This paper derives an explicit approximation for the tail probability of a sum of sample values taken without replacement from an unrestricted finite population. The approximation is shown to hold under no conditions in a wide range with relative error given in terms of the standardized absolute third moment of the population,
. This approximation is used to obtain a result comparable to the well-known Cramér large deviation result in the independent case, but with no restrictions...
This paper derives an explicit approximation for the tail probability of a sum of sample
values taken without replacement from an unrestricted finite population. The approximation
is shown to hold under no conditions in a wide range with relative error given in terms of
the standardized absolute third moment of the population,
. This approximation is used to obtain
a result comparable to the well-known Cramér large deviation result in the independent
...
Let
be a Studentized U-statistic. It is proved that a Cramér type moderate deviation (
≥ )/(1 − Φ()) → 1 holds uniformly in ∈ [0, (
)) when the kernel satisfies some regular conditions.
Let
be a Studentized U-statistic. It is proved that a Cramér type
moderate deviation (
≥ )/(1 − Φ()) → 1 holds uniformly in
[0, (
))
when the kernel satisfies some regular conditions.
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