Category: Mathematical Economics and Econometrics

Expected Values or Mathematical Expectations

The expected value, or mean, of a random variable is a measure of the central location for the random variable. The formula for the expected value of a discrete random variable X follows.Expected value of a discrete random variable X can be written as i.e.,Properties of Mathematical Expectations The expected value of constant ‘C’ is equal …

F-Test

F- test is generally known as the variance ratio test and it is used mostly in  context of analysis of variance. This technique was developed by Prof.Fisher. Prof. Fisher developed this test on the basis of agricultural experiment. For test of hypothesis of equality among several sample means. The F-test is considered to be more appropriate. …

Gauss Markov Theorem [BLUE Properties]

Given the assumptions of the classical linear regression model, the least-squares estimators, in the class of unbiased linear estimators, have minimum variance, that is, they are BLUE. In other words Gauss-Markov theorem holds the properties of Best Linear Unbiased Estimators. Following are some of the assumptions which should be taken into consideration for the mathematical derivation …

Properties of Good Estimator

Small Sample properties Unbiased Estimator : Biased means the difference of true value of parameter and value of estimator. When the difference becomes zero then it is called unbiased estimator. i.e., Best Estimator : An estimator is called best when value of its variance is smaller than variance is best. i.e . Where   is another estimator. Efficient Estimator : …

Chi-Square Distribution [Properties]

Chi- Square is an important non-parametric test and as such now rigid assumptions are necessary is respect of the type of population we require only the degree of freedom for using this test. Non- parametric chi-square test can be used  As a test of goodness of fit As a test of independence  This test was developed …