3 Statistical methods 4 3.1 Wald-Wolfowitz test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.2 Kolmogorov-Smirnov tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.3 Mean deviation tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.4 Aggregated F-test . . . . . . ....

We address the classic problem of interval estimation of a binomial proportion. The Wald interval p̂ ± zα/2n−1/2(p̂(1 − p̂))1/2 is currently in near universal use. We first show that the coverage properties of the Wald interval are persistently poor and defy virtually all conventional wisdom. We then proceed to a theoretical comparison of the standard interval and four additional alternative inter...

We evaluate by simulation three model-based methods to test the influence of a single nucleotide polymorphism on a pharmacokinetic parameter of a drug: analysis of variance (ANOVA) on the empirical Bayes estimates of the individual parameters, likelihood ratio test between models with and without genetic covariate, and Wald tests on the parameters of the model with covariate. Analyses are perfo...

We test the presence of a change of slope in a logistic regression model with covariate measured with errors. Under the null hypothesis of no change-point, estimation of a single intercept and slope can be carried out straightforwardly by various conditional score based methods. If the alternative hypothesis holds and indeed there exists a change-point, estimation becomes more challenging, neve...

Testing whether two parameters have the same sign is a nonstandard problem due to the non-convex shape of the parameter subspace satisfying the composite null hypothesis, which is a nonlinear inequality constraint. We describe a simple example where the ordering of likelihood ratio (LR), Wald, and Bayesian sign equality tests reverses the “usual” ordering: the Wald rejection region is a subset ...

1 MRC Vitamin Study Research Group. Prevention of neural tube defects: results of the MRC vitamin study. Lancet 1991;338:132–7. 2 Little J, Elwood M. Geographic variation. In: Elwood JM, Little J, Elwood JH, eds. The epidemiology and control of neural tube defects. Oxford: Oxford University Press, 1992:96–145. 3 Rogers SC, Weatherall JAC. Anencephalus, spina bifida and congenital hydrocephalus....

Theoretical justifications can be easier to derive for score test-based screening compared to Wald test-based screening. The main task is to find a finite-sample bound for P{|U j (0)| ≥ γn}, which can often be done by applying Bernstein-type inequalities. In contrast, Wald testbased screening requires deriving non-asymptotic tail bounds for the marginal estimators, which can be considerably mor...