov(@) of the ML estimate ở (b) If 0 has prior distribution 0 ~ N(0, 10²I3), then find the distribu- tion of posterior (0|Y) using ridge regression. (c) Show that the component correlations Corr(0;|Y), (0;|Y)) of (0|Y) are smaller than those of Corr(0;, 0;) of the ML estimate 0 for i + j.
Expert Solution
steps

Step by step

Solved in 4 steps with 30 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
SEE MORE TEXTBOOKS