Question: Let X = (X,..., Xn) be a random sample from N(0, 1), where 0 = 0 or 1. Consider the estimation of 0 with

Let X = (X,..., Xn) be a random sample from N(0, 1),

Let X = (X,..., Xn) be a random sample from N(0, 1), where 0 = 0 or 1. Consider the estimation of 0 with action space {0, 1}, i.e., the range of any estimator is {0, 1}. (i) Show that there does not exist any unbiased estimator of 0. (ii) Find an estimator lim, E() = 0. of that is approximately unbiased, that is,

Step by Step Solution

★★★★★

3.43 Rating (166 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Solution i Since the action space is 0 1 any randomized estim... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Let X1, X2,..., Xn be a random sample from a uniform distribution on the interval [0, Ã¸], so that Then if Y = max (Xi), it can be shown that the rv U = Y/Ã¸ has density...

Let X1, X2,..., Xn be a random sample from a continuous probability distribution having median m, (so that P(Xi ¤ µÌ) = P(Xi ¥ µÌ) = .5). a. Show that So that...

Let X1,.., Xn be a random sample from a population with mean Î¼ and variance Ï2. (a) Show that the estimator is an unbiased estimator of Î¼ if (b) Among all unbiased...

Let X, ...,Xn be a random sample from a GEO() distribution and let the prior distribution of be BETA(2, 2). (i) Find the posterior distribution (|x) and obtain the Bayes estimator of assuming...

5. Let (X1, X2, . .., Xn) be a random sample from a Poisson()) distribution where A is an unknown parameter. (a) Suppose that the sample size n is large. Find a pivotal variable in terms of the...

2) Let X1, X2, ...Xn are i.i.d random sample from U(0, 0). We know that X(n) = Max(X1, X2, .Xn) is sufficient for e. (20 points) a) Recall the distribution of 7 = X() and find the MVUE of 0" where r...

Let X1, X2, . . . , Xn be a random sample from N(0, 2). (1) Find a sufficient statistic Y for 2. (2) Show that the maximum likelihood estimator for 2 is a function of Y . (3) Is the maximum...

5. (10 points) Let X1, X2, .... Xn be a random sample from f(r; 0) = de-1(0.09)(r). Find a 100y or (1 - a)100 percent confidence interval for the mean of the population

4. Let X1, X2, ..., Xn be a random sample from N(0,0), 0 > 0. Give an example of a pivotal quantity, and use it to obtain a confidence-interval estimator of 0

Subject: Statistical Interference-1) Q1 : Let X1, X2... Xn be the random sample from the density: (, ) = (1 + ) (1+) , 0

Without the consent of the entity, a CPA should not disclose confidential entity information contained in working papers to a(n) a. Authorized quality control review board. b. CPA firm that has been...

What is hatching? What advantage is provided by investment casting hatch styles?

Which of the following are typically factors used to apportion income? Multiple select question. Sales Payroll Property Income

A rectangular loop of wire in free space joins points A (1,0,1) to B (3,0,1) to C (3,0,4) to D (1,0,4) to A again. The wire carries a current of 6mA, flowing in the az direction from B to C. A...

ne of the organic compounds whose structure is given below, when undergoes combustion evolved 43.5 MJ/Kg heat. Find out the heat of combustion of this compound in J/g. ON NO2 NO2 Select one: O a 1.92...

3. The following table shows the cash flows of the investment in a financial product XYZ: Year Cash Flow ($) -150,000 1 72,000 3 82,000 5 10,500 Suppose that the annual interest rate of the...

From the given sentences, choose the sentence in which prepositions, adverbs, or phrasal verbs are used correctly. The names of the A students are listed by alphabetical order. Take those dirty shoes...

From the given sentences, choose the sentence in which prepositions, adverbs, or phrasal verbs are used correctly. The three friends had a A lot of common. The distance from one B) city until the...

What are those two Congresses, how are they different, and how does that impact how a newly-elected member might do her job

Order Statistics. Let X1, X2, , Xn be a random sample of size n from X, a random variable having distribution function F(x). Rank the elements in order of increasing numerical magnitude, resulting in...

Consider the problem of generating a random sample Iron, a specified distribution on a single variable. You can assume that a random number generator is available that returns a random number...

The discrepancies between p-values and Bayes posterior probabilities are not as dramatic in the one-sided problem, as is discussed by Casella and Berger (1987) and also mentioned in the Miscellanea...

Consider a random process X (t) expanded in the form N, where W? (t) is a remainder noise term. The {? i? (t)} N i = 1 form an orthonormal set over interval 0 ? t ? T, and the X j are defined by. Let...

I need help with finding the proof and logic of sequence (ii). It is similar to that of sequence (i) provided bellow: 2.2.2 Continuity of algebraic operations Limits interact nicely with algebraic...

5. (i) Let X = (Xl' . . . , Xn) have probability density (1/0 n)f[(XI - ~)/O" ",(xn - ~)/O] where -00