A Course in Statistics with R

Chapter 7Parametric Inference

Package(s): UsingR

Dataset(s): ns, ps, bs, cs, galton, sleep, airquality

7.1 Introduction

In Chapter 4 we came across one form of analyzing data, viz., the exploratory data analysis. That approach mainly made no assumptions about the probability mechanism for the data generation. In later chapters we witnessed certain models which plausibly explain the nature of the random phenomenon. In reality, we seldom have information about the parameters of the probability distributions. Historically, or intuitively, we may have enough information about the probability distributions, sparing a few parameters. In this chapter we consider various methods for inferring about such parameters, using the data generated under the assumptions of these probability models.

Parametric statistical inference arises when we have information for the model describing an uncertain experiment sans a few values, called parameters, of the model. If the parameter values are known, we have problems more of the probabilistic kind than statistical ones. The parameter values need to be obtained based on some data. The data may be a pure random sample in the sense of all the observations being drawn with the same probability. However, it is also the practical case that obtaining a random sample may not be possible in many stochastic experiments. For example, the temperature in the morning and afternoon are certainly not identical observations. We undertake statistical inference of ...