4.Suppose that Y is a random variable whose density function isf(y|0) = 1-0 (y- -1), 0≤y≤1,where 0 << 1 is a parameter.(a) Based on only this single Y, determine the rejection region of the likelihood ratio test ofHo: 0= 1/4 against HA: 0 = 1/2 at significance level a where 0 < a < 1. Be sure to expressyour rejection region in terms of a. There should be no arbitrary constants in your answer.(b) Determine the power of the test you constructed in (a)? (Express your answer in terms of a.)(c) Based on only this single Y, determine the rejection region of the likelihood ratio test ofHo: 0= 1/2 against HA: 0 = 1/4 at significance level a where 0 < a < 1. Be sure to expressyour rejection region in terms of a. There should be no arbitrary constants in your answer.(d) Determine the power of the test you constructed in (c)? (Express your answer in terms of a.)

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Answered: f(y|0)=1-0(y- • (1-1), OSU≤1, where 0…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider the maximum likelihood estimation of a parameter 0 and a test of the hypothesis Ho: c(0) = 0. Describe the 3 basic approaches used for testing the hypothesis.
If the coefficient B₁ has a nonzero value, then it is helpful in predicting the value of the response variable. If B₁ = 0, it is not helpful in predicting the value of the response variable and can be eliminated from the regression equation. To test the claim that B₁ = 0 use the test statistic t = (b₁-0) /sp. Critical values or P-values can be found using the t distribution with n - (k+1) degrees of freedom, where k is the number of predictor (x) variables and n is the number of observations in the sample. The standard error sp, is often provided by software. For example, see the accompanying technology display, which shows that sp=0.076885101 (found in the column with the heading of "Std. Err." and the row corresponding to the first predictor variable of height). Use the technology display to test the claim that B₁ = 0. Also test the claim that B₂ = 0. What do the results imply about the regression equation? Click the icon to view the technology output. Test the claim that B₁ = 0. For…
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(4) Consider n i.i.d. samples of X ~ N(µ,0²). Find the maximum likelihood estimate of o?.
Assume that we estimate a model and that we're holding other things constant in a hypothesis test about a single parameter in that model. If the degrees of freedom are higher, the critical value(s) of the t-distribution under the null (Used to determine the rejection region(s) for the test)will be? (A) Unchanged (B) Lower in magnitude (C) Greater in magnitude
Heteroskedasticity arises because of non-constant variance of the error terms. We said proportional heteroskedasticity exists when the error variance takes the following structure: Var(et)=σt^2=σ^2 xt. But as we know, that is only one of many forms of heteroskedasticity. To get rid of that specific form of heteroskedasticity using Generalized Least Squares, we employed a specific correction – we divided by the square root of our independent variable x. And the reason why that specific correction worked, and yielded a variance of our GLS estimates that was sigma-squared, was because of the following math: (Picture 1) Where var(et)=σ^2 according to our LS assumptions. In other words, dividing everything by the square root of x made this correction work to give us sigma squared at the end of the expression. But if we have a different form of heteroskedasticity (i.e. a difference variance structure), we have to do a different correction to get rid of it. (a) what correction would you use…
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