Question

Power outages during winter storms is common. A utility company which provides electricity to Pacific Northwest wants to estimate the true proportion of outages that affect an area large enough (denoted as class A) that will take longer than 24 hours to restore electricity. The company collects some data over three winters for 365 outages. 62 outages are recorded as class A. We would like to assess the properties (Bias, Variance, MSE) of the estimator of the true population proportion of class A outages.

Assuming that the estimate is the true value of the parameter, state a stepwise simulation procedure to estimate the Bias, Variance, and the MSE of this estimator.

Answer 1

Following are the steps to calculate the values of Bias, Variance, and the MSE of this estimator

1) We should have estimator say 'theta'

2) Fixed the sample size to estimate the 'theta' say 'theta0' as estimator

3) Following are the formulaese to estimate the the quantities of interest

And MSE = Bias(theta0) + Var(theta0)

4) Using the above formula we can calculate or simulate the values for  Bias, Variance, and the MSE of this estimator

5) If in case we have underlying model then we can use the predicted values in order to calculate Bias, Variance, and the MSE of this estimator