Estimation and Sampling

In general, estimation is the best use of information in a sample to form one of several types of estimates in the parameter’s value. These estimates help us infer what would likely be found in the population.

Broadly speaking, estimates can be categorized into 2 types:

• Point Estimation- A single value that estimates the parameters of the population.
• Interval Estimation - Also called confidence interval, a range of values that bracket the unknown population parameter with some specified level of probability.

Point Estimators

The formulas that we use to compute the sample statistics (such as the mean) are examples of point estimators. The three desirable properties of a point estimator are:

• Unbiasedness
• Efficiency
• Consistency

Interval Estimators

A range of values, within which the actual parameter will lie with a given probability.

Confidence Interval = point estimate ± (reliability factor x standard error)

Where, 

Reliability Factor is a number based on the assumed distribution of the point estimate and the degree of confidence of the confidence interval.

Standard error of the sample statistic providing the point estimate.

Sampling, in general, refers to the selection of a sample from the population and data to make inferences about what would be found in the population.

We can use sample values, such as sample mean, sample standard deviation, and so on, as valid estimators of the population.

Fig: Sampling from a population

(Source: Wikipedia)