What is the mean square error of an estimator?

In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value.

What is the relationship between the population mean and the mean of the sample means?

Sample Mean is the mean of sample values collected. Population Mean is the mean of all the values in the population. If the sample is random and sample size is large then the sample mean would be a good estimate of the population mean.

How do you estimate the population mean from the sample mean?

In the large-sample case, a 95\% confidence interval estimate for the population mean is given by x̄ ± 1.96σ/ √n. When the population standard deviation, σ, is unknown, the sample standard deviation is used to estimate σ in the confidence interval formula.

What is the mean squared?

In mathematics and its applications, the mean square is defined as the arithmetic mean of the squares of a set of numbers or of a random variable, or as the arithmetic mean of the squares of the differences between a set of numbers and a given “origin” that may not be zero (e.g. may be a mean or an assumed mean of the …

What does it mean when we say that the sample mean is an unbiased estimator of μ?

When a statistic like the sample mean X is aimed at a population parameter like μ, we call X an estimator of μ. An estimator is unbiased if its mean over all samples is equal to the population parameter that it is estimating.

What happens to the mean and standard deviation of the distribution of sample means as the size of the sample decreases?

The population mean of the distribution of sample means is the same as the population mean of the distribution being sampled from. Thus as the sample size increases, the standard deviation of the means decreases; and as the sample size decreases, the standard deviation of the sample means increases.

How do you compare mean of the sample means and the mean of the population How about the variance of the sample means and the variance of the population?

The mean of the sample means is the same as the population mean, but the variance of the sample means is not the same as the population variance.