Basics of estimation

Basics of estimation 

In many real-life problems, the population parameter(s) is (are) unknown and 
someone is interested to obtain the value(s) of parameter(s). But, if the whole 
population is too large to study or the units of the population are destructive in 
nature or there is a limited resources and manpower available then it is not 
practically convenient to examine each and every unit of the population to find
the value(s) of parameter(s). In such situations, one can draw sample from the 
population under study and utilize sample observations to estimate the 
parameter(s). 
Every one of us makes estimate(s) in our day to day life. For example, a house 
wife estimates the monthly expenditure on the basis of particular needs, a sweet 
shopkeeper estimates the sale of sweets on a day, etc. So the technique of 
finding an estimator to produce an estimate of the unknown parameter on the 
basis of a sample is called estimation.
There are two methods of estimation:
1. Point Estimation
2. Interval Estimation

It is to be noted that a large number of estimators can be proposed for an
unknown parameter. For example, if we want to estimate the average income 
of the persons living in a city then the sample mean, sample median, sample 
mode, etc. can be used to estimate the average income. Now, the question
arises, “Are some of possible estimators better, in some sense, than the others?”
Generally, an estimator can be called good for two different situations:
(i) When the true value of parameter is being estimated is known− An 
estimator might be called good if its value close to the true value of the 
parameter to be estimated. In other words, the estimator whose sampling 
distribution concentrates as closely as possible near the true value of the 
parameter may be regarded as the good estimator. 
(ii) When the true value of the parameter is unknown− An estimator may 
be called good if the data give good reason to believe that the estimate will 
be closed to the true value. 
In the whole estimation, we estimate the parameter when the true value of the 
parameter is unknown. Hence, we must choose estimates not because they are 
certainly close to the true value, but because there is a good reason to believe 
that the estimated value will be close to the true value of parameter. In this unit,
we shall describe certain properties, which help us in deciding whether an
estimator is better than others.
Prof. Ronald A. Fisher was the man who pushed ahead the theory of estimation 
and introduced these concepts and gave some properties of good estimator as
follows:
1. Unbiasedness
2. Consistency
3. Efficiency
4. Sufficiency

Estimation is important in business and economics, because too many variables exist to figure out how large-scale activities will develop. Estimation in projects, planning can be particularly significant, because plans for the distribution of labor and for purchases of raw materials must be made, despite the inability to know every possible problem that may come up. consider an example that you have to estimate the rate of flat in some luxurious area. Estimation is also useful in planning of government. 

Thanks for reading...

Content created by - Chandrashekhar Awate, Priyanka Pawar and Akash Patil

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