Question
Which of the following conditions is not necessary for
ordinary least squares to be the best unbiased linear estimator (BLUE)?Solution
The Ordinary Least Squares (OLS) method is used to estimate the parameters in a linear regression model. For the OLS estimator to be the Best Linear Unbiased Estimator (BLUE), it must satisfy the Gauss-Markov assumptions. These assumptions are: 1. Linearity : The relationship between the independent variables and the dependent variable is linear. 2. Random Sampling : The data is obtained through a random sample of the population. 3. No Perfect Multicollinearity : There is no perfect multicollinearity between the independent variables. 4. Zero Conditional Mean : The errors have an expectation of zero given any value of the independent variables. 5. Homoscedasticity : The errors have constant variance (σ2). 6. No Autocorrelation : The errors are uncorrelated with each other. Given these assumptions, the condition that is not necessary for OLS to be BLUE is: (a) All errors are normally distributed Normality of the errors is not required for the OLS estimator to be BLUE according to the Gauss-Markov theorem. Normality is only necessary if we want to make specific inference statements (like t-tests and F-tests) or for the errors to follow a normal distribution.
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