STA248H1 Lecture Notes - Lecture 4: Sampling Distribution, Point Estimation, Statistical Inference
27 Oct 2015
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Document Summary
Besides reporting a value of a point estimate we should consider some indication of its precision. Standard error of an estimator is the standard deviation of its sampling distribution. 2 and we are interested in estimating . If is also an unknown parameter, we substitute an estimate for : Some special cases of sampling distributions is the chi-square distribution with degrees of freedom. (cid:3041) are independent (cid:3041) the estimator of. Important note: by the central limit theorem, estimator that is the sum of independent identically distributed random variables will have approximately a normal distribution for large n. Example (normal approximation to the binomial distribution): (cid:3041) be independent bernoulli random variables with parameter p. A point estimate provides no information about the precision and reliability of estimation. For example, the sample mean is a point estimate of the population mean but because of sampling variability, it is virtually never the case that.
