A Course in Mathematical Statistics and Large Sample Theory by Rabi Bhattacharya Lizhen Lin & Victor Patrangenaru

A Course in Mathematical Statistics and Large Sample Theory by Rabi Bhattacharya Lizhen Lin & Victor Patrangenaru

Author:Rabi Bhattacharya, Lizhen Lin & Victor Patrangenaru
Language: eng
Format: epub
Publisher: Springer New York, New York, NY


(7.104)

where

(7.105)

Proof.

(7.106)

where Grad is the p × p matrix who (i, r) element is , and ɛ n is a p × p matrix whose elements converge in probability to zero. □

Example 7.6.

Let be i.i.d. with common p.d.f. , 0 < x < ∞; μ ∈ (0, ∞), α ∈ (0, ∞). Note that EX 1 = α μ, EX 1 2 = (α + 1)α μ 2. Therefore, solve

(7.107)

for α, μ to get

(7.108)

Here (check)

(7.109)

Therefore, with ,

(7.110)

can be computed from (7.110). For example,



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