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Liklehood ratio test
Let ... to be a fu) at ostco consider testing HoozOo vs. H,...
n be a random sample from a Gamma distribution with (a) Show there exists a uniformly most powerful test for testing Ho vs H. Show that the critical region can be expressed as an inequality for Y-:-1...
n be a random sample from a Gamma distribution with (a) Show there exists a uniformly most powerful test for testing Ho vs H. Show that the critical region can be expressed as an inequality for Y-:-1X, that is it will have the form [Y>cor the form Y < c]. Explain which one of the two and why (b) Is there a uniformly most powerful test for testing Ho : θ 1 vs H1 : θメ1? axqplai
n be a...
2. Let Xi, , Х, be a random sample gamma(a, β). In parts (a-(d) assume a is known. 30 points a. Consider testing H. : β--βο. Derive Wald statistic for testing H, using the MLE of B both in the nu...
2. Let Xi, , Х, be a random sample gamma(a, β). In parts (a-(d) assume a is known. 30 points a. Consider testing H. : β--βο. Derive Wald statistic for testing H, using the MLE of B both in the numerator and denominator of the statistic. b. Derive a test statistic for testing H, using the asymptotic distribution of the MLE of β. What is the relation between the two statistics in parts (a) and (b)? c. Derive the Score...
4. Let X,X,Bernoulli(p), and let Y Xi. Then we know that Y-Binomial(n.p) Consider the hypotheses Hop-Po...
4. Let X,X,Bernoulli(p), and let Y Xi. Then we know that Y-Binomial(n.p) Consider the hypotheses Hop-Po against Hip#po- a. c. For the particular case of po0.25 and n 5, fill in the table: 0 3 4 λ(y) P(Y - y) Find the (generalized) likelihood ratio test φ(y) of size α for testing Ho:p-po vs. H,: p d. po. Your test should be expressed in terms of y and α.
. Let Yi.... Yn be a random sample from a distribution with the density function 393 fe(y) =- Is there a UMP test at level α for testing Ho : θ test? vs. Hi : θ > 6? If so, what is the . Let...
. Let Yi.... Yn be a random sample from a distribution with the density function 393 fe(y) =- Is there a UMP test at level α for testing Ho : θ test? vs. Hi : θ > 6? If so, what is the
. Let Yi.... Yn be a random sample from a distribution with the density function 393 fe(y) =- Is there a UMP test at level α for testing Ho : θ test? vs. Hi : θ >...
Let X1, . . . , Xn ∼ independent N(µ, τ ) for µ known. Find the Likelihood Ratio Test for H0 : τ ...
Let X1, . . . , Xn ∼ independent N(µ, τ ) for µ known. Find the Likelihood Ratio Test for H0 : τ ≥ τ_0 vs H1 : τ < τ_0. Use the fact that MLE of τ is (1/n)S^2.
3. Let X,,X,,..., X, be a random sample from a Gamma 40distribution, where 6>0. we wish to test H0 : θ-1 vs. Hi : θ #1. Show that the likelihood ratio test statistic, A , can be written as A(V) wh...
3. Let X,,X,,..., X, be a random sample from a Gamma 40distribution, where 6>0. we wish to test H0 : θ-1 vs. Hi : θ #1. Show that the likelihood ratio test statistic, A , can be written as A(V) where a. What is the distribution of V? what is the null distribution of what will be the rejection region for an α level test? b. 20 d.
3. Let X,,X,,..., X, be a random sample from a Gamma 40distribution,...
LetX,X2, , XnLLd. Bernoulli(p), and let Y-Σ,Xi. Then we know that Y-Binomial(n, p). 5. Consider t...
LetX,X2, , XnLLd. Bernoulli(p), and let Y-Σ,Xi. Then we know that Y-Binomial(n, p). 5. Consider the hypotheses Hop-po against HA:p#po- a. Find the likelihood function of p in terms of random variable Y, L(p). b. Construct the (generalized) likelihood ratio λ(v). Hint: what is pMLE?] C. (i) For the particular case of po 0.25 and n 5, fill in the table: 3 4 A(y) (ii) Rearrange the table in the order of increasing of values of 2, and compute cumulative...
Degrees of Freedom of a Known Test 2 points possible graded) Let us consider a statistical...
Degrees of Freedom of a Known Test 2 points possible graded) Let us consider a statistical model with parameter ER". Let O be the parameter that generates the n lid samples X1,..., X, Let I ) be the Fisher information and assume that the MLE is asymptotically normal. Assume that I(C) is a diagonal matrix with positive entries 1/t1,...,1/td. We wish to perform a test for the hypotheses H : 8 - and H:8 + . Let the test statistic...
4. Find the critical region of the likelihood ratio test for testing the null hypothesis Ho...
4. Find the critical region of the likelihood ratio test for testing the null hypothesis Ho o aainst Ho on the basis of a random sample of sizen from a Follow the steps below normal population with the unknown mean for be the parameter space for(,o), and o be the subs et of 4-1) Let hypothesis , The parameter space can be expressed as Q= {-0< uo,0>0 Express similarly. (1 point) [Hint] 2 under the null hypothes is. Express the...
and with minitab please. 4. Consider the hypothesis test Ho: o? =ož vs. H: 0}<03. Suppose...
and
with minitab please.
4. Consider the hypothesis test Ho: o? =ož vs. H: 0}<03. Suppose that the sample sizes are nl = 5 and n2 = 10, and that S -23.2 and 53-28. Test this hypothesis using 5% significance.
n be a random sample from a Gamma distribution with (a) Show there exists a uniformly most powerful test for testing Ho vs H. Show that the critical region can be expressed as an inequality for Y-:-1X, that is it will have the form [Y>cor the form Y < c]. Explain which one of the two and why (b) Is there a uniformly most powerful test for testing Ho : θ 1 vs H1 : θメ1? axqplai
n be a...
2. Let Xi, , Х, be a random sample gamma(a, β). In parts (a-(d) assume a is known. 30 points a. Consider testing H. : β--βο. Derive Wald statistic for testing H, using the MLE of B both in the numerator and denominator of the statistic. b. Derive a test statistic for testing H, using the asymptotic distribution of the MLE of β. What is the relation between the two statistics in parts (a) and (b)? c. Derive the Score...
4. Let X,X,Bernoulli(p), and let Y Xi. Then we know that Y-Binomial(n.p) Consider the hypotheses Hop-Po against Hip#po- a. c. For the particular case of po0.25 and n 5, fill in the table: 0 3 4 λ(y) P(Y - y) Find the (generalized) likelihood ratio test φ(y) of size α for testing Ho:p-po vs. H,: p d. po. Your test should be expressed in terms of y and α.
. Let Yi.... Yn be a random sample from a distribution with the density function 393 fe(y) =- Is there a UMP test at level α for testing Ho : θ test? vs. Hi : θ > 6? If so, what is the
. Let Yi.... Yn be a random sample from a distribution with the density function 393 fe(y) =- Is there a UMP test at level α for testing Ho : θ test? vs. Hi : θ >...
3. Let X,,X,,..., X, be a random sample from a Gamma 40distribution, where 6>0. we wish to test H0 : θ-1 vs. Hi : θ #1. Show that the likelihood ratio test statistic, A , can be written as A(V) where a. What is the distribution of V? what is the null distribution of what will be the rejection region for an α level test? b. 20 d.
3. Let X,,X,,..., X, be a random sample from a Gamma 40distribution,...
LetX,X2, , XnLLd. Bernoulli(p), and let Y-Σ,Xi. Then we know that Y-Binomial(n, p). 5. Consider the hypotheses Hop-po against HA:p#po- a. Find the likelihood function of p in terms of random variable Y, L(p). b. Construct the (generalized) likelihood ratio λ(v). Hint: what is pMLE?] C. (i) For the particular case of po 0.25 and n 5, fill in the table: 3 4 A(y) (ii) Rearrange the table in the order of increasing of values of 2, and compute cumulative...
Degrees of Freedom of a Known Test 2 points possible graded) Let us consider a statistical model with parameter ER". Let O be the parameter that generates the n lid samples X1,..., X, Let I ) be the Fisher information and assume that the MLE is asymptotically normal. Assume that I(C) is a diagonal matrix with positive entries 1/t1,...,1/td. We wish to perform a test for the hypotheses H : 8 - and H:8 + . Let the test statistic...
4. Find the critical region of the likelihood ratio test for testing the null hypothesis Ho o aainst Ho on the basis of a random sample of sizen from a Follow the steps below normal population with the unknown mean for be the parameter space for(,o), and o be the subs et of 4-1) Let hypothesis , The parameter space can be expressed as Q= {-0< uo,0>0 Express similarly. (1 point) [Hint] 2 under the null hypothes is. Express the...
and
with minitab please.
4. Consider the hypothesis test Ho: o? =ož vs. H: 0}<03. Suppose that the sample sizes are nl = 5 and n2 = 10, and that S -23.2 and 53-28. Test this hypothesis using 5% significance.
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