Advanced Statistics with Applications in R

Chapter 6Parameter estimation

Fundamental to the statistical approach are the concepts of general population and sample. Statistics analyzes observations contained in the sample with the purpose of drawing conclusions about the general population. Collectively, the ensemble of statistical techniques is called statistical inference. For example, we may think of a general population of household incomes in a state or the entire country and conduct a survey that provides a sample of incomes. Statistics projects the knowledge gained from the sample to the general population. The simplest example of a statistical inference is a comparison of the average household income from the town's survey with the average income in the state, supposedly known. Importantly, we do not claim that the survey average equals the state family income. There is always an error of such estimation; the uncertainty associated with any statement regarding the comparison is unavoidable. However, one may expect that large sample size yields small uncertainty. Typically, the sample is random, so that the reported incomes are independent and identically distributed (iid) observations drawn from a general population of all families with the probability density function (pdf), or shortly the density, that can be succinctly ...