25. Let X₁,. Xn be a sample from a population with o² = Var(X) < ∞, µ = E(X) and let T = X² be an estimate of μ². (a) When μ ‡ 0, find the asymptotic distribution of √n(T-µ²) using the delta method. fl (b) When μ = 0, find the asymptotic distriution of nT using P(nT ≤ t) = P(-√t ≤ √nX ≤ √t). Compare your answer to the answer in part (a). (c) Find the limiting laws of √n(X − µ)² and n(Ỹ − µ)².
25. Let X₁,. Xn be a sample from a population with o² = Var(X) < ∞, µ = E(X) and let T = X² be an estimate of μ². (a) When μ ‡ 0, find the asymptotic distribution of √n(T-µ²) using the delta method. fl (b) When μ = 0, find the asymptotic distriution of nT using P(nT ≤ t) = P(-√t ≤ √nX ≤ √t). Compare your answer to the answer in part (a). (c) Find the limiting laws of √n(X − µ)² and n(Ỹ − µ)².
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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