The method of obtaining the most likely value of the population parameter using statistic is called estimation.

**Estimation:**

It is possible to draw
valid conclusion about the population parameters from sampling distribution.
Estimation helps in estimating an unknown population parameter such as
population mean, standard deviation, etc., on the basis of suitable statistic
computed from the samples drawn from population.

**Definition 8.4**

The method of
obtaining the most likely value of the population parameter using statistic is
called estimation.

**Definition 8.5**

Any sample statistic
which is used to estimate an unknown population parameter is called an
estimator ie., an estimator is a sample statistic used to estimate a population
parameter.

When we observe a specific
numerical value of our estimator, we call that value is an estimate. In other
words, an estimate is a specific observed value of a statistic.

A good estimator must
possess the following characteristic:

(i) Unbiasedness

(ii) Consistency

(iii) Efficiency

(iv) Sufficiency.

i. Unbiasedness: An
estimator *T _{n}* =

ii. Consistency: An
estimator *T _{n}* =

iii. Efficiency:If *T*_{1}
is the most efficient estimator with variance *V*_{1} and *T*_{2}
is any other estimator with variance *V*_{2} , then the efficiency
E of *T*_{2} is defined as E=V_{1}/V_{2}. Obviously,*
E *cannot exceed unity.

iv. Sufficiency:
If *T* = *t*(*x*_{1}
, *x*_{2} ,...., *x _{n}* ) is an estimator of a
parameter

Tags : Definition, Characteristic | Statistical Inference , 12th Business Maths and Statistics : Chapter 8 : Sampling Techniques and Statistical Inference

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12th Business Maths and Statistics : Chapter 8 : Sampling Techniques and Statistical Inference : Estimation | Definition, Characteristic | Statistical Inference

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