Point estimation is the process of finding a point that best represents a population. This point can be the mean, median, or mode of the population, dependi...
Point estimation is the process of finding a point that best represents a population. This point can be the mean, median, or mode of the population, depending on the characteristics of the data.
Properties of estimators refer to how they are resistant to certain types of errors.
Unbiasedness is a property of an estimator that makes it unbiased, meaning that its expected value is equal to the population parameter being estimated. For example, if the sample mean is unbiased, then the expected value of the sample mean will also be equal to the population mean.
Efficiency is a property of an estimator that indicates how efficient it is relative to other estimators. An efficient estimator can be more accurate with less data, meaning it will have lower variance.
Some important properties of estimators include:
Consistency: An estimator is consistent if it converges to the population parameter as the sample size increases.
Efficiency: An estimator is efficient if it has lower variance than other estimators.
Robustness: An estimator is robust if it remains relatively accurate even when the underlying population is not normally distributed.
Examples of unbiased and efficient estimators include:
Sample mean: The sample mean is unbiased and efficient, but it can be biased if the population is not normally distributed.
Sample median: The sample median is an unbiased and efficient estimator, but it is not invariant if the population is not symmetric.
Sample mode: The sample mode is an unbiased estimator, but it is not efficient and can be sensitive to outliers