Variance estimation with post stratification. Suppose we post stratify the sample into L post strata, with population

Question:

Variance estimation with post stratification. Suppose we post stratify the sample into L post strata, with population counts N1, N2. . . NL. Then the post stratified estimator for the population total is

Where

And xli =1 if unit i is in post stratum l and 0 otherwise. Show, using linearization, that

We can thus let

and estimate V(á¹«post) by

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

Step by Step Answer:

Related Book For book-img-for-question

Sampling Design And Analysis

ISBN: 627

2nd Edition

Authors: Sharon L. Lohr

See More Books

Question Posted: Nov 27, 2015 01:55 AM

See More Questions

The linearization estimator of V () can be found by the method outlined in Section 9.1 (see Shah et al., 1977). However, the calculations are easier using the DemnatiRao (2004) method discussed in...
The linearization estimator of V (á¸) can be found by the method outlined in Section 9.1 (see Shah et al., 1977). However, the calculations are easier using the DemnatiRao (2004) method...
Suppose a population contains n1 objects of one kind, n2 objects of a second kind, . . . , and nt objects of a tth kind, where n1 +n2 + +nt = N. A sample of size n is drawn at random and without...
Discuss what you see as the role of ethics as it pertains to management and managers. Does management, in your view, help shape the values and ethics of an organization? What about an organization's...
Describe the alterations from the standard report when a scope limitation has occurred and the auditors have issued a qualified opinion.
The speed of sound in air at 20oC is 344 m/s. (a) What is the wavelength of a sound wave with a frequency of 784 Hz, corresponding to the note 0, on a piano, and how many milliseconds does each...
Two popular methods of fi nancial statement analysis are horizontal analysis and vertical analysis. Explain the difference between these two methods. LO15
In water-resources engineering, the sizing or reservoirs depends on accurate estimates of water flow in the river that is being impounded. For some rivers, long-term historical records of such flow...
A portfolio has 40% of its assets invested in stocks and 60% invested in bonds. If the stocks have a return of 6% and the bonds have a return of 9%, calculate the portfolio return:
Your investment bank has an investment of $100 million in the stock of the Swiss Roll Corporation and a short position in the stock of the Frankfurter Sausage Company. Here is the recent price...
The correlation coefficient for the population is a. Express R as a function of population totals So that R = h (t1, t2, t3, t4, t5). b. Let r = h (á¹«1. . ....
Consider the random group estimator of the variance from Section 9.2.2. The parameter of interest is Î¸ =U. A simple random sample with replacement of size n is taken from the population....
Which pricing method (cost, demand/supply, competition, profit-based) would you recommend for the following items being sold in other countries? Defend your reasoning.
Let $N$ be a positive integer. Consider the relation $\circledast$ among pairs of integers $r, s \in \mathbb{Z}$ defined as $r \circledast s$ when $r-s$ is an integer multiple of $N$. Prove that...
Draw a circuit diagram for a typical home hair dryer. To which form (or forms) of energy is electric potential energy converted when you use the dryer?
Draw a vector field diagram for particles carrying charges $+2 q$ and $-q$ separated by a distance $r$. Comment on the significance of the vector diagram.
(a) Show that the Jones matrix of a polarization analyzer set at angle $\alpha$ to the $X$-axis is given by \[ \underline{\mathbf{L}}(\alpha)=\left[\begin{array}{cc} \cos ^{2} \alpha & \sin...
Let $\mathbf{V}(t)$ be a linearly filtered complex-valued, wide-sense stationary random process with sample functions given by \[ \mathbf{v}(t)=\int_{-\infty}^{\infty} \mathbf{h}(t-\tau)...
For the given watershed in Figure 4.2 , calculate the channel and watershed slope based on the altitude data given in Table 4.1 . Subwatershed 1, Subwatershed 2 Subwatershed 3/ FIGURE 4.2 Watershed...
In muscle tissue, the ratio of phosphorylase a to phosphorylase b determines the rate of conversion of glycogen to glucose 1phosphate. Classify how each event affects the rate of glycogen breakdown...
Using Excel Wood Products Company would like to purchase a computerized wood lathe for $$100,000.$ The machine is expected to have a life of five years, and a salvage value of $$5,000.$ Annual...
Determine the probability that in a sample of 100 the sample proportion is less than .75 if p = .80.
A binomial experiment where p = .4 is conducted. Find the probability that in a sample of 60 the proportion of successes exceeds .35.
The proportion of eligible voters in the next election who will vote for the incumbent is assumed to be 55%. What is the probability that in a random sample of 500 voters less than 49% say they will...
Long-term liabilities are shown in two places in the business firm's balance sheet depending upon when the long-term liabilities are scheduled for payment. True False
Julio is single with 1 withholding allowance. He earned $1,025.00 during the most recent semimonthly pay period. He needs to decide between contributing 3% and $30 to his 401(k) plan. If he chooses...
Acquirer firm plans to launch a takeover of Target firm. The manager of Acquirer indicates that the deal will increase the free cash flow of the combined business by $13.6m per year forever. The beta...

Variance estimation with post stratification. Suppose we post stratify the sample into L post strata, with population

Question:

Ni Ν; l-I l=2.wixliyi, Ni= ies 1-1

Step by Step Answer:

Write the function ...View the full answer

Sampling Design And Analysis

Students also viewed these Statistics questions