2. Suppose § is an unbiased OLS estimator of parameter B, and the t-statistic t =...
Complete the sentence: An unbiased estimator is _____. a. any sample statistic used to approximate a population parameter b. a sample statistic, which has an expected value equal to the value of the population parameter c. a sample statistic whose value is usually less than the value of the population parameter d. any estimator whose standard error is relatively small
Suppose you have an unbiased, normally distributed estimator of a parameter B, and are testing the null hypothesis B=0 with a two tail test. For the present sample, the standard error of the estimator is 1.0 Suppose the true value of B=0.5. Professor X conducts the study and finds a positive and significant B. If you attempt to replicate Professor X's study in other data sets of the same size, what percentage of those data sets would you expect the...
a) Find the variance of each unbiased estimator. b) Use the Central Limit Theorem to create an approximate 95% confidence interval for theta. c) Use the pivotal quantity Beta(alpha=13, beta=13) to create an approximate 95% confidence interval for theta. d) Use the pivotal quantity Beta(alpha=25, beta=1) to create an approximate 95% confidence interval for theta. Suppose that Xi, , x25 are i.i.d. Unifom(0,0), where θ is unknown. Consider three unbiased estimators of 6 25 26 25 25 26 max (X...,...
7. When we impose a restriction on the OLS estimation that the intercept estimator is zero, we call it regression through the origin. Consider a population model Y- Au + βίχ + u and we estimate an OLS regression model through the origin: Y-β¡XHi (note that the true intercept parameter Bo is not necessarily zero). (i) Under assumptions SLR.1-SLR.4, either use the method of moments or minimize the SSR to show that the βί-1-- ie1 (2) Find E(%) in terms...
Which of the statements about large-sample estimation is correct? (1) An estimator should be unbiased and the spread (as measured by the mean) should be as small as possible. (2) The distance between an estimate and the true value of the statistic is called the error of estimation. (3) The 95% Margin of error is: 1.96 Standard error of the estimator. (4) A good confidence interval is as wide as possible.
Which of the statements about large-sample estimation is correct? (1) An estimator should be unbiased and the spread (as measured by the mean) should be as small as possible. (2) The distance between an estimate and the true value of the statistic is called the error of estimation. (3) The 95% Margin of error is: 1.96 x Standard error of the estimator. (4) A good confidence interval is as wide as possible.
7.20 Consider Y1,...,Yn as defined in Exercise 7.19. (a) Show that Yilti is an unbiased estimator of B. (b) Calculate the exact variance of Yi/ xi and compare it to the variance of the MLE. 7.19 Suppose that the random variables Yı, ..., Yn satisfy Yi = Bli +ti, i = 1,...,n, where x1, ..., In are fixed constants, and €1,..., En are iid n(0,02), o2 unknown. (a) Find a two-dimensional sufficient statistic for (0,0%). (b) Find the MLE of...
2. (a) Define the bias of ˆ θ as an estimator for the parameter θ. [2 marks] (b) For independent random variables X1,X2,...,Xn, assume that E(Xi) = µ and var(Xi) = σ2, i = 1,...,n. (i) Show that ˆ µ1 = {(X1+Xn)/2}is an unbiased estimator for µ and determine its variance. [3 marks] (ii) Find the relative efficiency of ˆ µ1 to the unbiased estimator ˆ µ2 = X, the sample mean. [2 marks] (iii) Is ˆ µ1 a consistent...
7. True/False a. If Cov(x,u)>0, then the OLS estimator βι will then to be higher than β b. Suppose you run a regression and obtain the estimate B1 - 3.4. Stata tells you that the test statistic for the null hypothesis that B12 is equal to 2. This implies that the standard error of the slope coefficient is also equal to 2.
Q1 a) Explain what it means that the ordinary least squares regression estimator is a linear estimator, paying specific attention to how it implies independent variables interact with each other. b) Give two examples of models where the parameters of interest cannot be directly estimated using OLS regression because of nonlinear relationships between them. c) What is the minimum set of conditions necessary for the OLS estimator to be the most efficient unbiased estimator (BLUE) of a parameter? List each...