The best linear unbiased predictor of the population

Reference no: EM131122330

Assume that the Y -values in the population are related to an auxiliary variable x through the ratio model Y_i = βx_i + i, for i = 1, 2,...,N, where the random errors i are independent with E( i) = 0 and var( i) = viσ2 R, in which the vi are known and β and σ2 R are unknown constants. A simple random sample of size n is selected. The best linear unbiased predictor of the population total τ is τˆ = Y_s + βs, where Ys is the total of the Y -values in the sample and xs is the total of the x-values not in the sample and

When the variance of Yi is proportional to xi, that is, v_i = x_i, the best linear unbiased estimator β is the ratio estimator

Compute the value of with this estimator with the data in Example 1.

(b) Show that when the variance of Yi is proportional is the mean-of-the-ratios estimator

Compute the value of τˆ with this estimator with the data in Example 1.

Reference no: EM131122330

Questions Cloud

An unequal probability sample of size : An unequal probability sample of size 3 is selected from a population of size 10 with replacement. The y-values of the selected units are listed along with their draw-by-draw selection probabilities:

Principles of job crafting described above relevant to work : Consider for a moment a midlevel manager at a multinational foods company, Fatima, who would seem to be at the top of her career. Why do you think many people are in jobs that are not satisfying? Do organizations help people craft satisfying and moti..

What other factor or factors should be considered : Suppose the Swiss CHF declines in value by 5 percent relative to the U.S. dollar over the next 180 days. Determine the net gain (loss) of the Zurich Bank CD in U.S. dollars relative to the PNB CD for an uncovered position. Determine the net gain (los..

Determine the appropriate type of market structure : From the scenario for Katrina's Candies, determine the appropriate type of market structure for the situation in question. Cite at least four defining characteristics that have helped you reach this decision regarding the appropriateness of the ch..

The best linear unbiased predictor of the population : Assume that the Y -values in the population are related to an auxiliary variable x through the ratio model Yi = βxi + i, for i = 1, 2,...,N, where the random errors i are independent with E( i) = 0 and var( i) = viσ2 R, in which the vi are known an..

Prepare a t account for the accounts receivable customer : Verify the equality of the sum of the customer account balances and the accounts receivable control account balance.

Create three optimal decision rules for katrinas candies : Create three optimal decision rules for Katrina's Candies (e.g., whether to hire more staff or hire temporary workers to meet production schedules).

Define health information portability and accountability act : In 1996, the Health Information Portability and Accountability Act was put into effect. This legislation profoundly changed the way the healthcare industry work in the United States. As such, healthcare organizations have had to create and change ..

Find how fast the winds were in the tropical cyclone eyewall : A reconnaissance flight performed by the hurricane hunter found that the winds in this tropical cyclone near the Philippines below were 70 mph at a distance of 60 miles from the center of the hurricane. find how fast the winds were in the tropical ..

User Account

All Pages