What is meant by more efficient estimator?
Essentially, a more efficient estimator, experiment, or test needs fewer observations than a less efficient one to achieve a given performance. An efficient estimator is characterized by a small variance or mean square error, indicating that there is a small deviance between the estimated value and the “true” value.
Is difference of sample mean unbiased estimator?
The expected value of the sample mean is equal to the population mean µ. Therefore, the sample mean is an unbiased estimator of the population mean. Since only a sample of observations is available, the estimate of the mean can be either less than or greater than the true population mean.
What does MVUE stand for?
minimum-variance unbiased estimator
In statistics a minimum-variance unbiased estimator (MVUE) or uniformly minimum-variance unbiased estimator (UMVUE) is an unbiased estimator that has lower variance than any other unbiased estimator for all possible values of the parameter.
Is the sample mean always an optimal estimator?
Though the sample mean is an unbiased estimator of the unknown population mean, it cannot be optimal in general. Take the case of the log-normal distribution. The maximum likelihood estimator of the mean on the original scale is a function of the sample mean and sample variance both computed on the log scale.
What’s the difference between an estimator and an estimate?
A distinction is made between an estimate and an estimator. The numerical value of the sample mean is said to be an estimate of the population mean figure. On the other hand, the statistical measure used, that is, the method of estimation is referred to as an estimator.
Which is better the sample median or the sample mean?
The sample mean is an unbiased estimator of µ no matter what form the population distribution assumes, while the sample median is an unbiased estimate of µ only if the population distribution is symmetrical. The sample mean is better than the sample median as an estimate of µ in terms of both unbiasedness and consistency.
What are the properties of a good estimator?
Properties of Good Estimator A distinction is made between an estimate and an estimator. The numerical value of the sample mean is said to be an estimate of the population mean figure. On the other hand, the statistical measure used, that is, the method of estimation is referred to as an estimator.