Here we reformulate the multitaper-based simple linear regression model of Equation (409d) in standard vector/matrix notation (see, e.g., Weisberg, 2014), with the goal of verifying Equation (410b),...


Here we reformulate the multitaper-based simple linear regression model of Equation (409d) in standard vector/matrix notation (see, e.g., Weisberg, 2014), with the goal of verifying Equation (410b), which gives the variance of the OLS estimator
  of the power-law exponent α. Let Y be a column vector containing the responses
  and let X be a matrix with two columns of predictors, the first column with elements all equal to unity, and the second, with elements equal to
  as defined in Equation (409e).


(a) With
  being a two-dimensional column vector of regression coefficients whose second element is α, argue that
  is equivalent to the model of Equation (409d), where is a column vector containing the error terms


(b) A standard result says that the OLS estimator of
  (see, e.g., Weisberg, 2014). Show that the second element of βˆ is the multitaper-based OLS estimator ˆα (MT) of Equation (409e).


(c) Taking the elements of the covariance matrix Σ for to be dictated by Equation (410a); noting that




and evoking a standard result from the theory of multivariate RVs, namely, that the covariance matrix for Mis given by
  show that var  is given by.




May 22, 2022
SOLUTION.PDF

Get Answer To This Question

Related Questions & Answers

More Questions »

Submit New Assignment

Copy and Paste Your Assignment Here