Question

Determine the form of a minimal sufficient statistic for a sample of size n from the...

Determine the form of a minimal sufficient statistic for a sample of size n from the Uniform[0,θ] model where θ> 0

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose that (X1, · · · , Xn) is a random sample from uniform distribution U(0,...
Suppose that (X1, · · · , Xn) is a random sample from uniform distribution U(0, θ). (a) Prove that T(X1, · · · , Xn) = X(n) is minimal sufficient for θ. (X(n) is the largest order statistic, i.e., X(n) = max{X1, · · · , Xn}.) (b) In addition, we assume θ ≥ 1. Find a minimal sufficient statistic for θ and justify your answer.
Show that the sum of the observations of a random sample of size n from a...
Show that the sum of the observations of a random sample of size n from a gamma distribution that has pdf f(x; θ) = (1/θ)e^(−x/θ), 0 < x < ∞, 0 < θ < ∞, zero elsewhere, is a sufficient statistic for θ. Use Neyman's Factorization Theorem.
Let Y1, · · · , yn be a random sample of size n from a...
Let Y1, · · · , yn be a random sample of size n from a beta distribution with parameters α = θ and β = 2. Find the sufficient statistic for θ.
Suppose a random sample of size n is drawn from the pdf f(sub)Y(y;θ) =1/θ, 0 ≤...
Suppose a random sample of size n is drawn from the pdf f(sub)Y(y;θ) =1/θ, 0 ≤ y ≤ θ. Find a sufficient statistic for θ.
Let Y1,Y2,...,Yn denote a random sample of size n from a population with a uniform distribution...
Let Y1,Y2,...,Yn denote a random sample of size n from a population with a uniform distribution on the interval (0,θ). Let Y(n)= max(Y1,Y2,...,Yn) and U = (1/θ)Y(n) . a) Show that U has cumulative density function 0 ,u<0, Fu (u) =   un ,0≤u≤1, 1 ,u>1
Suppose that X1,..., Xn form a random sample from the uniform distribution on the interval [0,θ],...
Suppose that X1,..., Xn form a random sample from the uniform distribution on the interval [0,θ], where the value of the parameter θ is unknown (θ>0). (1)What is the maximum likelihood estimator of θ? (2)Is this estimator unbiased? (Indeed, show that it underestimates the parameter.)
Let X be the mean of a random sample of size n from a N(θ, σ2)...
Let X be the mean of a random sample of size n from a N(θ, σ2) distribution, −∞ < θ < ∞, σ2 > 0. Assume that σ2 is known. Show that X 2 − σ2 n is an unbiased estimator of θ2 and find its efficiency.
Let X1, X2,...,Xn be a random sample from Bernoulli (p). Determine a sufficient statistic for p...
Let X1, X2,...,Xn be a random sample from Bernoulli (p). Determine a sufficient statistic for p and derive the UMVUE and MLE of T(p)=p^2(1-p)^2.
a. If ? ̅1 is the mean of a random sample of size n from a...
a. If ? ̅1 is the mean of a random sample of size n from a normal population with mean ? and variance ?1 2 and ? ̅2 is the mean of a random sample of size n from a normal population with mean ? and variance ?2 2, and the two samples are independent, show that ?? ̅1 + (1 − ?)? ̅2 where 0 ≤ ? ≤ 1 is an unbiased estimator of ?. b. Find the value...
Suppose that X1,...,Xn ∼ U(0,θ); that is, a sample of N observations from a random variable...
Suppose that X1,...,Xn ∼ U(0,θ); that is, a sample of N observations from a random variable with a uniform distribution where the lower bound is 0 and the upper bound θ is unknown. Find the maximum likelihood estimate of θ, also demonstrating this in R. Draw the pdf and the likelihood, and explain what they represent, in R.