Contents
- 1 Do you think a sample mean estimator will always be a good estimate for the population variance?
- 2 Is the sample mean a good estimator of the population mean?
- 3 What is the best estimator for the population mean?
- 4 Is the sample mean always the best estimator?
- 5 Which is the best estimator for population mean?
- 6 Which is the maximum likelihood of sample mean?
Do you think a sample mean estimator will always be a good estimate for the population variance?
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.
Is the sample mean a good estimator of the population mean?
Provided a simple random sample the sample mean is an unbiased estimator of the population parameter because over many samples the mean does not systematically overestimate or underestimate the true mean of the population.
Is sample mean a good estimator?
The sample mean is an estimator for the population mean. An estimator is a statistic that estimates some fact about the population. You can also think of an estimator as the rule that creates an estimate. For example, the sample mean(x̄) is an estimator for the population mean, μ.
What is the best estimator for the population mean?
6 replies. The best estimate of a population mean is the sample mean.
Is the sample mean always the best estimator?
No, the sample mean is not always the best estimator. See for instance (besides the example of the mean of a uniform distribution by StubbornAtom) the case of a sample from a Laplace distributed population in the image below (code to compute that image is in this q&a)
How to calculate the sample mean of an observation?
The sample mean from a group of observations is an estimate of the population mean . Given a sample of size n, consider n independent random variables X1, X2., Xn, each corresponding to one randomly selected observation.
Which is the best estimator for population mean?
It can be shown that the uniformly minimum variance unbiased estimator (UMVUE) of the population mean is instead T 2 = n + 1 2 n max ( X 1, …, X n). So T 2 is the best estimator within the unbiased class where ‘best’ means ‘having the smallest variance’. No, the sample mean is not always the best estimator.
Which is the maximum likelihood of sample mean?
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. This prevents outliers from ruining either the mean or SD.