Nonparametric Testing Procedure Research Articles

Nonparametric multiple test procedures with data-driven order of hypotheses and with weighted hypotheses

Recently, Kropf (Shaker Verlag, Aachen, 2000) and Kropf and Läuter (Biometrial J. 44(7) 2002 789) proposed a procedure for testing separate hypotheses concerning the single variables of a multivariate normal population with strong control of the familywise type I error. The procedure is particularly focussed on situations where all variables have approximately equal variances. It establishes a suitable data-driven order of hypotheses and carries out unadjusted tests in that order until the first nonsignificant result. This proposal has been generalised by Westfall et al. (In: Benjamini, Y., Bretz, F., Sarkar, S.K. (Eds.), Recent developments in multiple comparison procedures, IMS Lecture Notes and Monograph Series, IMS, Haywood CA, 2004) in a weighted Bonferroni–Holm procedure that can be tuned with a free parameter η and involves the above procedure as limiting case for η→∞. Here, a nonparametric counterpart is given. Whereas the original parametric procedures utilise properties of spherically distributed matrices to maintain the exact type I error despite the data-dependent sorting or weighting of the variables, the nonparametric procedure exploits the independence of rank and order statistics under the null hypothesis to arrange the variables in a suitable order for unadjusted sequential testing or to weight the variables. Again, the procedures are sensible if the variables have a similar variance. The procedures are demonstrated with data from gene-expression studies in hot or cold thyroid nodules using Affymetrix GeneChips. Furthermore, simulation results are shown to consider the power under various conditions.

Quantitative CTG appraisal sub partu with a new CTG score: diagnostic significance of the parameters of the acid-base balance in umbilical blood?

As a role, the severity of "CTG pathology" in acute or chronic fetal hypoxia could only be registered but not quantified exactly by visual examination. For this reason, the term "CTG pathology" has not been unequivocally defined. The objective of the present study was to describe the dependence of fetal heart rate phenomena on the parameters of the acid-base balance quantitatively and to subject the latter to statistical analysis. The last 120 minutes of a total of 411 interference-free cardiotocograms directly registered intra partum (HP, 2 cm/min) were evaluated in terms of the visual appearance of CTG: the frequency level and the fluctuation of every single minute and the deceleration-area sum were considered for 30 CTG minutes per fetus. A new CTG score was conceived which envisages six points for the mean frequency according to specific definitions, three points for the deceleration-area and further six points for the fluctuation (long-term variability). The heart rate data and clinical factors were analyzed off-line using parametric and non-parametric test procedures with special programs (FORTRAN) on an IBM system (6150). Besides the pH values in the umbilical arterial and venous blood, direct measurements of blood gases (pO(2), pCO(2)) were also available in 113 cases, so that the base excess (mmol/l) and the oxygen saturation (%) could be calculated according to known algorithms. For the last 30 minutes ante partum, the CTG score correlates highly significantly (P << 10(-4)) with the actual pH value in the umbilical arterial blood (r = -0.6002). The correlation with the base excess is better (r = 0.642, P << 10(-4)), whereas the correlation with the directly measured pCO (2) is weaker (r = 0.587). Such strict correlations could not be demonstrated for oxygen saturation in the umbilical arterial or umbilical venous blood (r = -0.258, P = 0.0057 and r = -0.308, P = 0.0009). The good correlations of the variables of the fetal acid-base balance with the CTG phenomena registered with the score can be used for clinical purposes. However, analysis of the CTG with the naked eye is not practically feasible for the obstetricians; it must therefore be done per computer. Quantitative CTG analysis has created the perspective of a promising new method for fetal monitoring sub partu.

An adaptive allocation for continuous response using Wilcoxon–Mann–Whitney score

In clinical trials, adaptive designs are sometimes used to force imbalance in allocation between two or more competitive treatments. Existing works are mostly based on dichotomous or polychotomous responses. In the present work, assuming that the responses are continuous variables, we investigate a two-treatment allocation scheme based on Wilcoxon–Mann–Whitney scores. The proposed scheme is used to provide two nonparametric test procedures for identity of two univariate continuous populations against location alternatives. Again, we give an exactly distribution free solution for generalized Behrens–Fisher problem.

Nonparametric Tests for Interval‐Censored Failure Time Data

AbstractThis paper discusses two sample nonparametric comparison of survival functions when only interval‐censored failure time data are available. The problem considered often occurs in, for example, biological and medical studies such as medical follow‐up studies and clinical trials. For the problem, we present and study several nonparametric test procedures that include methods based on both absolute and squared survival differences as well as simple survival differences. The presented tests provide alternatives to existing methods, most of which are rank‐based tests and not sensitive to nonproportional or nonmonotone alternatives. Simulation studies are performed to evaluate and compare the proposed methods with existing methods and suggest that the proposed tests work well for nonmonotone alternatives as well as monotone alternatives. An illustrative example is presented.

A New Nonparametric Test of Cointegration Rank

This paper suggests a new nonparametric testing procedure for determining the rank of nonstationary multivariate cointegrated systems. The asymptotic properties of the procedure are determined and a Monte Carlo study is carried out.

A Pearson's test for symmetry with an application to the Spanish business cycle

In this paper, we look for asymmetries in the Spanish business cycle. To that end, we firstly propose an easy nonparametric testing procedure to test for symmetry based on a Pearson's chi-squared statistic, which we call P-test. Then, we test for two popular forms of asymmetry, deepness and steepness, using a battery of nonparametric tests. In addition, we analyse possible complementarities between the tests used in this paper, and we compute p-value adjustments for multiple tests.

Generalized nonparametric test procedures for comparing multiple cause-specific hazard rates

In this paper, a generalized nonparametric test procedure for comparing k types of failure in a competing risks model is proposed. The test'procedure is based on the test process defined as a set of weighted integrals of the difference between Aalen-estimated cumulative cause-specific hazards and the average of these estimators. Estimation of the distribution function of the testing process under the null hypothesis is usually the main barrier in developing a test procedure. We introduce a vector of symmetrically inputed processes conditional on the competing risks data and show that the two processes have the same asymptotic distribution under the null hypothesis. This result gives us flexibility in selecting types of statistics and weight functions for various alternatives. Several types of tests including Chi-square type and supremum type for testing the null hypothesis H0 versus various alternative hypotheses are discussed in this paper. With an appro-priate selection of weight function, we also obtain a class of distribution-free tests for competing risks data with k-types of failure.

Cyclin D and cyclin E expression in normal and adenomatous pituitary.

Cyclins play an important role in the regulation of cell progression through the cell cycle. Over-expression of the cyclins has been shown in many different tumour types. Pituitary adenomas are a common form of endocrine neoplasia in the human, but have been little studied in terms of the expression of the principal cyclins regulating checkpoint exit, cyclin D1 and cyclin E. We therefore investigated the expression of cyclin D1 and cyclin E in a range of benign and metastatic pituitary tumours. We studied a total of 95 pituitaries, including normal pituitary (n=20), Cushing's disease (n=19), somatotroph tumours (n=19), non-functioning adenomas (n=18), prolactinomas (n=7), aggressive tumours (n=9) and pituitary carcinoma (n=3). All tumours and normal tissue were immunostained for cyclin D1 and cyclin E using a standard technique, and were then subjected to blinded analysis by a single observer and the extent of staining quantified on the basis of 500 cell counts per tissue. The distribution of positive staining between different tissues was analysed by non-parametric test procedures. There was no cytoplasmic staining for cyclin D1 in any tissue. Nuclear staining was generally sparse, but was statistically more frequent in non-functioning and aggressive tumours compared with other tumour types or normal pituitary. Cyclin E was also sparsely expressed, but was specifically increased in corticotroph tumours from patients with Cushing's disease. We report cyclin D1 over-expression in aggressive and non-functioning pituitary tumours, and that cyclin E expression is more frequently seen in Cushing's disease. The high level of cyclin E expression in Cushing's disease may relate to the low level of p27 protein expression previously reported in corticotroph tumours.

Nonparametric empirical bayes procedures, asymptotic optimality And rates Of convergence For two‐tail tests In exponential family*

This paper provides nonparametric empirical Bayes (EB) solutions to two-tail test in the exponential family , under the standard product loss function which is proportional to (θ-θ1) (θ-θ2) for incorrectly accepting H1. Based on empirical data X1,…X n , and the present data X from nonparametric (in the sense that G is completely unknown and unspecified) EB test procedures are proposed. These procedures are asymptotically optimal (a.o.) whenever Further, for every integer s > 0 a class of non-parametric EB test procedures is proposed. These procedures are shown to be a.o. with rates for 0 < λ ≤ 2 satisfying certain conditions. Examples of exponential families and gamma densities are given where these conditions reduce to some simple moment conditions on G. No assumption on the smoothness of the function u(.), (and hence of the density function of X), is made at all for any of the results of this paper. By an example of a family of distributions, it is demonstrated that the rates arbitrarily close to o(n -1) can be attained by these procedures in some situations. It is noted, however, that the actual rates of convergence really depends on the nature of the unknown prior distribution G.

Optimal allocation procedure in ranked set sampling for unimodal and multi-modal distributions

This paper presents a ranked set sample allocation procedure that is optimal for a number of nonparametric test procedures. We define a function that measures the amount of information provided by each observation given the actual joint ranking of all the units in a set. The optimal ranked set sample allocates order statistics by maximizing this information function. This paper shows that the optimal allocation of order statistics in a ranked set sample is determined by the location of the mode(s) of the underlying distribution. For unimodal, symmetric distributions, optimal allocation always quantifies the middle observation(s). If the underlying distribution with cdf F is a multi-modal distribution with modes \(R, \ldots ,R_k \), then the optimal allocation procedure quantifies observations at \(mF(R_1 ), \ldots ,mF(R_1 )\) in a set of size m. We provide similar results for unimodal, asymmetric distributions. We also propose a new sign test which considers the relative positions of the quantified observations from the same cycle in a ranked set sample. The proposed sign test provides improvement in the Pitman efficiency over the ranked set sample sign test of Hettmansperger (1995). It is shown that the information optimal allocation procedure induced by Pitman efficiency is equivalent to the optimal allocation procedure induced by the information criteria. We show that the finite sample distribution of the proposed test based on this optimal design is binomial.

Spatial autocorrelation analysis of individual multiallele and multilocus genetic structure.

Population genetic theory predicts that plant populations will exhibit internal spatial autocorrelation when propagule flow is restricted, but as an empirical reality, spatial structure is rarely consistent across loci or sites, and is generally weak. A lack of sensitivity in the statistical procedures may explain the discrepancy. Most work to date, based on allozymes, has involved pattern analysis for individual alleles, but new PCR-based genetic markers are coming into vogue, with vastly increased numbers of alleles. The field is badly in need of an explicitly multivariate approach to autocorrelation analysis, and our purpose here is to introduce a new approach that is applicable to multiallelic codominant, multilocus arrays. The procedure treats the genetic data set as a whole, strengthening the spatial signal and reducing the stochastic (allele-to-allele, and locus-to-locus) noise. We (i) develop a very general multivariate method, based on genetic distance methods, (ii) illustrate it for multiallelic codominant loci, and (iii) provide nonparametric permutational testing procedures for the full correlogram. We illustrate the new method with an example data set from the orchid Caladenia tentaculata, for which we show (iv) how the multivariate treatment compares with the single-allele treatment, (v) that intermediate frequency alleles from highly polymorphic loci perform well and rare alleles poorly, (vi) that a multilocus treatment provides clearer answers than separate single-locus treatments, and (vii) that weighting alleles differentially improves our resolution minimally. The results, though specific to Caladenia, offer encouragement for wider application.

Theory &amp; Methods: A Nonparametric Test for the Parallelism of Two First‐Order Autoregressive Processes

A nonparametric testing procedure for the parallelism of two first‐order autoregressive processes is presented. This paper discuss the Mann–Whitney statistic, its natural competitor two‐sample t‐test, and the bootstrap method. It studies the asymptotic efficacies of the studentized Mann–Whitney statistic and the t‐test statistic with their relative efficiency. Simulation results for comparing the powers of these test statistics are also presented.

Nonparametric Regression and Causality Testing:A Monte‐Carlo Study

In this paper we propose a new procedure for causality testing using nonparametric additive models. We argue that the major advantage of our proposed method is that it can be used if the underlying data generation process (DGP) is either linear or nonlinear. Our results show that the nonparametric testing procedure provides a more robust test of causality. Furthermore, we show that the loss of power associated with the nonparametric procedure is minimal if the true DGP is linear.

Explanatory factors for trading volume responses to annual earnings announcements: Evidence from the Korean stock market

This study provides empirical evidence regarding the effect of annual accounting earnings announcements on investors' trading behavior in the Korean stock market. Unexpected earnings (UE), the degree of predisclosure information asymmetry and risk change are hypothesized to have positive correlations with abnormal trading volume around the disclosure date. On the other hand, a negative relationship between firm size and trading volume around the disclosure date is hypothesized. Empirical studies using non-parametric testing procedures confirm most of the research hypotheses except for risk change effect.

A Simple Three-Step Procedure for Parametric and Nonparametric Assessment of Bioequivalence

A simple three-step approach for the assessment of bioequivalence is proposed. According to the decision rule of this approach, average bioequivalence is assessed first (Step 1). If approved, then population bioequivalence will be assessed next (Step 2). Again, if approved, then individual bioequivalence can be assessed as the final stage (Step 3). For the evaluation of these bioequivalence criteria, parametric and nonparametric testing procedures are suggested on the original and logarithmic scale of measurement. A clear advantage of these testing procedures is that they can be set up using elementary test statistics and, therefore, they are readily accessible to the practitioners. An example is also presented to illustrate the method.

Log-concave Probability Distributions: Theory and Statistical Testing

This paper studies the broad class of log-concave probability distributions that arise in economics of uncertainty and information. For univariate, continuous, and log-concave random variables we prove useful properties without imposing the dierentiability of density functions. Discrete and multivariate distributions are also discussed. We propose simple non-parametric testing procedures for log-concavity. The test statistics are constructed to test one of the two implications of log-concavity: increasing hazard rates and new-is-better-than-used (NBU) property. The tests for increasing hazard rates are based on normalized spacing of the sample order statistics. The tests for NBU property fall into the category of Hoeding’s U-statistics.

Long term effects of ritodrine on blood pressure and heart rate of adolescents exposed during the prenatal stage

Objective: To determine the long term cardiovascular effects in adolescents exposed to ritodrine during prenatal stage. Study design: Twenty-seven ritodrine-exposed subjects and 19 controls, of both sexes, clinically healthy, and born at normal term, were evaluated for systolic blood pressure (SBP), diastolic blood pressure (DBP) and heart rate (HR) each during 48 hours, with a Colin Ambulatory monitor. Data analysis were performed by individual Cosinor method, and non-parametric Mann Whitney's test and Lamotte procedures. Adolescents who were exposed to ritodrine showed losses in the HR rhythm and rising middle pulse values. Although SBP and DBP rhythm remains constant, the increase of maximum and minimum values for SBP as well as a rise of maximal rates of DBP suggest a possible hypertensive effect mediated by beta mimetic exposure. This study suggests a hypertensive effect mediated by beta mimetic exposure.

Volatility Shifts in Stock Market Returns : A Look at Emerging Markets

The volatility or risk parameter, usually defined as the standard deviation of stock returns, forms the cornerstone of contemporary finance theories. Reliability of results obtained from various financial decision making models depends on the stability, finiteness, and accuracy of risk estimates. This paper by Broca examines the stability of this parameter using weekly market data over 1990-91 in respect of 17 emerging markets identified by the International Finance Corporation. Through an application of nonparametric test procedures, the study detects variance heterogeneity for 6 out of 17 markets. Though not pervasive, a review of major political-economic events over the sample period, with special reference to the Gulf crisis of August 1990, is attempted to partly validate empirical findings.

The Stabilizing Effect of the ERMon Exchange Rates and Interest Rates: An Empirical Investigation

This paper applies nonparametric test procedures to test for a shift in the volatility of nominal and real exchange rates for ERM members and nonmembers. The results imply a reduction in volatility for the ERM members, especially during the second half of the period of operation of the ERM. We also demonstrate that this enhanced stability was not bought at the expense of increased interest rate volatility. The issue of interest rate volatility during sterling’s participation in the ERM is also examined.

The Stabilizing Effect of the Erm on Exchange Rates and Interest Rates: An Empirical Investigation

This paper applies nonparametric test procedures to test for a shift in the volatility of nominal and real exchange rates for ERM members and nonmembers. The results imply a reduction in volatility for the ERM members, especially during the second half of the period of operation of the ERM. We also demonstrate that this enhanced stability was not bought at the expense of increased interest rate volatility. The issue of interest rate volatility during sterling`s participation in the ERM is also examined.