Question

what do you understand by point estimation? when would you say that estimate of a parameter is good? also discuss the requirements of consistency unbiasedness of an estimate?

Answer 1

>> In statistics, point estimation refers to the best-guess estimate for a population parameter using sample data. For example, in order to find point estimation for mean of the population, the sample average is taken as a point estimation.

>> An estimate is good if it posses the following characteristics

1) unbiasedness: An estimate is said to be unbiased if the expected value of the sample estimate is equal to the actual population parameter value.

2) Consistency: An estimate is consistent when the variance or standard deviation of the estimate decreases with increases in sample size

3) Efficient: An unbiased estimate is said to be efficient if the estimate has the least standard deviation amongst all other estimates

-----------------------------------

NOTE: Generally, in statistics, a statistician prefer an estimate to be BLUE

BLUE ( Best Linear unbiased estimator)

here Best means efficient