Section A
Q1.
(a) Describe cumulative total and Lahiri's methods of selecting a sample. Show that both the methods provide probability proportional to sample size.
(b) For a multiple linear regression model satisfying all the basic assumptions, show that ordinary least squares (OLS) estimators of regression coefficient vector β and estimator of error variance σ^2 based on OLSE of β are unbiased, jointly sufficient and efficient estimators of β and σ^2.
(c)
Given Xt = β_1 + β_2 t + wt, wt \sim \textiid(0, σ^2), where β_1 and β_2 are constants.
(i) Determine whether Xt is stationary.
(ii) Show that Yt = Xt - Xt-1 is stationary.
(iii) Show that the mean of moving average vt = (1)/(2q + 1) sumi=-qq Xt-i is β_1 + β_2 t.
