Use the problem of estimating θ for the Unif(0, θ) distribution to illustrate how the bootstrap c...
Use the problem of estimating θ for the Unif(0, θ) distribution to illustrate how the bootstrap can fail for extremes.
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Use the problem of estimating θ for the Unif(0, θ) distribution to illustrate how the bootstrap c...
Use the problem of estimating the mean of a standard Cauchy distribution to illustrate how the bo...
Use the problem of estimating the mean of a standard Cauchy distribution to illustrate how the bootstrap can fail for heavy-tailed distributions.
a) b) c) May be helpful to solve with simulation Unif(0, 1), what's the distribution of...
a)
b)
c) May be helpful to solve with simulation
Unif(0, 1), what's the distribution of -10 ln(U)? If U If U1, U2, U are i.i.d. Unif(0,1), what's the distribution of -3nU(1-U2 (1-U3))? If U and V are i.i.d. Unif(0,1), what's the distribution of -2 -ln(U)cos(27V) n(U )sin(27V)?
Unif(0, 1), what's the distribution of -10 ln(U)? If U
If U1, U2, U are i.i.d. Unif(0,1), what's the distribution of -3nU(1-U2 (1-U3))?
If U and V are i.i.d. Unif(0,1), what's the...
Select the appropriate response a)The bootstrap assumes that data is normally distributed b)The bootstrap is applicable...
Select the appropriate response a)The bootstrap assumes that data is normally distributed b)The bootstrap is applicable for any distribution of independently identically distributed random samples c)The bootstrap is applicable only to large samples Select the appropriate answer a)The bootstrap provides a procedure for estimating the uncertainty of parameter estimates b)The bootstrap provides a closed form formula for computing the uncertainty of any statistics c)The bootstrap provides an exact measure of uncertainty of distribution parameters Select the appropriate answer a)The bootstrap...
Additional Question i.i.d. ˆ Fix θ > 0 and let X1,...,Xn ∼ Unif[0,θ]. We saw in...
Additional Question i.i.d. ˆ Fix θ > 0 and let X1,...,Xn ∼
Unif[0,θ]. We saw in class that the MLE of θ, θMLE = max(X1, . . .
, Xn), is biased. I give two other estimators of θ, which can be
made unbiased by appropriate choice of constants C1, C2:
ADDITIONAL QUESTION Fix θ 0 and let Xi, . . . , Xn iid. Unifl0.0]. We saw in class that the MLE of θ, θΜ1E- max(Xi,..., Xn), is biased....
Fix θ > 0 and let Xi, , x, i d. Unif[0.0]. We saw in class...
Fix θ > 0 and let Xi, , x, i d. Unif[0.0]. We saw in class that the MLE of θ, oMLE- I give two other estimators of θ, which can be made unbiased by appropriate choice of -C1 max(Xs , . . . , X,) max(X., Xn), is biased. constants C1,C2 We have two questions: (1) Find values of C1, C2 for which these estimators are unbiased. Note that Ci,C2 may depend on n (2) Which of these estimators...
Consider X1,X2, , Xn be an iid random sample fron Unif(0.0). Let θ = (끄+1) Y where Y = max(X1, x...
Consider X1,X2, , Xn be an iid random sample fron Unif(0.0). Let θ = (끄+1) Y where Y = max(X1, x. . . . , X.). It can be easily shown that the cdf of Y is h(y) = Prp.SH-()" 1. Prove that Y is a biased estimator of θ and write down the expression of the bias 2. Prove that θ is an unbiased estimator of θ. 3. Determine and write down the cdf of 0 4. Discuss why...
Suppose X1 and X2 are continuous random variables with X1 ~ Unif(0, 1), X2 | X1...
Suppose X1 and X2 are continuous random variables with X1 ~ Unif(0, 1), X2 | X1 = x1 ~ Unif(0, X1) (a) Find the pdf for the joint distribution of X1 and X2 (b) Find the pdf for the marginal distribution of X1 (c) Find the pdf for the marginal distribution of X2 (d) Find the pdf for the conditional distribution of X1 | X2 = x2 (e) Write 1 or 2 sentences explaining how this problem relates to Bayes’...
Below is a bootstrap distribution of atlanta commute times. Please use the figure in the document...
Below is a bootstrap distribution of atlanta commute
times.
Please use the figure in the document titled Atlanta Commute
times; posted on canvas to answer the following 5
questions.
1- The number of bootstrap samples used is
a)100
b)1000
c)Unkown
2-The sample size is
a)100
b)1000
c)Unkown
3- The average commute time can be estimated as
4- The upper bounds for a 95% Confidence interval for the
actual commute time in Atlanta is :
5- The 99th percentile of the...
5.8 If the independent r v.'s X1 X have the u-θ 9) distribution 0€ Ω =...
5.8 If the independent r v.'s X1 X have the u-θ 9) distribution 0€ Ω = construct a moment estimate of θ? 0, o how can one (Hint: do not use the first moment.)
Problem 1. (Bootstrap tests for goodness-of-fit)We saw in lecture that when it comes togoodness-of-fit (GOF) testing, it...
Problem 1. (Bootstrap tests for goodness-of-fit)We saw in lecture that when it comes togoodness-of-fit (GOF) testing, it is quite “natural” to obtain a p-value by permutation. It is alsopossible, however, to use the bootstrap for that purpose. Consider the two-sample situation forsimplicity, although this generalizes to any number of samples. Thus assume a situation where weobserveX1, . . . , Xmiid fromFand (independently)Y1, . . . , Yniid fromG, whereFandGare twodistributions on the real line. We want to testF=GversusF6=G. We...
a)
b)
c) May be helpful to solve with simulation
Unif(0, 1), what's the distribution of -10 ln(U)? If U If U1, U2, U are i.i.d. Unif(0,1), what's the distribution of -3nU(1-U2 (1-U3))? If U and V are i.i.d. Unif(0,1), what's the distribution of -2 -ln(U)cos(27V) n(U )sin(27V)?
Unif(0, 1), what's the distribution of -10 ln(U)? If U
If U1, U2, U are i.i.d. Unif(0,1), what's the distribution of -3nU(1-U2 (1-U3))?
If U and V are i.i.d. Unif(0,1), what's the...
Additional Question i.i.d. ˆ Fix θ > 0 and let X1,...,Xn ∼
Unif[0,θ]. We saw in class that the MLE of θ, θMLE = max(X1, . . .
, Xn), is biased. I give two other estimators of θ, which can be
made unbiased by appropriate choice of constants C1, C2:
ADDITIONAL QUESTION Fix θ 0 and let Xi, . . . , Xn iid. Unifl0.0]. We saw in class that the MLE of θ, θΜ1E- max(Xi,..., Xn), is biased....
Fix θ > 0 and let Xi, , x, i d. Unif[0.0]. We saw in class that the MLE of θ, oMLE- I give two other estimators of θ, which can be made unbiased by appropriate choice of -C1 max(Xs , . . . , X,) max(X., Xn), is biased. constants C1,C2 We have two questions: (1) Find values of C1, C2 for which these estimators are unbiased. Note that Ci,C2 may depend on n (2) Which of these estimators...
Consider X1,X2, , Xn be an iid random sample fron Unif(0.0). Let θ = (끄+1) Y where Y = max(X1, x. . . . , X.). It can be easily shown that the cdf of Y is h(y) = Prp.SH-()" 1. Prove that Y is a biased estimator of θ and write down the expression of the bias 2. Prove that θ is an unbiased estimator of θ. 3. Determine and write down the cdf of 0 4. Discuss why...
Below is a bootstrap distribution of atlanta commute
times.
Please use the figure in the document titled Atlanta Commute
times; posted on canvas to answer the following 5
questions.
1- The number of bootstrap samples used is
a)100
b)1000
c)Unkown
2-The sample size is
a)100
b)1000
c)Unkown
3- The average commute time can be estimated as
4- The upper bounds for a 95% Confidence interval for the
actual commute time in Atlanta is :
5- The 99th percentile of the...
5.8 If the independent r v.'s X1 X have the u-θ 9) distribution 0€ Ω = construct a moment estimate of θ? 0, o how can one (Hint: do not use the first moment.)
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