Topic: Quantitative Methods for Finance

Please answer a. here. I'll create a second question for b.

Sampling and Estimation Given a simple random sample Y1, 72, ..., Yn, you would like to estimate the population mean ju. Instead of computing the sample average Y= 1 3 Yi, a researcher suggests to use the following weighted average: r=ov+3x2+x+3x2+...+Y). where weights alternate between and . Assume that n is even and denote the popu- lation variance o? a. Define an unbiased estimator. Is Y* unbiased? b. Define an efficient estimator. Is Y* efficient? Hint: compute the variance of Y* and compare it to the variance of 7. Sampling and Estimation Given a simple random sample Y1, 72, ..., Yn, you would like to estimate the population mean ju. Instead of computing the sample average Y= 1 3 Yi, a researcher suggests to use the following weighted average: r=ov+3x2+x+3x2+...+Y). where weights alternate between and . Assume that n is even and denote the popu- lation variance o? a. Define an unbiased estimator. Is Y* unbiased? b. Define an efficient estimator. Is Y* efficient? Hint: compute the variance of Y* and compare it to the variance of 7