Point Estimation


So far we know that when the constants of a population (the parameters) are unknown, we estimate them by finding estimates based on the samples drawn from the same population. This method is called “estimation”.
Now, since we are estimating the parameters so there must be two types of possibility:



With the help of sample observations, we obtain a single / particular value for estimating the parameter i.e. single estimated value of parameter (say θ), it is called point estimate or simply estimate. This method of estimation is known as point estimation.
In other words, point estimate is our best guess of the true value of the parameter.                                                                         It should be kept in mind that in order to find a point estimate to be so accurate, the sample size should be large.



There are a variety of point estimators each posses different properties, most commonly are:
          1) Minimum variance unbiased estimator (MVUE)
          2) Best linear unbiased estimator (BLUE)
          3) Minimum mean squared error estimator (MMSE)
          4) Maximum likelihood estimator (MLE)
          5) Method of moments


1) Point estimates are oftenly  used as part of other statistical calculations, like a point estimate of standard deviation is used in calculation of confidence interval for µ.
2) Point estimates play an important role in formulas of significance testing.

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