Page 277 - Contributed Paper Session (CPS) - Volume 7

CPS2099 Takatsugu Yoshioka et al.

The constants and are decided using the first and second moments of U.
That is, we can follow

Therefore, using the asymptotic expansions of E[U]and E[U ], the new
2
approximation to the values of and are given. In addition, we propose
another approximate solution by adjusting the degrees of freedom of F
distribution. In the above results, we estimated the second degree of
freedom and the coefficient , but further estimate the first degree of
freedom as

and the constants , and are decided using the first, second and third
2
moments of T . That is, we can follow

Therefore, using the asymptotic expansions of E[T ], E[(T ) ] and E[(T ) ],
2 2
2 3
2
the new approximation to the values of , and are given.

3. Result
We give the two-step monotone missing data to be generated from
4
multivariate normal distribution by Monte Carlo simulation (10 runs) and
2
calculate the upper 100α percentile of T type statistics and F approximations,
and type I error with significant level α=0.05,0.01 where = 4(( , ) =
1
2
(2,2)), which are given by
()
,
2
2
2
α = P ( > ()) , = ( > )
2
1

Note that the simulated values approach closer to the upper percentiles of
chi-squared distribution when sample size become large. The type I error rates
show that α2 are very good approximations.

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