Empirical power comparisons of two mrpp rank tests

Simulated powers of the MRPP two-sample rank test statistic ?₁- are compared with the powers of the MRPP test statistic ?₂(the two-sided Wilcoxon-Mann-Whitney test) for large samples from several underlying populations. Powers are obtained using two approximate distributions of ?₁ involving three and four moments

respectively, The use of the fourth moment indicates that an approximation to the null distribution of ? based on four moments can perform better     

Validation of an Arabic ADAM questionnaire for androgen deficiency screening in the Arab community

Background.?It is well documented that testosterone levels decline with age, this decline is associated with symptoms which could be assessed denoting androgen deficiency. We investigated the validity of an Arabic version of the Saint Louis University androgen deficiency in ageing men (ADAM) questionnaire to screen for androgen deficiency in Saudi and non Saudi Arabic speaking men.

Methods.?It was a cross sectional study of ambulatory community-based Arabic Saudi men recruited from Volunteers in Riyadh city, Capital of Saudi Arabia, aged 18–80 years. Seven hundred thirty men agreed to fill the Arabic ADAM questionnaire, they were invited to a morning blood sample for total testosterone and sex hormone binding globulin and those who agreed to complete the whole study were only 407 men. Low serum bioavailable testosterone (BT) levels (androgen deficiency) were defined as <10th percentile of serum BT levels in young healthy Saudi men (18–30 years).

Results.?Cronbach's Alpha of 0.71 (n?=?730) showed a good internal consistency of the Arabic ADAM questionnaire. Among participants, 18.2% and 77.6% had low serum BT levels and a positive ADAM questionnaire, respectively. The prevalence of positive ADAM and low serum BT is increasing with age. The Arabic ADAM questionnaire had a high sensitivity of 86.5%, a low specificity of 24.3%, and positive predictive values (+PVs) and negative (?PVs) of 20.3% and 89%, respectively.

Conclusion.?The Arabic ADAM questionnaire has a very good sensitivity but very low specificity for screening of androgen deficiency in Saudi men, therefore biological confirmation is needed especially when clinical symptoms of androgen deficiency are present.     

Inference procedures for the variance gamma model and applications

Goodness-of-fit tests for the family of the four-parameter normal–variance gamma distribution are constructed. The tests are based on a weighted integral incorporating the empirical characteristic function of suitably standardized data. Non-standard algorithms are employed for the computation of the maximum-likelihood estimators of the parameters involved in the test statistic, while Monte Carlo results are used in order to compare the new test with some classical goodness-of-fit methods. A real-data application is also included.     

On the theory of modified randomization tests for nonparametric hypotheses

A general randomization test for nonparametric hypotheses which is a modification of permutation tests in proposed. The exact level of the test is derived and under mild gegularity conditions, a general result on the consistency of the power function is obtained. Applications to several testing problems are considered. Asymptotic expansions of the power of this test are derived with respect to contiguous alternatives thus test are derived with respect to contiguous alternatives thus enabling us to make deficiency comparisons with permutation tests. The paper concludes with some Monte Carlo simulations verifying the theoretical results derived.     

Bartlett-corrected tests for normal linear models when the error covariance matrix is nonscaiar

This paper provides Bartlett corrections to improve likelihood ratio tests for heteroskedastic normal linear models when the error covariance matrix is nonscaiar and depends on a set of unknown parameters. The Bartlett corrections are simple enough to be used algebraically to obtain several closed-form expressions in special cases. The corrections have also advantages for numerical purposes because they involve only simple operations on matrices and vectors.     

Likelihood ratio tests for testing for multiple contaminants in the shocks and labelled slippage models

In the literature related to the study of lifelengths of experimental units, little attention has been paid to the models where shocks to the units generate outliers. In the present article, we consider a situation where n experimental units under investigation receive shocks at several time points. The parameter values of the lifelength distribution may change due to each shock, resulting in the generation of outliers. We derive the likelihood ratio test statistic to investigate if the shocks have significantly altered the parameter values. We also derive a likelihood ratio test under the labelled slippage alternative with multiple contaminations. Monte Carlo studies have been carried out to investigate the power of the proposed test statistics.     

Testing in semiparametric models with interaction, with applications to gene–environment interactions

Summary.  Motivated from the problem of testing for genetic effects on complex traits in the presence of gene–environment interaction, we develop score tests in general semiparametric regression problems that involves Tukey style 1 degree-of-freedom form of interaction between parametrically and non-parametrically modelled covariates. We find that the score test in this type of model, as recently developed by Chatterjee and co-workers in the fully parametric setting, is biased and requires undersmoothing to be valid in the presence of non-parametric components. Moreover, in the presence of repeated outcomes, the asymptotic distribution of the score test depends on the estimation of functions which are defined as solutions of integral equations, making implementation difficult and computationally taxing. We develop profiled score statistics which are unbiased and asymptotically efficient and can be performed by using standard bandwidth selection methods. In addition, to overcome the difficulty of solving functional equations, we give easy interpretations of the target functions, which in turn allow us to develop estimation procedures that can be easily implemented by using standard computational methods. We present simulation studies to evaluate type I error and power of the method proposed compared with a naive test that does not consider interaction. Finally, we illustrate our methodology by analysing data from a case–control study of colorectal adenoma that was designed to investigate the association between colorectal adenoma and the candidate gene NAT2 in relation to smoking history.     

False Discovery Rate Control of Step‐Up‐Down Tests with Special Emphasis on the Asymptotically Optimal Rejection Curve

Abstract. This paper is concerned with exact control of the false discovery rate (FDR) for step‐up‐down (SUD) tests related to the asymptotically optimal rejection curve (AORC). Since the system of equations and/or constraints for critical values and FDRs is numerically extremely sensitive, existence and computation of valid solutions is a challenging problem. We derive explicit formulas for upper bounds of the FDR and show that under a well‐known monotonicity condition, control of the FDR by a step‐up procedure results in control of the FDR by a corresponding SUD procedure. Various methods for adjusting the AORC to achieve finite FDR control are investigated. Moreover, we introduce alternative FDR bounding curves and study their connection to rejection curves as well as the existence of critical values for exact FDR control with respect to the underlying FDR bounding curve. Finally, we propose an iterative method for the computation of critical values.     

Likelihood ratio test for discordancy with slippage alternatives

A likelihood ratio test for discordancy in the sample is considered with slippage alternatives. It is shown for a wide class of univariate distributions that only the extreme observations in the sample need to be tested for discordancy. This result provides a firmer support to many commonly used discordancy tests that take only extreme observations as candidates. The problem of testing multiple discordant observations is also discussed.