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Higher-order approximations to p-values can be obtained from the loglikelihood function and a reparameterization that can be viewed as a canonical parameter in an exponential family approximation to the model. This approach clarifies the connection between Skovgaard (1996) and Fraser et al. (1999a), and shows that the Skovgaard approximation can be obtained directly using the mean loglikelihood function. Copyright 2010, Oxford University Press.

SUMMARY Although Simes' modification of the Bonferroni procedure tends to perform very well, albeit often being slightly liberal for negatively dependent hypotheses, there are special cases where it fails more dramatically. We prove that these special cases are indeed special, applying only to specific significance levels, and obtain a strong bound on the average deviation of the Simes corrected P-value from the true probability over any interval of P-values. From this, it is argued that Simes' procedure should be expected to perform well except for pathological examples.

To compensate for item nonresponse, hot deck imputation procedures replace missing values with values that occur in the sample. Fractional hot deck imputation replaces each missing observation with a set of imputed values and assigns a weight to each imputed value. Under the model in which observations in an imputation cell are independently and identically distributed, fractional hot deck imputation is shown to be an effective imputation procedure. A consistent replication variance estimation procedure for estimators computed with fractional imputation is suggested. Simulations show that fractional imputation and the suggested variance estimator are superior to multiple imputation estimators in general, and much superior to multiple imputation for estimating the variance of a domain mean.

SUMMARY Saddlepoint approximations are shown to be easy to use and accurate in a variety of simple bootstrap and randomization applications. Examples include mean estimation, ratio estimation, two-sample comparisons, and autoregressive estimation.