Let X1, X2,..., Xn be i.i.d N(0, 1).(a) Derive o the most powerful test for testing H 0 0 against K: 0 = 01 at given levela, where 0, > 0.(b) Derive the power of the test derived in (a).(c) Let Pe be the measure associated N(0, 1) and Calculate the total error Sp pn (6) (asdefined in the class).(d) Derive the test o that minimizes Sp pn (o) and calculate its error Spm pn (*).(e) Fix h >0 and let 0, = hn-1/2. Use the result in (d) to derive S(P, P) and its limiting%3D01value as n 0o.

Answered: Let X1, X2,..., X, be i.i.d N(0, 1). e…

Let X1, X2,..., X, be i.i.d N(0, 1). e most powerful test for testing H : 0 = 0 against K > 0. ower of the test derived in (a). ne measure associated N(0, 1) and Calculate the tot.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 32EQ

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Question

Let X1, X2,..., Xn be i.i.d N(0, 1).
(a) Derive o the most powerful test for testing H 0 0 against K: 0 = 01 at given level
a, where 0, > 0.
(b) Derive the power of the test derived in (a).
(c) Let Pe be the measure associated N(0, 1) and Calculate the total error Sp pn (6) (as
defined in the class).
(d) Derive the test o that minimizes Sp pn (o) and calculate its error Spm pn (*).
(e) Fix h >0 and let 0, = hn-1/2. Use the result in (d) to derive S(P, P) and its limiting
%3D
01
value as n 0o.

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