Prove the following analogs to Stein 's Lemma, assuming appropriate conditions on the function g (a) If X gamma( Icirc plusmn , Icirc sup2 ), then E(g(X)(X a Icirc sup2 ) Icirc sup2 E (Xg '(X)) (b) If X beta(a, Icirc sup2 ), then (1 X) Elg(X) ( (a 1) A2 ) E ((1 X)g,(X)) 1)...

a Let u gx du gx dv x x 1 e x v x e x Then Assuming gx to be di ...

Prove the following analogs to Stein's Lemma, assuming appropriate conditions on the function g. (a) If X

Question:

Prove the following analogs to Stein's Lemma, assuming appropriate conditions on the function g.
(a) If X ~ gamma(Î±, Î²), then
E(g(X)(X-aÎ²)= Î²E (Xg'(X)) .
(b) If X ~ beta(a, Î²), then

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Statistical Inference

ISBN: 978-0534243128

2nd edition

Authors: George Casella, Roger L. Berger

See More Books

Question Posted: May 26, 2016 05:18 AM

See More Questions

Prove Lemma 7.3.11.
Use Fishers Lemma to prove Theorem 12.2.2. jel i=1
Prove that the image of a span equals the span of the images. That is, where h: V W is linear, prove that if S is a subset of V then h([S]) equals [h(S)]. This generalizes Lemma 2.1 since it shows...
Please help I am confused and really stuck here and can't properly answer this one. Does it meet all the assumptions? b. Do the data meet all the assumptions of the appropriate statistical test...
What accounting concept justifies charging low-cost plant asset purchases immediately to an expense account?
Use the principle of minimum potential energy developed in Section 2.6 to solve the spring problems shown in Figure P2-18. That is, plot the total potential energy for variations in the displacement...
A study in one state compared the traffic fatality rates (number of fatalities per miles driven) on highways with 55, 65, and 75 miles per hour speed limits. They found that highways with a 75 mph...
Last year, Douthett Inc. had sales of $2,400,000, based on a unit selling price of $600. The variable cost per unit was $440, and fixed costs were $544,000. The maximum sales within Douthetts...
How do advances in digital communication technologies reshape the landscape of interpersonal relationships and social dynamics ?
Sachs Brands's defined benefit pension plan specifies annual retirement benefits equal to 1.3% * service years x final year's salary. payable at the end of each year. Angela Davenport was hired by...
Derive recursion relations, similar to the one given in (3.6.2), for the binomial, negative binomial, and hypergeometric distributions.
A standard drug is known to be effective in 80% of the cases in which it is used. A new drug is tested on 100 patients and found to be effective in 85 cases. Is the new drug superior? (Evaluate the...
Matrix Accounting pays all salaried employees biweekly. Overtime pay, however, is paid in the next biweekly period. Matrix accrues salary expense only at its December 31 year end. Information about...
A truck costs $90,000 when new and has accumulated depreciation of $80,000. Suppose Dave Towing exchanges the truck for a new truck. The new truck has a market value of $72,000, and Dave pays cash of...
An operating system is a program that manages the complete operation of your computer or mobile device and lets you interact with it. a. True b. False
Suppose Wildhorse Company uses a periodic inventory system. Details related to inventory for the month of January are as follows: Units Unit Cost Total Balance, 1/1 280 $5.00 $1400 Purchase, 1/15 140...
Scipio Company had 1,000 common shares issued and outstanding at January 1. During the year, Scipio also had the common stock transactions listed below. April 1 Issued 300 previously unissued shares...
On January 1, 2024, Blossom issued $6,300,000, 10% bonds. Interest is payable semi-annually on June 30 and December 31. The bonds mature on January 1, 2034. The bonds are sold to yield 12%.
You have been issued a patent giving you exclusive rights to sell a new type of software. You believe the patent will produce sales of $200,000 each year as long as the software remains in demand....
Use critical values to test the null hypothesis H0: 1 2 = 20 versus the alternative hypothesis H0: 1 2 20 by setting a equal to .10, .05, .01, and .001. How much evidence is there that the...
In bowling, it is often possible to score well in the first game and then bowl poorly in the second game, or vice versa. The following six pairs of numbers give the scores of the first and second...
By squaring the binomial expression [(Yi ) (SxY/s2x)(xi )], show that ri i-1 i=1 equals (n-1)S,(1-R2), where Xi = xi,X2 = X2, ,
In sampling from a bivariate normal distribution, it is true that the sample correlation coefficient R has an approximate normal distribution N[, (1 2)2/n] if the sample size n is large. Since, for...
The quality-control department of Starr Communications, the manufacturer of video-game DVDs, has determined from records that 1.6% of the DVDS sold have video defects, 0.9% have audio defects, and...
What is the half-life in hours of procainamide in a patient whose total clearance is estimated to be 20 L/h and the volume of distribution is 120 L assuming one compartment, open model, first- order...
1. The technologies, such as ChatGPT, has been launched before introducing even a baseline of safety measures. This goes back to trade-offs that companies make, and people just watch the impact from...

Prove the following analogs to Stein's Lemma, assuming appropriate conditions on the function g. (a) If X

Question:

(1 - X) Elg(X) (β- (a-1)-A2 ) | = E ((1-X)g,(X)) 1)

Step by Step Answer:

a Let u gx du gx dv x x 1 e x v x e x Then Assuming gx to be di...View the full answer

Statistical Inference

Students also viewed these Statistics questions