Define convergence in probability

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Reference no: EM133454128

Questions:

A. Define convergence in Probability. Define a consistent Estimator.

B. Define convergence in Distribution.

C. Define unbiasedness of an estimator. Is unbiasedness related to consistency of an estimator? Why or why not?

D. In the bivariate Linear Regression model, prove OLS estimator of the slope coefficient is consistent. Make clear the assumptions under which you provide your proof.

E. In the Multiple Linear Regression model, describe the "partialing method of regressions, give the formula for any slope coefficient and interpret the inflation factor in its variance formula. Show (obtain) the bias (or inconsistency due to an omitted variable (you can use a simple regression example to show this bias.

F. Obtain the 95% confidence interval for any slope coefficient in the multiple linear regression model. State the assumptions that allow exact distribution of the t-ratio to be established. How would you test multiple hypothesis on the regression coefficients?

G. Explain how and what asymptotic distribution theory may be used in Part F, if you drop the assumption of Normal distributed errors.

Reference no: EM133454128

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