An Introduction To Generalized Linear Models - Solutions (Third Edition, 2008) By Annette Dobson Adrian Barnett文档.pdf

An Introduction to Generalized Linear Models (third edition, 2008) by Annette Dobson Adrian Barnett Outline of solutions for selected exercises CHAPTER 1 W ⎡ 5 23 2 ⎤ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ 1 1.1 ⎜ ⎟~ N ⎢ , ⎥. ⎜ ⎟ ⎜ ⎟ W 2 2 53 2 ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎣ ⎦ 2 1.2 (a) χ (1) , by property 1 for the chi-squared distribution (page 7). 2 T 2 ⎛Y −3 ⎞ 2 (b) y y Y =+ 2 ~ χ (2) , by property 3. 1 ⎜ ⎟ ⎝ 2 ⎠ T -1 2 2 2 (c) y V y = Y +Y /4 ~ χ (2, 9 / 4) , by property 6. 1 2 Q T -1 1 ⎡9 Y 2 2 2 2 3 4 3 2 ⎤~ 2 (2) 1.3 (a) y - μ V y - μ − − Y − Y − + Y − χ . This 1 ( ) ( ) 35 ⎣ ( 1 ) ( 1 )( 2 ) ( 2 ) ⎦ 1 1 U Υ +2Υ Υ Υ V 3 2 12 can be verified by considering (=−3 ) and ( =+ − ) 1 2 1 2 2 15 2 21 and showing that U and V are independent, identically distributed random variables with the distribution N(0, 1) and that Q U 2 =+V 2 . T -1 1 2 2 2 (b) Q y V y (