Page 382 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 29: Methods of Point Estimation and Interval Estimation

29.3 Summary Notes

• The object of sampling is to study the features of the population on the basis of sample
observations. A carefully selection sample is expected to reveal these features, and hence we
shall infer about the population from a statistical analysis of the sample. This process is known
as Statistical Inference.
• In interval estimation, an interval within which the parameter is expected to lie is given by
using two quantities based on sample values. This is known as Confidence Interval, and the two
quantities which are used to specify the interval, are known as Confidence Limits.
• The Method of Maximum Likelihood consists in choosing as an estimator of θ that statistic, which
when substituted for θ , maximises the likelihood function L. Such a statistic is called a maximum
likelihood estimator (m.l.e.). We shall denote the m.l.e. of θ by the symbol θ .
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• The parameters enter into the population moments, these relations when solved for the
parameters give the estimates by the method of moments. Of course, this method is applicable
only when the population moments exist. The method is generally applied for fitting theoretical
distributions to observed data.
• In the theory of point estimation, developed earlier, any unknown parameter is estimated by a
single quantity. Thus the sample mean ( ) x is used to estimate the population mean () μ , and
the sample proportion (p) is taken as an estimator of the population proportion (P). A single
estimator of this kind, however good it may be, cannot be expected to coincide with the true
value of the parameter, and may in some cases differ widely from it. In the theory of interval
estimation, it is desired to find an interval which is expected to include the unknown parameter
with a specified probability.
• The significance of confidence limits is that if many independent random samples are drawn
from the same population and the confidence interval is calculated from each sample, then the
parameter will actually be included in the intervals in c proportion of cases in the long run.
Thus the estimate of the parameter is stated as an interval with a specified degree of confidence.

29.4 Key-Words

1. First order interaction : The interaction of two variables. Also known as a "simple interaction."
2. Fixed marginal totals : The situation in which the marginal totals in a contingency table are
known before the data are collected and are not subject to sampling
error.
3. Fixed model : Anova An analysis of variance model in which the levels of the
independent variable are treated as fixed.
29.5 Review Questions

1. Discuss the methods of point estimation.
2. What is the difference between point estimation and interval estimation ? Is interval estimation
better than point estimation ?
3. Explain the procedure of constructing a confidence interval for estimating population mean μ .
4. Explain interval estimation.
5. The central limit theorem for sample proportion can be used for estimating the population
proportion. Elaborate.

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