2. Suppose that Y; ~ N(Bxi, o²) for i = 1, 2, ..., n, all independent, where x; is a knowncovariate.(a) Find the Fisher information matrix.(b) State the asymptotic distributions of the maximum likelihood estimators ß and ô?of B and o?.(c) Explain why the distribution of 3 is exact.

Given that Yi~Nβxi, σ2 for i=1, 2, ...,n, all independent, where xi is a known covariate.

Answered: 2. Suppose that Y; ~ N(Bxi,o²) for i =…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

12. Define a Gamma distribution and prove that the sum of two independent Gamma variates with parameters I and m is a Gamma variate with parameter 1 + m.
If X is a uniformly distributed random varibale with a=8 and b=13, then Calculate the mean and variance of X? Round to three decimal places
2) Let X₁, X2, X3, X4 be a random sample of size 4 from a population with the following distribution function Where, ß > 0. 1 f(x; 0) = B 0, e (x-4) B for x > 4 otherwise f) Is the maximum likelihood estimator of the parameter ß unbiased or not? g) What is the maximum likelihood estimator of g (B) = 2(B + 1). h) Is the maximum likelihood estimator of g (B) = 2(ß + 1) unbiased or not?
Suppose that the unknown X is uniformly distributed between 0 and 2. What is the expected value of (4X3 + 1)?
7. Let (z,.,) be a random sample from a normal distribution with mean ja and a variance at. Alo let S.. = , - z)* be the sum of squares of the randou sample. State without proof the sampling distribution of the following; (a) t(z) - ạ + b i-, 1,. n, as e positive eal constants. (- ) (b) t(z) - (E) (x) = (e) ti2) - (g) (r) = (e) t(2) = (d) t(a) Er, - E > ( - P (h) 시)- - -1 (-) (e) t(z)
2) Let X₁, X2, X3, X4 be a random sample of size 4 from a population with the following distribution function Where, ß > 0. If fram e ¹- {** f(x;0)=B for x > 4 otherwise "1 g) What is the maximum likelihood estimator of g (B) = 2(ß + 1). h) Is the maximum likelihood estimator of g (B) = 2(B + 1) unbiased or not?
8) Consider the data (1,1), (3,9), (4,16), If f[1,3] = 4, f[3,4] = z, f[1,3,4] 1. find z %3D
Suppose model (XY, XZ, YZ) holds in a 2 x 2 x 2 table, and the common XY conditional log odds ratio at the two levels of Z is positive If the XY and YZ conditional log odds ratios are both positive or both negative, show that the XY marginal odds ratio is larger than the XY conditional odds ratio.
Please help me with this questions. thank you!
Please no written by hand solution
X, X, and X, is a random sample of size 3 from a population 2. with mean value u and variance o?, T., T, T, are the 2' *3 estimators used to estimate mean value u, where T=X,+X,-X, T,= 2X,+3X, - 4X, & T, %3D 3 2 1. 3. 2. 3 1 =(ax,+X,+X,) 3 1. (i) Are T, and T, unbiased estimators ? 1 2 (ii) Find the value of A such that T, is unbiased estimator 3 for u.
Let X1, X2, X3, be a r. s. from normal distribution with mean 0 and variance 1, let the prior distribution of 0 is normal with mean zeroand variance 1. Let L(6,0) = (ô - 0). Find the Bayes estimator of 0

SEE MORE QUESTIONS

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS

2. Suppose that Y; ~ N(Bxi,o²) for i = 1, 2, ..., n, all independent, where x; is a known covariate. (a) Find the Fisher information matrix. (b) State the asymptotic distributions of the maximum likelihood estimators ß and ô of B and o?. (c) Explain why the distribution of 3 is exact.