Proposed Test Procedure Research Articles

Celebrating the 25th International Conference of The International Environmetrics Society

Celebrating the 25th International Conference of The International Environmetrics Society

A test of sphericity for high-dimensional data and its application for detection of divergently spiked noise

In this article, we consider a test of the sphericity for high-dimensional covariance matrices. We produce a test statistic by using the extended cross-data-matrix (ECDM) methodology. We show that the ECDM test statistic is based on an unbiased estimator of a sphericity measure. In addition, the ECDM test statistic enjoys consistency properties and the asymptotic normality in high-dimensional settings. We propose a new test procedure based on the ECDM test statistic and evaluate its asymptotic size and power theoretically and numerically. We give a two-stage sampling scheme so that the test procedure can ensure a prespecified level both for the size and power. We apply the test procedure to detect divergently spiked noise in high-dimensional statistical analysis. We analyze gene expression data by the proposed test procedure.

Interpretation of the DMT in Silts

This paper describes a proposed testing procedure and interpretation method for the characterization of silts using the flat dilatometer test (DMT). This method aims to compensate for errors that are introduced by the partial-drainage conditions that take place around the DMT blade. In transient soils, the after-installation DMT readings change continuously with time because excess pore pressure dissipation. By monitoring the variation in A-readings, it is possible to extrapolate the results back to the origin to estimate an equivalent undrained A0 value. In addition, in seeking to obtain a closed-form solution for the membrane expansion problem in the elastic regime, a simple correction is introduced in the analysis where the B-reading is expressed in terms of average mean stresses that take place prior to expansion. Preliminary results in clay demonstrate that the method is effective and can be introduced in practice with minimal costs by considering simple adaptations to procedures originally developed for clay.

How Falsifiable Is Collective Rationality?

Collective rationality is seldom if ever rejected in the literature, raising doubt about its falsifiability. We show that the standard approach to test the collective model with distribution factors may yield misleading inference. We develop a new test procedure to assess its validity. Our approach extends to households that potentially include more than two decision-makers (e.g., polygamous households, adult children). We provide a brief and informal meta-analysis that suggests that much of the evidence in favour of collective rationality in the empirical literature appears to be inconsistent with our test. We illustrate the latter using data from a survey we have conducted in Burkina Faso. Collective rationality within monogamous households is not rejected using the standard testing procedure while it is clearly rejected using our proposed test procedure. Furthermore, our test also rejects collective rationality for bigamou households. We conclude that the household efficiency does yield empirically falsifiable restrictions despite being scarcely rejected in the literature.

Testing conditional independence via integrating-up transform

ABSTRACTThe main purpose of this paper is to test the conditional independence of two random vectors Y and Z given another random vector X. A new test statistic is developed relying on the Cramér–von Mises distance between two unconditional moments transformed from the conditional distributions, say and , through ‘integrating up’. It is shown that the proposed test is consistent against fixed alternatives and has nontrivial power against local deviations of order from the null hypothesis. Since the test statistic has a non-standard limiting distribution, a bootstrap procedure is also constructed to the calculation of critical values. Simulation studies indicate that the proposed testing procedure performs quite well and is very competitive comparing to the existing methods in terms of both size and power.

Multi-sample nonparametric treatments comparison in medical follow-up study with unequal observation processes through simulation and bladder tumour case study

In medical follow-up study, the diseases recurrent processes evolved in continuous time and the patients are usually monitor at distinct and different intervals. Therefore, most of the existing methods that assumed identical observation processes might provide misleading results in this case. To address this, a nonparametric test based on integrated weighted different between the mean cumulative functions which characterized both the recurrent processes and observation processes with condition on treatment is proposed to allow unequal observation processes. The empirical power of the proposed test has been investigated via Monte Carlo simulation study and bladder tumour case study. The results arein line with earlier research; the proposed test procedure works well for practical situations and had a good power in detecting treatment difference.Keywords: nonparametric; unequal observation; multi-sample; treatments comparison.

Jonckheere Type Test Procedure with Optimal Criterion Under Order Restrictions

SYNOPTIC ABSTRACTIn many practical applications, there is a need for testing of an hypothesis under order restrictions. We propose a general class of tests which generalizes the tests proposed by Jonckheere (1954), Kumar et al. (1994a, b), and Patil (2007). The asymptotic distribution of test statistic under null hypothesis, as well as under an equally spaced sequence of local alternatives, is derived. Pitman asymptotic relative efficiency comparisons with respect to competing tests are made to evaluate the performance of the proposed class of tests. An example is provided in Hundal (1969) data for implementing the proposed test procedure. Furthermore, a simulation study is carried out to estimate the power and level of significance of the proposed class of tests.

Testing for constancy in varying coefficient models

ABSTRACTWe consider varying coefficient models, which are an extension of the classical linear regression models in the sense that the regression coefficients are replaced by functions in certain variables (for example, time), the covariates are also allowed to depend on other variables. Varying coefficient models are popular in longitudinal data and panel data studies, and have been applied in fields such as finance and health sciences. We consider longitudinal data and estimate the coefficient functions by the flexible B-spline technique. An important question in a varying coefficient model is whether an estimated coefficient function is statistically different from a constant (or zero). We develop testing procedures based on the estimated B-spline coefficients by making use of nice properties of a B-spline basis. Our method allows longitudinal data where repeated measurements for an individual can be correlated. We obtain the asymptotic null distribution of the test statistic. The power of the proposed testing procedures are illustrated on simulated data where we highlight the importance of including the correlation structure of the response variable and on real data.

Two-Sample Tests for High-Dimensional Linear Regression with an Application to Detecting Interactions.

Motivated by applications in genomics, we consider in this paper global and multiple testing for the comparisons of two high-dimensional linear regression models. A procedure for testing the equality of the two regression vectors globally is proposed and shown to be particularly powerful against sparse alternatives. We then introduce a multiple testing procedure for identifying unequal coordinates while controlling the false discovery rate and false discovery proportion. Theoretical justifications are provided to guarantee the validity of the proposed tests and optimality results are established under sparsity assumptions on the regression coefficients. The proposed testing procedures are easy to implement. Numerical properties of the procedures are investigated through simulation and data analysis. The results show that the proposed tests maintain the desired error rates under the null and have good power under the alternative at moderate sample sizes. The procedures are applied to the Framingham Offspring study to investigate the interactions between smoking and cardiovascular related genetic mutations important for an inflammation marker.

Efficient two-stage designs and proper inference for animal studies.

Cost-effective yet efficient designs are critical to the success of animal studies. We propose a two-stage design for cost-effectiveness animal studies with continuous outcomes. Given the data from the two-stage design, we derive the exact distribution of the test statistic under null hypothesis to appropriately adjust for the design's adaptiveness. We further generalize the design and inferential procedure to the K-sample case with multiple comparison adjustment. We conduct simulation studies to evaluate the small sample behavior of the proposed design and test procedure. The results indicate that the proposed test procedure controls the type I error rate for the one-sample design and the family-wise error rate for K-sample design very well; whereas the naive approach that ignores the design's adaptiveness due to the interim look severely inflates the type I error rate or family-wise error rate. Compared with the standard one-stage design, the proposed design generally requires a smaller sample size.

The performance assessment on the lifetime performance index of products following Chen lifetime distribution based on the progressive type I interval censored sample

In the competitive manufacturing markets, quality engineers frequently are dedicated to evaluate whether the quality performance of products met the desire level. The lifetime performance index (LPI) C L is used to monitor the larger-the-better performance of lifetimes of products. Chen lifetime distribution with bathtub shape or increasing failure rate function has many applications in the lifetime data analysis. The maximum likelihood estimator for C L is derived and used to propose a hypothesis testing procedure under a lower specification limit based on the progressive type I interval censored sample. Finally, two practical examples are given to demonstrate the application of our proposed testing procedure to assess whether the lifetime performance reached the desire level.

A New Field Test Method for Determining Energy Efficiency of Induction Motor

Electric motors and the drive systems approximately consume half of the global electricity consumption. In the European Union (EU), electric motors and the drive systems are estimated to account for about 70% of all industrial electricity consumption. Therefore, mandatory applications accrue from the legislation of governments or unions like the EU for customs and market surveillance or eco-design requirements. The mandatory applications and the global market size find out the necessity of efficiency measurement. There are several compliance and precompliance efficiency test methods in the literature. The compliance tests should execute reliable, accurate, and reproducible results. The purpose of this paper is to define a simple field method that will be used for measuring and determining in-service efficiency at industrial conditions. The proposed method in this paper is an inexpensive and easy method that would help to energy managers and engineers to make correct decision in replacing inefficient motors with efficient and new ones. In this paper, a novel induction motor-efficiency model function has been proposed based on the International Electrotechnical Commission 60034-2-1 standard equations, and a new field test procedure has been used in efficiency estimation. The new efficiency model function variables and constants are determined from the regression analysis, which depends on 86 tests of 437 different load points’ efficiency data. Furthermore, the proposed field test procedure, equations, and compliance test methods are tested on a sample motor in laboratory, and the results are compared to each other.

Multivariate Uniformity Test Based on Incomplete Samples

The purpose of this paper is to propose an approach for testing multivariate uniformity. The proposed test procedure works for both complete sample case and incomplete sample case. What multivariate uniformity test does is to check whether the population distribution, from which a random sample is drawn is a multivariate uniform distribution. Particularly, it is desired to check whether the population distribution is a uniform distribution on a [Formula: see text]-dimensional unit cube. There are some existing research papers in the literature. The proposed method works when only some arbitrarily selected order statistics are available for the test.

Distribution Free Test for Unequal Observation of Panel Count Data with Application in Medical Follow-Up Study

Objectives: In medical follow-up study, patients are treated with different treatments may have different follow-up schedule and the number of patients assigned in each treatment group may not be balanced. To address this, a nonparametric test procedure is proposed. Methods/Statistical Analysis: The proposed test statistics is constructed based on the integrated weighted differences between the mean cumulative function of the recurrences event with condition on treatment group. For performance evaluation, the empirical power of proposed test statistics are evaluated via Monte Carlo simulation study conducted using R statistical software. Findings: Based on simulation results, the proposed method gives a good power for both identical and unequal follow-up processes, even when the sample sizes are imbalanced. Applications/Improvement: The proposed test procedure is also applied to a set of panel count data arises from the National Cooperative Gallstone Study to compare the treatment efficiency. The proposed test procedure able to detect treatment differences and is in line with earlier research.

Unified Empirical Likelihood Ratio Tests for Functional Concurrent Linear Models and the Phase Transition from Sparse to Dense Functional Data

SummaryWe consider the problem of testing functional constraints in a class of functional concurrent linear models where both the predictors and the response are functional data measured at discrete time points. We propose test procedures based on the empirical likelihood with bias-corrected estimating equations to conduct both pointwise and simultaneous inferences. The asymptotic distributions of the test statistics are derived under the null and local alternative hypotheses, where sparse and dense functional data are considered in a unified framework. We find a phase transition in the asymptotic null distributions and the orders of detectable alternatives from sparse to dense functional data. Specifically, the tests proposed can detect alternatives of √n-order when the number of repeated measurements per curve is of an order larger than nη0 with n being the number of curves. The transition points η0 for pointwise and simultaneous tests are different and both are smaller than the transition point in the estimation problem. Simulation studies and real data analyses are conducted to demonstrate the methods proposed.

Testing homogeneity of difference of two proportions for stratified correlated paired binary data

ABSTRACTIn ophthalmologic or otolaryngologic study, each subject may contribute paired organs measurements to the analysis. A number of statistical methods have been proposed on bilateral correlated data. In practice, it is important to detect confounding effect by treatment interaction, since ignoring confounding effect may lead to unreliable conclusion. Therefore, stratified data analysis can be considered to adjust the effect of confounder on statistical inference. In this article, we investigate and derive three test procedures for testing homogeneity of difference of two proportions for stratified correlated paired binary data in the basis of equal correlation model assumption. The performance of proposed test procedures is examined through Monte Carlo simulation. The simulation results show that the Score test is usually robust on type I error control with high power, and therefore is recommended among the three methods. One example from otolaryngologic study is given to illustrate the three test procedures.

A nonparametric two-sample hypothesis testing problem for random graphs

We consider the problem of testing whether two independent finite-dimensional random dot product graphs have generating latent positions that are drawn from the same distribution, or distributions that are related via scaling or projection. We propose a test statistic that is a kernel-based function of the estimated latent positions obtained from the adjacency spectral embedding for each graph. We show that our test statistic using the estimated latent positions converges to the test statistic obtained using the true but unknown latent positions and hence that our proposed test procedure is consistent across a broad range of alternatives. Our proof of consistency hinges upon a novel concentration inequality for the suprema of an empirical process in the estimated latent positions setting.

Nonparametric Tests for Convexity/Monotonicity/Positivity of Multivariate Functions with Noisy Observations

We propose a new method of testing for a function's convexity, monotonicity, or positivity, based on some noisy observations of the function made over a finite set $\mathcal{T}$ of points in the domain, where the observations can be made multiple times at each point in $\mathcal{T}$. One of the traditional approaches to the test of a function's shape characteristic is to fit a convex, a monotone, or a positive function, depending on the shape characteristic we wish to test for, to the data set minimizing the sum of squared errors, and to compute the sum of squared differences (SSD) between the fit and the data set. While the traditional approach proceeds by observing the SSD as the number of points in $\mathcal{T}$ increases to infinity, we propose observing the SSD as $r$, the number of observations taken at each point in $\mathcal{T}$, increases to infinity. This new way of observing the asymptotic behavior of the SSD leads to a test procedure that does not require the estimation of any additional parameters, and hence, is easy to implement. The proposed test procedure is proven to achieve a prescribed power as $r \rightarrow \infty$. Numerical examples illustrate that the proposed test successfully detects the convexity/monotonicity/positivity of a function, as well as the non-convexity/non-monotonicity/non-positivity of a function.

Integrated genomic analysis of biological gene sets with applications in lung cancer prognosis

BackgroundBurgeoning interest in integrative analyses has produced a rise in studies which incorporate data from multiple genomic platforms. Literature for conducting formal hypothesis testing on an integrative gene set level is considerably sparse. This paper is biologically motivated by our interest in the joint effects of epigenetic methylation loci and their associated mRNA gene expressions on lung cancer survival status.ResultsWe provide an efficient screening approach across multiplatform genomic data on the level of biologically related sets of genes, and our methods are applicable to various disease models regardless whether the underlying true model is known (iTEGS) or unknown (iNOTE). Our proposed testing procedure dominated two competing methods. Using our methods, we identified a total of 28 gene sets with significant joint epigenomic and transcriptomic effects on one-year lung cancer survival.ConclusionsWe propose efficient variance component-based testing procedures to facilitate the joint testing of multiplatform genomic data across an entire gene set. The testing procedure for the gene set is self-contained, and can easily be extended to include more or different genetic platforms. iTEGS and iNOTE implemented in R are freely available through the inote package at https://cran.r-project.org//.

Optimizing the Lee-Carter Approach in the Presence of Structural Changes in Time and Age Patterns of Mortality Improvements.

Researchers using the Lee-Carter approach have often assumed that the time-varying index evolves linearly and that the parameters describing the age pattern of mortality decline are time-invariant. However, as several empirical studies suggest, the two assumptions do not seem to hold when the calibration window begins too early. This problem gives rise to the question of identifying the longest calibration window for which the two assumptions hold true. To address this question, we contribute a likelihood ratio-based sequential test to jointly test whether the two assumptions are satisfied. Consistent with the mortality structural changes observed in previous studies, our testing procedure indicates that the starting points of the optimal calibration windows for most populations fall between 1960 and 1990. Using an out-of-sample analysis, we demonstrate that in most cases, models that are estimated to the optimized calibration windows result in more accurate forecasts than models that are fitted to all available data or data beyond 1950. We further apply the proposed testing procedure to data over different age ranges. We find that the optimal calibration windows for age group 0-49 are generally shorter than those for age group 50-89, indicating that mortality at younger ages might have undergone (another) structural change in recent years.