Question: For multinomial sampling, use the asymptotic variance of log Î¸Ì to show that for Yules Q the asymptotic variance of Vn ( Q) is o?

For multinomial sampling, use the asymptotic variance of log θ̂ to show that for Yule€™s Q the asymptotic variance of

Vn (ệ – Q) is o? = (E;E;

Vn ( Q) is o? = (E;E;";')(1 - Q)/4 (Yule 1900, 1912).

Step by Step Solution

★★★★★

3.52 Rating (159 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

One can apply the delta method directly or else use wh... View full answer

blur-text-image
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 Categorical Data Analysis Questions!

Q:

Consider the model for a 2 2 table. 11 = 2 , 12 = 21 = (1 ), 22 = (1 ) 2 , where is unknown (Problems 3.31 and 10.34). a. Find the matrix A in (14.14) for this model. b. Use A to obtain the...

Q:

a. Refer to Problem 14.6. If T n is Poisson, show T n has asymptotic variance 1/4. b. For a binomial sample with n trials and sample proportion p, show the asymptotic variance of sin -1 (p) is 1/4n....

Q:

Let Î²Ì M = log (p +1 p 2+ /p +2 p 1+ ) refer to marginal model (10.6) and Î²Ì C = log (n 21 /n 12 ) to conditional model (10.8). Using the delta method, show that...

Q:

3.28 For multinomial sampling, use the asymptotic variance of log to show that for Yule's Q (Exercise 2.38) the asymptotic variance of n(Q-Q) is (; ) (1 Q)2/4 (Yule 1900, 1912).

Q:

3 In 0900'0 500O'D 1000 0 FIG. 4. Process H alloy composition: (a) & chart, (b) "chart based on log ratios, (o) X' versus 73. S 0900'0 50COD 100070 S602 R. A. Boyles For this data set, step (3) in...

Q:

Refer to Problem 3.27. The sample size may need to be quite large for the sampling distribution of to be approximately normal, especially if || is large. The Fisher-type transform = 1/2 log[(1 +...

Q:

Forum 1 We were asked to chosen and research a topic and we had to answer questions about our topics. Abortion if Woman want for any reason. FREQUENCIES VARIABLES=abany /ORDER=ANALYSIS Abortion and...

Q:

please answer all the questionsthanks a) [2m] Let (X1,..., X) Multin(n......6m) with 0; > 0 and 21-10; = 1. Show that the Dirichlet distribution is the conjugate prior to the Multinomial sampling...

Q:

4. Consider data from Aseffa et al. (1998) that examines the prevalence of HIV among women visiting health care clinics in northwest Ethiopia. Along with testing individuals for HIV, additional...

Q:

Consider X 2 W in (10.8). 1. Use the linearization method of Section 9.1 to approximate V () in terms of V ( ij ) and Cov( ij , kl ). Show that if we let y ijk = 1 if observation k is in cell (i, j)...

Q:

(a) Draw an orthorhombic unit cell, and within that cell a (210) plane. (b) Draw a monoclinic unit cell, and within that cell a (002) plane.

Q:

Let x be an element of the inner product space V in Exercise 31, and let p1 and p2 be the projections of x onto S1 and S2, respectively. Show that (a) x = P1 + P2. (b) If x S1, then p1 = 0 and hence...

Q:

Some marketing practitioners consider publicity to be too difficult to control and measure. Evaluate these criticisms.

Q:

1.3.4 Let U be a Poisson random variable with mean . Determine the expected value of the random variable V D 1=.1CU/.

Q:

The mean annual salaries earned in 2005 by year-round workers with various educational degrees are given in the table: Degree Mean Salary No diploma....... $19,964 High school diploma... $29,448...

Q:

Consider the Whooping Cough data file on the text CD. a. Identify the response variable and the explanatory variable. b. Construct a graph using bars to display the incidence rate of whooping cough...

Q:

The following side by-side bar graph appeared in a 2003 issue of the Monthly Labor Review about women as managers in the work force. The graph summarized the percentage of managers in different...

Q:

Pat is the manager of a real estate group that is part of a larger real estate company. Here are the total number of home sales from 2019 for all the agents at the entire company. 15 20 3 5 6 8 9 10...

Q:

BE10-15: Use the information presented for Ottawa Corporation in BE 10-14, but assume the machinery is sold for $ 5,200 instead of $10,500. Prepare journal entries to (a) update depreciation for 2013...

Q:

An excavator has a purchase price of $1,200,000, has a rating of 1,900 kW, an estimated life of 10 years an annual operating usage of 4,000 hours. A return on investment of 10% is required. For the...