Proposed Test Procedure Research Articles

Goodness-of-fit tests in parametric regression based on the estimation of the error distribution

Consider a heteroscedastic regression model Y = m(X) + s(X) e, where m(X) = E(Y vertical bar X) and sigma(2)(X) = Var(Y vertical bar X) are unknown, and the error e is independent of the covariate X. We propose a new type of test statistic for testing whether the regression curve m(.) belongs to some parametric family of regression functions. The proposed test statistic measures the distance between the empirical distribution function of the parametric and of the nonparametric residuals. The asymptotic theory of the proposed test is developed, and the proposed testing procedure is illustrated by means of a small simulation study and the analysis of a data set.

New Tests for Null Hypothesis of Non Unity Ratio of Proportions

Testing for noninferiority and equivalence between an experimental therapy and a standard therapy in terms of the ratio of binomial proportions is considered. New tests based on the Fieller–Hinkley distribution of the ratio of random variables are proposed. Restricted maximum likelihood estimates of the null variances are used to derive the tests. Sample size determination is discussed. The proposed test procedure is extended to multiple tables. The tests are applied to numerical examples.

The Analysis of Bivariate Truncated Data Using the Clayton Copula Model

In individuals infected with human immunodeficiency virus (HIV), distributions of quantitative HIV RNA measurements may be highly left-censored due to values falling below assay detection limits (DL). It is of the interest to find the relationship between plasma and semen viral loads. To address this type of problem, we developed an empirical goodness-of-fit test to check the Clayton model assumption for bivariate truncated data. We also used truncated tau to estimate the dependence parameter in the Clayton model for this type of data. It turns out that the proposed methodology works for both truncated and fixed left censored bivariate data. The proposed test procedure is demonstrated using an HIV data set, and statistical inference is drawn based on corresponding test result.

Detecting Multiple Changes in Persistence

This paper considers the problem of testing for and dating changes (at unknown points) in the order of integration of a time series between different trend-stationary and difference-stationary regimes. While existing procedures in the literature are designed for processes displaying only a single such change in persistence, our proposed methodology is also valid in the presence of multiple changes in persistence. Our procedure is based on sequences of doubly-recursive implementations of the regression-based unit root statistic of Elliott et al. (1996). The asymptotic validity of our procedure is demonstrated analytically. We use Monte Carlo methods to simulate both finite sample and asymptotic critical values for our proposed testing procedure and to simulate the finite sample behaviour of our procedure against a variety of single and multiple persistence change series. The procedure is shown to work well in practice. The impact of deterministic level and trend breaks on our procedure is also discussed. An empirical application of the procedure to interest rate data is considered.

Assessment of the dustiness and the dust liberation mechanisms of limestone quarry operations

In surface mineral workings, dust is potentially generated from a range of activities like site preparation, stockpiling, loading, transportation and mineral processing operations. Aggregate quarries are one of the largest extractive industrial sectors in UK. This project investigates the propensity of a limestone ore to generate dust due to handling and comminution processes. The dustiness of a limestone ore is assessed using the Warren Spring Laboratory rotating drum (HSE-WSL). The effect of the operating parameters of the WSL rotating drum to the dustiness of limestone is evaluated prior to testing. Preliminary testing on the effect of the operational parameters to the dustiness values showed that the consistency of the end results is closely related to them, thus they need to be carefully controlled. Also, control testing took place to identify the maximum dustiness value per operational parameter, so as to define an optimum set for the limestone sample. This testing procedure is compared with the HSL proposed testing procedure and their differences are quantified. The use of the optimum experimental protocol (OPT-TP) determined by preliminary testing yielded much higher dustiness values even though the initial mass of test material is less than the sample mass used in the HSL testing procedure (HSL-TP). A variety of different fractions is tested and the dustiness indices of the total dust and the health related fractions are determined. Different limestone fractions were found to exhibit different dustiness levels, whereas the concentration of fine material in the test sample is closely related to the dust yield. The airborne fraction was collected for particle size analysis. The dust particle size distributions and the cumulative percentages of volume concentrations below 10 and 2.5 μm were determined. Experimental conclusions proved that control over operational parameters of industrial processes (i.e. conveying of materials, stockpiling) such as the time scale of a process or the limestone mass could contribute to potentially lower levels of particulate matter. Also, lower concentrations of fine material within industrial processes could conclude to lower dust yield. The minimization of fine material could be achieved through optimization practices of the degradation—classification processes (comminution, sieving, etc.). Dustiness measurements and particle size analysis are valuable tools to the mining sector, legislative parties and occupational hygienists as they can assist the development of a correct dust assessment plan as well as mitigation methodologies, work practices and health and safety regulations.

Statistical inference for a semiparametric measurement error regression model with heteroscedastic errors

Efficient inference for regression models requires that the heteroscedasticity be taken into account. We consider statistical inference under heteroscedasticity in a semiparametric measurement error regression model, in which some covariates are measured with errors. This paper has multiple components. First, we propose a new method for testing the heteroscedasticity. The advantages of the proposed method over the existing ones are that it does not need any nonparametric estimation and does not involve any mismeasured variables. Second, we propose a new two-step estimator for the error variances if there is heteroscedasticity. Finally, we propose a weighted estimating equation-based estimator (WEEBE) for the regression coefficients and establish its asymptotic properties. Compared with existing estimators, the proposed WEEBE is asymptotically more efficient, avoids undersmoothing the regressor functions and requires less restrictions on the observed regressors. Simulation studies show that the proposed test procedure and estimators have nice finite sample performance. A real data set is used to illustrate the utility of our proposed methods.

Simultaneous Testing for the Successive Differences of Exponential Location Parameters

Suppose that k (k ≥ 3) treatments under comparison are ordered in a certain way. For example, the treatments may be increasing dose levels in dose response experiments. The exponential distribution E(μ,Θ) is generally used to model the effective duration of a drug, where the location parameter μ is referred to as latency period that may decrease/increase with the increase in dose level of the drug. In such situations, the experimenter may be interested in the successive comparisons of the treatments. Let E(μ1,Θ1),…,E(μ k ,Θ k ) be k independent exponential distributions/populations with μ i (Θ i ) as the location (scale) parameter of the i th population, i = 1,…,k. In this article, we propose test procedures for simultaneously testing the family of hypotheses A recursive method for computing the critical constants is discussed. The required tables of critical constants for the implementation of the proposed test procedures are presented. The test procedure is used to derive the simultaneous confidence intervals for the successive differences between the location parameters; that is, μ2 − μ1,μ3 − μ2,…,μ k − μ k−1. We also extend these simultaneous confidence intervals for successive differences to a larger class of contrasts of the location parameters.

Simulation based selection of competing structural econometric models

Abstract This paper proposes a formal model selection test for choosing between two competing structural econometric models. The procedure is based on a novel lack-of-fit criterion, namely, the simulated mean squared error of predictions (SMSEP), taking into account the complexity of structural econometric models. It is asymptotically valid for any fixed number of simulations, and allows for any estimator which has a n asymptotic normality or is n α -consistent for α > 1 / 2 . The test is bi-directional and applicable to non-nested models which are both possibly misspecified. The asymptotic distribution of the test statistic is derived. The proposed test is general, regardless of whether the optimization criteria for estimation of competing models are the same as the SMSEP criterion used for model selection. A Monte Carlo study demonstrates good power and size properties of the test. An empirical application using timber auction data from Oregon illustrates the usefulness and generality of the proposed testing procedure.

Tests for a Simple Tree Order Restriction with Application to Dose–Response Studies

Summary We propose ‘Dunnett-type’ test procedures to test for simple tree order restrictions on the means of p independent normal populations. The new tests are based on the estimation procedures that were introduced by Hwang and Peddada and later by Dunbar, Conaway and Peddada. The procedures proposed are also extended to test for ‘two-sided’ simple tree order restrictions. For non-normal data, nonparametric versions based on ranked data are also suggested. Using computer simulations, we compare the proposed test procedures with some existing test procedures in terms of size and power. Our simulation study suggests that the procedures compete well with the existing procedures for both one-sided and two-sided simple tree alternatives. In some instances, especially in the case of two-sided alternatives or for non-normally distributed data, the gains in power due to the procedures proposed can be substantial.

Test for Parameter Change in ARIMA Models

ABSTRACT In this article we consider the problem of testing for parameter changes in ARIMA models based on the cusum test. The proposed test procedure is applicable to testing for the change from stationary models to non stationary models, and vice versa. The idea is to transform the time series via differencing to make the whole time series as a combination of stationary subseries. For this task, we propose a graphical method to identify the right order of differencing. Then the cusum test statistic proposed by Lee et al. (2003) is constructed based the differenced time series. Simulation study and real data analysis are provided for illustration.

Testing for Crossover of Two Hazard Functions Using Gail and Simon's Method

Crossover of two hazard functions is sometimes called qualitative nonproportionality where the hazard ratio could be >1 in some time intervals but <1 in some other intervals. Investigators often wish to know whether a beneficial treatment effect exists over a long period of time (i.e., no crossover). This information is important for the management of safety and efficacy of a new treatment in long-term use. Also, if crossover occurs, the commonly used statistical methods, such as Cox proportional hazards model or linear rank tests, may not be appropriate. Graphical display may be used to visually examine whether there are crossovers in the observed hazard functions. A relevant question is whether the observed crossover of two hazard functions is due to chance variation. In this article, we propose a class of tests for crossover of two hazard functions. The study follow-up period is divided into nonoverlapping time intervals, and the weighted linear rank statistic, including logrank and generalized Wilcoxon statistics, can be calculated from each interval. These statistics are asymptotically independent and have normal distributions. Treating each interval as a “patient subset,” qualitative tests of interactions between treatment and patient subsets can naturally apply. For our purpose, we consider the likelihood ratio test proposed by Gail and Simon. Two examples are used to illustrate this approach. The proposed test procedures are also studied through simulations.

A test against an umbrella ordered alternative

Consider k ( k ⩾ 3 ) independent populations π 1 , … , π k such that cumulative distribution function (cdf) of an observation from population π i is F i ( x ) = F x - μ i / θ i , a member of general location scale family, where F ( . ) is any absolutely continuous cdf, μ i - ∞ < μ i < ∞ is the location parameter and θ i θ i > 0 is the scale parameter, i = 1 , … , k . It is assumed that scale parameters θ i s satisfy the umbrella ordering θ 1 ⩽ ⋯ ⩽ θ h ⩾ ⋯ ⩾ θ k with at least one strict inequality, where 1 ⩽ h ⩽ k is given. When h is equal to 1 or k the umbrella ordering is just the simple ordering. Gill and Dhawan [1999. A one-sided test for testing homogeneity of scale parameters against ordered alternative. Comm. Statist. Theory Methods 28(10), 2417–2439] considered the problem of testing the null hypothesis H 0 : θ 1 = ⋯ = θ k against the simple ordering alternative, and provided some critical points by using simulation technique. In this paper a one-sided test for testing null hypothesis H 0 against the umbrella ordered alternative H a : θ 1 ⩽ ⋯ ⩽ θ h ⩾ ⋯ ⩾ θ k with at least one strict inequality is proposed. A recursive method to compute the exact critical points for the test procedure is proposed and selected tables of critical points for exponential probability model are provided. The proposed test is inverted to obtain a set of one-sided simultaneous confidence intervals for all the ordered pairwise ratios θ j / θ i for 1 ⩽ i < j ⩽ h and for h ⩽ j < i ⩽ k , which enable the experimenter to infer which θ i s are different and by how much when H 0 is rejected. Applications of the proposed test procedure to normal and inverse Guassian distributions are also discussed.

Structural performance of bamboo 'bahareque' walls under cyclic load

In many Latin American countries, people have traditionally built and still build their houses with 'bamboo bahareque' walls (these walls have a timber frame with split bamboo in the middle, covered with cement plaster on both sides). However, this constructive technique has not been technically studied, which is necessary to validate or, if necessary, improve it as a previous step to a much needed dissemination effort. The objective of the research reported in this paper is (a) to experimentally evaluate the strength and deformation capacities of prefabricated 'bamboo bahareque' shear walls developed in Costa Rica by the Bamboo Foundation (FUNBAMBU), under horizontal cyclic loads simulating earthquake effects, and (b) to propose testing procedures and provide reliable design recommendations for 'bamboo bahareque' house design and construction. For this purpose, 7 full-scale 'bamboo bahareque' walls were built and tested at the Materials and Structural Models National Laboratory (LANAMME), School of Civil Engineering, University of Costa Rica. The dimensions of the walls are 2.4 m in height and 2.7 m in length with a thickness varying from 40 to 60 mm. The results showed that the tested 'bamboo bahareque' walls have enough capacity to withstand earthquake induced loads of considerable magnitude. They also presented some ductile behaviour under cyclic loading.

A Simple Test of the Homogeneity of Risk Difference in Sparse Data: An Application to a Multicenter Study

In this paper, we focus discussion on testing the homogeneity of risk difference for sparse data, in which we have few patients in each stratum, but a moderate or large number of strata. When the number of patients per treatment within strata is small (2 to 5 patients), none of test procedures proposed previously for testing the homogeneity of risk difference for sparse data can really perform well. On the basis of bootstrap methods, we develop a simple test procedure that can improve the power of the previous test procedures. Using Monte Carlo simulations, we demonstrate that the test procedure developed here can perform reasonable well with respect to Type I error even when the number of patients per stratum for each treatment is as small as two patients. We evaluate and study the power of the proposed test procedure in a variety of situations. We also include a comparison of the performance between the test statistics proposed elsewhere and the test procedure developed here. Finally, we briefly discuss the limitation of using the proposed test procedure. We use the data comparing two chemotherapy treatments in patients with multiple myeloma to illustrate the use of the proposed test procedure.

Leachability testing of metallic wastes

The performance of two tests, a batch test and a percolation test for the characterization of waste as suggested in the EU council decision 2003/33/EC was investigated. The tests were carried out on two solid waste streams from a metal recycling industry. The concentrations of heavy metals such as Cu, Zn and Pb were more than one order of magnitude lower than the proposed limit values. Generally, batch test values were equal or higher than percolation test values. With the proposed test procedures both materials could be considered as non-dangerous wastes. The test performance was also investigated using a leachant with higher ionic strength instead of demineralized water as prescribed. The results clearly show a significant increase in the concentration of some heavy metals. Total concentrations of phenolic compounds and polychlorinated biphenyls were less than 1 p.p.m. and 2 p.p.b., respectively. The precision of the batch and the percolation tests were on average 48 and 35%, respectively.

Performance assessment of health examination for freshmen

PurposeA health examination is one of important events for freshmen when they enter a university. Consequently, the quality and time required for the examination are components in any index measuring the service performance of a university. However, performance measure for the health examination with a performance index is comparatively seldom. This paper aims to provide an index to measure health examination performance for freshmen.Design/methodology/approachA health examination performance index (HEPI) is defined for a university's health examination procedure. To make accurate use of the HEPI in assessing health examination performance, this paper constructs a uniformly minimum variance unbiased (UMVU) estimator of the HEPI using an exponential distribution to develop a hypothesis testing procedure.FindingsSince health examination time exhibits the smaller‐the‐better type quality characteristic of time orientation, the HEPI is appropriate for evaluating the hospital's performance in providing freshmen health examinations. This study also investigates the relationship between the HEPI and the non‐conformance rate of health examination performance, and tabulates the non‐conformance rate under the exponential distribution.Originality/valueThe proposed testing procedure is easily applied and can accurately evaluate whether the true health examination performance for a hospital meets a university's requirement. It can also be used to select a qualified outsourcing hospital and improve the service provided by the school.

A unified sequential test procedure for simultaneous testing the equality of several binomial proportions to a specified standard

In this article, we propose a unified sequentially rejective test procedure for testing simultaneously the equality of several independent binomial proportions to a specified standard. The proposed test procedure is general enough to include some well-known multiple testing procedures such as the Ordinary Bonferroni procedure, Hochberg procedure and Rom procedure. It involves multiple tests of significance based on the simple binomial tests (exact or approximate) which can be easily found in many elementary standard statistics textbooks. Unlike the traditional Chi-square test of the overall hypothesis, the procedure can identify the subset of the binomial proportions, which are different from the prespecified standard with the control of the familywise type I error rate. Moreover, the power computation of the procedure is provided and the procedure is illustrated by two real examples from an ecological study and a carcinogenicity study.

Procedures for testing the homogeneity of relative difference in sparse data

To quantify the excess effect of an experimental treatment over a placebo group in clinical trials, we often consider use of the relative difference, defined as the proportion of patients who would respond to the experimental treatment among those who would not otherwise if they were assigned to the placebo group. To control the effects due to confounders on the response of interest, we frequently employ stratified analysis in practice. Before obtaining a summary estimate of the relative difference, it is desirable to assess whether this measure is constant across strata. Based on the beta-binomial model, we develop simple procedures for testing the homogeneity of relative difference for sparse data in which we have many strata but few patients per stratum. Using Monte Carlo simulations, we demonstrate that the proposed test procedures can generally perform well with respect to type I error in a variety of situations. We further evaluate and study the power of these test procedures. Finally, we note some robustness in using the test procedures proposed here.

Testing in mixed-effects FANOVA models

We consider the testing problem in the mixed-effects functional analysis of variance models. We develop asymptotically optimal (minimax) testing procedures for testing the significance of functional global trend and the functional fixed effects based on the empirical wavelet coefficients of the data. Wavelet decompositions allow one to characterize various types of assumed smoothness conditions on the response function under the nonparametric alternatives. The distribution of the functional random-effects component is defined in the wavelet domain and captures the sparseness of wavelet representation for a wide variety of functions. The simulation study presented in the paper demonstrates the finite sample properties of the proposed testing procedures. We also applied them to the real data from the physiological experiments.

Evaluation of fleet systems model for vehicle compatibility

On behalf of NHTSA, the European Commission, and the Dutch Ministry of Traffic and Transport, the Safety department of TNO Automotive is performing numerical fleet studies using multi-body models. Aim is to develop strategies for optimisation and evaluating the effects in new vehicles based on proposed test procedures to minimise the total harm in car-to-car crashes on a fleet-wide basis. For these studies multi-body models are being constructed from existing finite element models. The front-end structure and passenger compartment are modelled in detail to provide realistic deformation modes. Furthermore dummies, airbags, belts and main interior parts like dashboard and steering wheel are included. Currently seven models are available, each of a different vehicle class. Two geometrical variants of the smallest vehicles are also included. The objective of this paper is to show the potential of the multi-body vehicle models for crashworthiness optimisation and/or evaluation of a fleet. To this end a fleet study on offset frontal impacts is performed in which sensitivities of relevant accident and design parameters are investigated by means of parameter sweeps over these parameters. The accident parameters include vehicle type, impact speed and overlap. The design parameters relate to the front-end geometry of the two smaller vehicles. A total set of over 3200 scenarios is simulated. Analysis of results is done on the basis of measures for the overall injury risk and based on separate injury values for different body regions. For the separate injury values clear trends are observed with respect to variations in design variables. For overall injury risk measures these trends are not so clear due to contradicting influences of the design variables on separate injuries. This complicates usage of the overall injury measures.