STAT 210B HWK #5 SOLUTIONS
GARVESH RASKUTTI
(1) Let X1 , ., Xn be i.i.d according to the Pareto distribution with density
f (x) = c x(+1) ,
where 0 < and 0 < c < x. Determine the Wald, Rao and likelih
Stat 210B Homework Assignment 2 (due February 15)
n
1. Consider the V-statistic Vn = 1/n2 n
i=1
j =1 h(xi , xj ) for a symmetric kernel h such that
2 < . Show that V is asymptotically normal.
Eh
n
2.
STAT 210B HWK #1 SOLUTIONS
GARVESH RASKUTTI
(1) Given densities pn and qn with respect to some measure , dene the
likelihood ratio Ln (x) as Ln (x) = qn (x)/pn (x) for pn (x) > 0, Ln (x) = 1 if pn (x)
Stat 210B Homework Assignment 3 (due March 3)
1. Show that for all 1 p < , we have:
Hp (, Q, F ) Hp,B (, Q, F )
for all . Show that if Q is a probability measure, we have:
Hp,B (, Q, F ) H (/2, F ).
2
STAT 210B HWK #2 SOLUTIONS (DUE FEBRUARY 17)
GARVESH RASKUTTI
1
(1) Consider the V-statistic Vn = n2 n=1 j =1 h(xi , xj ) for a symmetric kernel
i
h such that1 Eh2 < . Show that Vn is asymptotically n
Stat 210B Homework Assignment 4 (due March 29)
1. Given densities p1 and p2 with respect to some -nite measure , dene that the Hellinger
distance as follows:
1/2
1
2
h(p1 , p2 ) =
( p1 p2 ) d
2
and de
STAT 210B HWK #3 SOLUTIONS (DUE MARCH 13)
GARVESH RASKUTTI
(1) Show that for all 1 p < , we have
Hp (, Q, F ) Hp,B (, Q, F )
for all . Show that if Q is a probability measure, we have
Hp,B (, Q, F ) H
Stat 210B Homework Assignment 5 (due April 19)
1. Let X1 , . . . , Xn be i.i.d. according to the Pareto distribution with density
f (x) = c x+1 ,
where 0 < and 0 < c < x. Determine the Wald, Rao and l
STAT 210B HWK #4 SOLUTIONS (DUE MARCH 29)
GARVESH RASKUTTI
(1) Given densities p1 and p2 with respect to some nite measure , dene
that the Hellinger distance as follows:
h(p1 , p2 ) =
( p1 p2 )2 d
1
2
Stat 210B Homework Assignment 1 (due February 1)
1. Given densities pn and qn with respect to some measure , let X be distributed according to
the distribution with density pn . Dene the likelihood ra