Search

This article presents an analysis of Ontario Fire Weather Index (FWI) data†The data used is ©1963–2004, Queen’s Printer for Ontario, Canada, and was referenced under agreement with the Ontario Ministry of Natural Resources.Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/lssp. using the block bootstrap for time series. Confidence intervals for parameters such as the first lag autocorrelation can have low coverage relative to the nominal level. Therefore, adjustments to the confidence intervals are necessary in order to achieve reasonable accuracy. We introduce a confidence interval calibration method in which the length of the confidence interval is adjusted according to an amount determined from a double bootstrap. We compare this method with the α-level adjustment method, and we find that the length-adjustment method is superior under scenarios similar to that of the FWI data: coverage proportions are slightly higher for the length-adjustment approac...

This paper employs a Monte Carlo study to compare the performance of equal-tailed bootstrap percentile-t, symmetric bootstrap percentile-t, bootstrap percentile, and standard asymptotic confidence intervals in two distinct heteroscedastic regression models. Bootstrap confidence intervals are constructed with both the XY and wild bootstrap algorithm. Theory implies that the percentile-t methods will outperform the other methods, where performance is based on the convergence rate of empirical coverage to the nominal level. Results are consistent across models, in that in the case of the XY bootstrap algorithm the symmetric percentile-t method outperforms the other methods, but in the case of the wild bootstrap algorithm the two percentile-t methods perform similarly and outperform the other methods. The implication is that practitioners that employ the XY algorithm should utilize the symmetric percentile-t interval, while those who opt for the wild algorithm should use either of the percentile-t methods.

In this research, we propose simultaneous confidence intervals for all pairwise multiple comparisons in a two-way unbalanced design with unequal variances, using a parametric bootstrap approach. Simulation results show that Type 1 error of the multiple comparison test is close to the nominal level even for small samples. They also show that the proposed method outperforms Tukey–Kramer procedure when variances are heteroscedastic and group sizes are unequal.

The accelerated failure time model is presented as an alternative to the proportional hazard model in the analysis of survival data. We investigate the effect of covariates omission in the case of applying a Weibull accelerated failure time model. In an uncensored setting, the asymptotic bias of the treatment effect is theoretically zero when important covariates are omitted; however, the asymptotic variance estimator of the treatment effect could be biased and then the size of the Wald test for the treatment effect is likely to exceed the nominal level. In some cases, the test size could be more than twice the nominal level. In a simulation study, in both censored and uncensored settings, Type I error for the test of the treatment effect was likely inflated when the prognostic covariates are omitted. This work remarks the careless use of the accelerated failure time model. We recommend the use of the robust sandwich variance estimator in order to avoid the inflation of the Type I error in the accelerated failure time model, although the robust variance is not commonly used in the survival data analyses.

Motivated by an application from finance, we study randomly left-censored data with time-dependent covariates in a parametric additive hazard model. As the log-likelihood is concave in the parameter, we provide a short and direct proof of the asymptotic normality for the maximal likelihood estimator by applying a result for convex processes from Hjort and Pollard (1993) . The technique also yields a new proof for right-censored data. Monte Carlo simulations confirm the nominal level of the asymptotic confidence intervals for finite samples, but also provide evidence for the importance of a proper variance estimator. In the application, we estimate the hazard of credit rating transition, where left-censored observations result from infrequent monitoring of rating histories. Calendar time as time-dependent covariates shows that the hazard varies markedly between years.

Non-inferiority of one treatment to another based on ratio is a common issue in medical research. Nam and Blackwelder derived a Fieller-type statistic from constrained maximum likelihood estimation of nuisance parameters. Although it improved that of Lachenbruch and Lynch, its size still exceeds the claimed nominal level alpha for some cases. This is in accordance with Sidik who has found that the asymptotic tests are inaccurate in testing a hypothesis of a non-zero difference between marginal probabilities. In this paper, we extend Sidik’s exact tests to non-inferiority in ratio, and propose two new methods—one based on the standard $$p$$ value and the other from restricted Bayesian estimation using an approximate $$p$$ value. Our tests are both based on only one point of the two-dimension nuisance parameter space for accuracy improvement and computational purposes. The sizes and powers of our tests are considered. Simulation results suggest that our tests can control the type I error rates well with competitive powers while the Fieller-type statistic cannot for some cases be investigated.

In this article, we propose a new test for additivity in nonparametric quantile regression with a high-dimensional predictor. Asymptotic normality of the corresponding test statistic (after appropriate standardization) is established under the null hypothesis, local and fixed alternatives. We also propose a bootstrap procedure which can be used to improve the approximation of the nominal level for moderate sample sizes. The methodology is also illustrated by means of a small simulation study, and a data example is analyzed.

Assessing the goodness-of-fit (GOF) for intricate parametric spatial point process models is important for many application fields. When the probability density of the statistic of the GOF test is intractable, a commonly used procedure is the Monte Carlo GOF test. Additionally, if the data comprise a single dataset, a popular version of the test plugs a parameter estimate in the hypothesized parametric model to generate data for the Monte Carlo GOF test. In this case, the test is invalid because the resulting empirical level does not reach the nominal level. In this article, we propose a method consisting of nested Monte Carlo simulations which has the following advantages: the bias of the resulting empirical level of the test is eliminated, hence the empirical levels can always reach the nominal level, and information about inhomogeneity of the data can be provided. We theoretically justify our testing procedure using Taylor expansions and demonstrate that it is correctly sized through various simulation...

Light Detection and Ranging (LiDAR) has become more widely used in the geotechnical community as its number of applications increases. It has been shown to be useful in tunneling for applications such as rockmass characterization and discontinuity measurement. LiDAR data can also be used to measure deformation in tunnels, but before a comprehensive methodology can be developed, the accuracy issues associated with scanning must be fully understood. Once the accuracy issues associated with LiDAR are well understood, any analysis technique that uses LiDAR data must be tested to ensure that the determined accuracy issues have minimal impact on the results of the analysis. To prove the usefulness of the newly developed elliptical fitting method for the measurement of convergence in tunnels and shafts proposed by Delaloye et al. (Eurock 2012), a comprehensive analysis of accuracy issues associated with LiDAR scanning was conducted and then a sensitivity test of the convergence measurement technique was completed. The results of the analysis show that using the statistical techniques built into the elliptical fit analysis and LiDAR profile analysis, levels of real change (convergence), within the nominal level of random and systematic noise included in the data, can be measured with confidence. Furthermore, the new analysis is robust enough to handle large amounts of occlusion or missing perimeter coverage within data sets.

Analyzing examinees’ responses using cognitive diagnostic models (CDMs) has the advantage of providing diagnostic information. To ensure the validity of the results from these models, differential item functioning (DIF) in CDMs needs to be investigated. In this article, the Wald test is proposed to examine DIF in the context of CDMs. This study explored the effectiveness of the Wald test in detecting both uniform and nonuniform DIF in the DINA model through a simulation study. Results of this study suggest that for relatively discriminating items, the Wald test had Type I error rates close to the nominal level. Moreover, its viability was underscored by the medium to high power rates for most investigated DIF types when DIF size was large. Furthermore, the performance of the Wald test in detecting uniform DIF was compared to that of the traditional Mantel-Haenszel (MH) and SIBTEST procedures. The results of the comparison study showed that the Wald test was comparable to or outperformed the MH and SIBTEST procedures. Finally, the strengths and limitations of the proposed method and suggestions for future studies are discussed.

Conformance proportion is the proportion of a performance characteristic of interest that falls within a prespecified acceptance region, which has been used in various applications. In this article, a simple closed-form interval estimation, based on Student’s t statistic, is proposed for unilateral conformance proportions in balanced and unbalanced random-effects models. Two real datasets are analyzed to illustrate the proposed method, whose performance is also evaluated through detailed simulation studies. The simulation results reveal that the empirical coverage probabilities for upper confidence limits of the method are sufficiently close to the nominal values, but those for lower confidence limits appear to be slightly less than the nominal level. Furthermore, a bootstrap-based calibration for both upper and lower confidence limits is provided to have empirical coverage probabilities closer to the nominal level. This article has supplementary material online.

The FAst Spectrum Transmutation Experimental Facility (FASTEF) core proposed for the MYRRHA reactor in Belgium is cooled by Lead–Bismuth Eutectic and can operate in both critical and subcritical modes (as an Accelerator-Driven System, ADS). FASTEF development is sponsored by EURATOM. In this paper subcritical 94 MWth ADS FASTEF is considered at the end of cycle conditions. To achieve a complete view on the safety behavior, several severe accident scenarios are investigated including Unprotected Blockage Accidents (UBA) without switch-off of the ADS neutron source. The UBA transients have been simulated in 3D with the SIMMER-IV code. To provide a basis for transient analyses, the core has been first analyzed under nominal conditions. Then several hypothetical blockage events in a single fuel subassembly (SA), starting from 50% of the nominal coolant flowrate to the Total Instantaneous Blockage (TIB) have been simulated. Using of SIMMER-IV instead of two-dimensional SIMMER-III allows simulation of the blockage event in the non-central fuel SA, while some approximations, such as ignoring coolant flow in gaps between the SAs and restricting the computation domain spatially are made to avoid excessive increase in the computation time. Thanks to the low power density and small variations in the power, no pin failure occurs if the flowrate is reduced by 70–75% from the nominal level. The 85–100% blockages lead to cladding failures in 6–7 s. After 15–20 s, SA walls also fail resulting in coolant redistribution between the blocked SA and neighboring channels thus increasing the flowrate and recovering the cooling in the affected SA. The SIMMER calculations indicate there is sufficient confidence that effects of the single SA blockage are limited in subcritical FASTEF by single and neighboring SA failures. The results are in line with SIMMER-III calculations obtained in the past for UBAs in other ADS designs.

Over/underdispersed count data arise in many biostatistical practices in which a number of different treatment groups are compared in an experiment. In the analysis of several treatment groups of such count data, a very common statistical inference problem is to test whether these data come from the same population. The usual practice for testing homogeneity of several treatment groups in terms of means and dispersions is first to test the equality of dispersions and then to test the equality of the means based on the result of the test for equality of dispersions. Previous studies reported test procedures for testing the homogeneity of the means of several treatment groups with an assumption of equal or unequal dispersions. This article develops test procedures for testing the validity of the equal or unequal dispersions assumption of several treatment groups in the analysis of over/underdispersed count data. We consider the C(α) test based on the maximum likelihood (ML) method using the negative binomial model as well as the three other C(α) tests based on the method of moments, extended quasi-likelihood, and double extended quasi-likelihood using the models specified by the first two moments of counts. Monte Carlo simulations are then used to study the comparative behavior of these C(α) tests along with the likelihood ratio test in terms of size and power. The simulation results demonstrate that all four statistics hold the nominal level reasonably well in most of the data situations studied here, and the C(α) test based on ML shows some edge in power over the other three C(α) tests. Finally, applications to biostatistical practices are analyzed.

Gestational diabetes mellitus (GDM) is defined as glucose intolerance with onset or first recognition during pregnancy. It is associated with an increased risk of pregnancy complications. Susceptibility to GDM is partly determined by genetics and linked with type 1 diabetes-associated high risk HLA class II genes. However, the evidence for this relationship is still highly controversial. In this study, we assessed the relationship between HLA class II variants and GDM. We performed meta-analysis on all of literatures available in PubMed, Embase, Web of Science and China National Knowledge Infrastructure databases. The odds ratio and 95% confidence interval of each variant were estimated. All statistical analyses were conducted using the Comprehensive Meta Analysis 2.2.064 software. At the allelic analysis, DQB1*02, DQB1*0203, DQB1*0402, DQB1*0602, DRB1*03, DRB1*0301 and DRB1*1302 reached a nominal level of significance, and only DQB1*02, DQB1*0602 and DRB1*1302 were statistically significant after Bonferroni correction. At the serological analysis, none of DQ2, DQ6, DR13 and DR17 was statistically significant following Bonferroni correction although they reached a nominal level of significance. In sum, our meta-analysis demonstrated that there were the associations between HLA class II variants and GDM but more studies are required to elucidate how these variants contribute to GDM susceptibility.

In high-dimensional linear models, the sparsity assumption is typically made, stating that most of the parameters are equal to zero. Under the sparsity assumption, estimation and, recently, inference have been well studied. However, in practice, sparsity assumption is not checkable and more importantly is often violated; a large number of covariates might be expected to be associated with the response, indicating that possibly all, rather than just a few, parameters are non-zero. A natural example is a genome-wide gene expression profiling, where all genes are believed to affect a common disease marker. We show that existing inferential methods are sensitive to the sparsity assumption, and may, in turn, result in the severe lack of control of Type-I error. In this article, we propose a new inferential method, named CorrT, which is robust to model misspecification such as heteroscedasticity and lack of sparsity. CorrT is shown to have Type I error approaching the nominal level for \textit{any} models and Type II error approaching zero for sparse and many dense models. In fact, CorrT is also shown to be optimal in a variety of frameworks: sparse, non-sparse and hybrid models where sparse and dense signals are mixed. Numerical experiments show a favorable performance of the CorrT test compared to the state-of-the-art methods., 43 pages

Background As new technologies allow investigators to collect multiple forms of molecular data (genomic, epigenomic, transcriptomic, etc) and multiple endpoints on a clinical trial cohort, it will become necessary to effectively integrate all these data in a way that reliably identifies biologically important genes. Methods We introduce CC-PROMISE as an integrated data analysis method that combines components of canonical correlation (CC) and projection onto the most interesting evidence (PROMISE). For each gene, CC-PROMISE first uses CC to compute scores that represent the association of two forms of molecular data with each other. Next, these scores are substituted into PROMISE to evaluate the statistical evidence that the molecular data show a biologically meaningful relationship with the endpoints. Results CC-PROMISE shows outstanding performance in simulation studies and an example application involving pediatric leukemia. In simulation studies, CC-PROMISE controls the type I error (misleading significance) rate very near the nominal level across 100 distinct null settings in which no molecular-endpoint association exists. Also, CC-PROMISE has better statistical power than three other methods that control type I error in 396 of 400 (99 %) alternative settings for which a molecular-endpoint association is present; the power advantage of CC-PROMISE exceeds 30 % in 127 of the 400 (32 %) alternative settings. These advantages of CC-PROMISE are also observed in an example application. Conclusion CC-PROMISE very effectively identifies genes for which some form of molecular data shows a biologically meaningful association with multiple related endpoints. Availability The R package CCPROMISE is currently available from www.stjuderesearch.org/site/depts/biostats/software. Electronic supplementary material The online version of this article (doi:10.1186/s12859-016-1217-0) contains supplementary material, which is available to authorized users.

Advancement in communication technology and its application to power systems have introduced a new era in power system scheduling. Demand Side Management (DSM) is one of the main outcomes of this combination. In this paper, a droop-based hierarchical control strategy has been proposed to execute automatic Demand Dispatch (DD). When the frequency of the system falls/rises below/above rated level, Balancing Authority (BA) issues droop-based signal to the aggregators to check the feasibility and availability of DD according to the capability of aggregated loads. Then, these signals will be sent to the Appliance Management Unit (AMU). According to the availability, priority, and features of appliances, the AMU sends these commands in form of deferral or interruptible signals to appliances. At the time of DD events, the proposed AMU algorithm keeps the total household power consumption within the required limit to maintain the system frequency at nominal level. A wide variety of residential loads has been considered in the DD applications. It will be demonstrated that the proposed AMU algorithm is capable of maintaining the total demand of a house below the limit determined by the BA. In the second part of this paper, the necessity of renewable energy resources and battery storage system to prevent load rebound is highlighted.

Comparisons of k independent binomial proportions are studied. Piegorsch (1991) compared the Studentized-range implementation of the Wald interval and the Bonferroni-adjusted interval, both of which performed poorly for small values of the true proportions. Agresti et al. (2008) showed that adding one pseudo observation of each type in forming the Wald interval, along with the Studentized-range implementation, greatly improved the performance. A new two-stage method of multiple comparisons (global test followed by pairwise tests) is proposed. For the pairwise tests, three procedures are proposed, which are the LSD type, modified LSD, and inverse-sine based. Simulation studies show that the new procedures have relatively high power and that the modified LSD and inverse-sine based procedures maintain the familywise error rate near the nominal level.

Currently, adaptive phase II/III clinical trials are typically carried out with a strict two-stage design. The first stage is a learning stage called phase II, and the second stage is a confirmatory stage called phase III. Following phase II analysis, inefficacious or harmful dose arms are dropped, then one or two promising dose arms are selected for the second stage. However, there are often situations in which researchers are in dilemma to make ‘go or no-go’ decision and/or to select ‘best’ dose arm(s), as data from the first stage may not provide sufficient information for their decision making. In this case, it is challenging to follow a strict two-stage plan. Therefore, we propose a varying-stage adaptive phase II/III clinical trial design, in which we consider whether there is a need to have an intermediate stage to obtain more data, so that a more informative decision could be made. Hence, the number of further investigational stages in our design is determined on the basis of data accumulated to the interim analysis. With respect to adaptations, we consider dropping dose arm(s), switching another plausible endpoint as the primary study endpoint, re-estimating sample size, and early stopping for futility. We use an adaptive combination test to perform final analyses. By applying closed testing procedure, we control family-wise type I error rate at the nominal level of α in the strong sense. We delineate other essential design considerations including the threshold parameters and the proportion of alpha allocated in the two-stage versus three-stage setting. Copyright © 2013 John Wiley & Sons, Ltd.

The multivariate log-normal distribution is a good candidate to describe data that are not only positive and skewed, but also contain many characteristic values. In this study, we apply the generalized variable method to compare the mean vectors of two independent multivariate log-normal populations that display heteroscedasticity. Two generalized pivotal quantities are derived for constructing the generalized confidence region and for testing the difference between two mean vectors. Simulation results indicate that the proposed procedures exhibit satisfactory performance regardless of the sample sizes and heteroscedasticity. The type I error rates obtained are consistent with expectations and the coverage probabilities are close to the nominal level when compared with the other method which is currently available. These features make the proposed method a worthy alternative for inferential analysis of problems involving multivariate log-normal means. The results are illustrated using three examples.

In this article, we consider a two-phase tandem queueing model with a second optional service. In this model, the service is done by two phases. The first phase of service is essential for all customers and after the completion of the first phase of service, any customer receives the second phase of service with probability α, or leaves the system with probability 1 − α. Also, there are two heterogeneous servers which work independently, one of them providing the first phase of service and the other a second phase of service. In this model, our main purpose is to estimate the parameters of the model, traffic intensity, and mean system size, in the steady state, via maximum likelihood and Bayesian methods. Furthermore, we find asymptotic confidence intervals for mean system size. Finally, by a simulation study, we compute the confidence levels and mean length for asymptotic confidence intervals of mean system size with a nominal level 0.95.

In this paper, we discuss asymptotic infimum coverage probability (ICP) of eight widely used confidence intervals for proportions, including the Agresti–Coull (A–C) interval (Am Stat 52:119–126, 1998) and the Clopper–Pearson (C–P) interval (Biometrika 26:404–413, 1934). For the A–C interval, a sharp upper bound for its asymptotic ICP is derived. It is less than nominal for the commonly applied nominal values of 0.99, 0.95 and 0.9 and is equal to zero when the nominal level is below 0.4802. The \(1-\alpha \) C–P interval is known to be conservative. However, we show through a brief numerical study that the C–P interval with a given average coverage probability \(1-\gamma \) typically has a similar or larger ICP and a smaller average expected length than the corresponding A–C interval, and its ICP approaches to \(1-\gamma \) when the sample size goes large. All mathematical proofs and R-codes for computation in the paper are given in Supplementary Materials.

This paper develops methods for assessing the sensitivity of empirical conclusions regarding conditional distributions to departures from the missing at random (MAR) assumption. We index the degree of nonignorable selection governing the missing data process by the maximal Kolmogorov–Smirnov distance between the distributions of missing and observed outcomes across all values of the covariates. Sharp bounds on minimum mean square approximations to conditional quantiles are derived as a function of the nominal level of selection considered in the sensitivity analysis and a weighted bootstrap procedure is developed for conducting inference. Using these techniques, we conduct an empirical assessment of the sensitivity of observed earnings patterns in U.S. Census data to deviations from the MAR assumption. We find that the well documented increase in the returns to schooling between 1980 and 1990 is relatively robust to deviations from the missing at random assumption except at the lowest quantiles of the distribution, but that conclusions regarding heterogeneity in returns and changes in the returns function between 1990 and 2000 are very sensitive to departures from ignorability.

Bootstrap likelihood ratio tests of cointegration rank are commonly used because they tend to have rejection probabilities that are closer to the nominal level than the rejection probabilities of asymptotic tests. The effect of bootstrapping the test on its power is largely unknown. We show that a new computationally inexpensive procedure can be applied to the estimation of the power function of the bootstrap test of cointegration rank. The bootstrap test is found to have a power function close to that of the level-adjusted asymptotic test. The bootstrap test therefore estimates the level-adjusted power of the asymptotic test highly accurately. The bootstrap test may have low power to reject the null hypothesis of cointegration rank zero, or underestimate the cointegration rank. An empirical application to Euribor interest rates is provided as an illustration of the findings.

Analysis of covariance (ANCOVA) is the standard procedure for comparing several treatments when the response variable depends on one or more covariates. We consider the problem of testing the equality of treatment effects when the variances are not assumed to be equal. It is well known that classical F test is not robust with respect to the assumption of equal variances and may lead to misleading conclusions if the variances are not equal. Ananda (1998) developed a generalized F test for testing the equality of treatment effects. However, simulation studies show that the actual size of this test can be much higher than the nominal level when the sample sizes are small, particularly when the number of treatments is large. In this article, we develop a test using the parametric bootstrap approach of Krishnamoorthy et al. (2007). Our simulations show that the actual size of our proposed test is close to the nominal level, irrespective of the number of treatments and sample sizes. Our simulations also indicat...

Internal pilot studies are a popular design feature to address uncertainties in the sample size calculations caused by vague information on nuisance parameters. Despite their popularity, only very recently blinded sample size reestimation procedures for trials with count data were proposed and their properties systematically investigated. Although blinded procedures are favored by regulatory authorities, practical application is somewhat limited by fears that blinded procedures are prone to bias if the treatment effect was misspecified in the planning. Here, we compare unblinded and blinded procedures with respect to bias, error rates, and sample size distribution. We find that both procedures maintain the desired power and that the unblinded procedure is slightly liberal whereas the actual significance level of the blinded procedure is close to the nominal level. Furthermore, we show that in situations where uncertainty about the assumed treatment effect exists, the blinded estimator of the control event rate is biased in contrast to the unblinded estimator, which results in differences in mean sample sizes in favor of the unblinded procedure. However, these differences are rather small compared to the deviations of the mean sample sizes from the sample size required to detect the true, but unknown effect. We demonstrate that the variation of the sample size resulting from the blinded procedure is in many practically relevant situations considerably smaller than the one of the unblinded procedures. The methods are extended to overdispersed counts using a quasi-likelihood approach and are illustrated by trials in relapsing multiple sclerosis.

In this article, a parametric bootstrap approach for testing the equality of coefficient of variation of $$k$$ k normal populations is proposed. Simulations show that the actual size of our proposed test is close to the nominal level, irrespective of the number of populations and sample sizes, and that this new approach is better than the other existing ones. Also, the power of our approach is satisfactory. An example is proposed for illustrating our new approach.

In a Poisson regression model in which observations are either clustered or represented by repeated measurements of counts, the number of observed zero counts is sometimes greater than the expected frequency by the Poisson distribution and overdispersion may remain even after modeling excess zeros. The zero-inflated negative binomial (ZINB) mixed regression model is suggested to analyze such data. Previous studies have proposed score statistics for testing zero-inflation and overdispersion separately in correlated count data. Here, we also deal with simultaneous score tests for zero-inflation and overdispersion in two-level count data by using the ZINB mixed regression model. Score tests are suggested for (1) zero-inflation in the presence of overdispersion, (2) overdispersion in the presence of zero-inflation, and (3) zero-inflation and overdispersion simultaneously. The level and power of score test statistics are evaluated by a simulation study. The simulation results indicate that score test statistics may occasionally underestimate or overestimate the nominal significance level due to variation in random effects. This study proposes a parametric bootstrap method to overcome this problem. The simulation results of the bootstrap test indicate that score tests hold the nominal level and provide good power.

For the traditional clinical trials, inclusion and exclusion criteria are usually based on some clinical endpoints; the genetic or genomic variability of the trial participants are not totally utilized in the criteria. After completion of the human genome project, the disease targets at the molecular level can be identified and can be utilized for the treatment of diseases. However, the accuracy of diagnostic devices for identification of such molecular targets is usually not perfect. Some of the patients enrolled in targeted clinical trials with a positive result for the molecular target might not have the specific molecular targets. As a result, the treatment effect may be underestimated in the patient population truly with the molecular target. To resolve this issue, under the exponential distribution, we develop inferential procedures for the treatment effects of the targeted drug based on the censored endpoints in the patients truly with the molecular targets. Under an enrichment design, we propose using the expectation-maximization algorithm in conjunction with the bootstrap technique to incorporate the inaccuracy of the diagnostic device for detection of the molecular targets on the inference of the treatment effects. A simulation study was conducted to empirically investigate the performance of the proposed methods. Simulation results demonstrate that under the exponential distribution, the proposed estimator is nearly unbiased with adequate precision, and the confidence interval can provide adequate coverage probability. In addition, the proposed testing procedure can adequately control the size with sufficient power. On the other hand, when the proportional hazard assumption is violated, additional simulation studies show that the type I error rate is not controlled at the nominal level and is an increasing function of the positive predictive value. A numerical example illustrates the proposed procedures.

A large-sample problem of illustrating noninferiority of an experimental treatment over a referent treatment for binary outcomes is considered. The methods of illustrating noninferiority involve constructing the lower two-sided confidence bound for the difference between binomial proportions corresponding to the experimental and referent treatments and comparing it with the negative value of the noninferiority margin. The three considered methods, Anbar, Falk-Koch, and Reduced Falk-Koch, handle the comparison in an asymmetric way, that is, only the referent proportion out of the two, experimental and referent, is directly involved in the expression for the variance of the difference between two sample proportions. Five continuity corrections (including zero) are considered with respect to each approach. The key properties of the corresponding methods are evaluated via simulations. First, the uncorrected two-sided confidence intervals can, potentially, have smaller coverage probability than the nominal level even for moderately large sample sizes, for example, 150 per group. Next, the 15 testing methods are discussed in terms of their Type I error rate and power. In the settings with a relatively small referent proportion (about 0.4 or smaller), the Anbar approach with Yates' continuity correction is recommended for balanced designs and the Falk-Koch method with Yates' correction is recommended for unbalanced designs. For relatively moderate (about 0.6) and large (about 0.8 or greater) referent proportion, the uncorrected Reduced Falk-Koch method is recommended, although in this case, all methods tend to be over-conservative. These results are expected to be used in the design stage of a noninferiority study when asymmetric comparisons are envisioned.

For several independent multivariate bioassays performed at different laboratories or locations, the problem of testing the homogeneity of the relative potencies is addressed, assuming the usual slope-ratio or parallel line assay model. When the homogeneity hypothesis holds, interval estimation of the common relative potency is also addressed. These problems have been investigated in the literature using likelihood-based methods, under the assumption of a common covariance matrix across the different studies. This assumption is relaxed in this investigation. Numerical results show that the usual likelihood-based procedures are inaccurate for both of the above problems, in terms of providing inflated type I error probabilities for the homogeneity test, and providing coverage probabilities below the nominal level for the interval estimation of the common relative potency, unless the sample sizes are large, as expected. Correction based on small sample asymptotics is investigated in this article, and this provides significantly more accurate results in the small sample scenario. The results are also illustrated with examples.

The Wilcoxon rank-sum test is a well-known nonparametric test for the equality of two distributions. In this article, we study a two-stage nonparametric procedure by first testing symmetry for the two underlying distributions and then using the Wilcoxon-type precedence test based on right-censored samples. Specifically, in the first stage, we use a test of symmetry for the two underlying distributions. Then, in the second stage, the minimal Wilcoxon rank-sum precedence test based on a partial sample is used for testing the equality of the two distributions against the stochastically ordered alternative, in which the size of the partial sample is determined by the outcome in the first stage. A simulation study reveals that the proposed two-stage procedure maintains the nominal level of significance and performs better than the classical Wilcoxon rank-sum test in terms of power in many situations. Finally, a numerical example is presented to illustrate the nonparametric procedures developed here.

Modeling multidimensional test data with a unidimensional model can result in serious statistical errors, such as bias in item parameter estimates. Many methods exist for assessing the dimensionality of a test. The current study focused on DIMTEST. Using simulated data, the effects of sample size splitting for use with the ATFIND procedure for empirically deriving a subtest composed of items that potentially measure a second dimension versus DIMTEST for assessing whether this subtest represents a second dimension were investigated. Conditions explored included proportion of sample used for ATFIND, sample size, test length, interability correlations, test structure, and distribution of item difficulties. Overall, it appears that DIMTEST has Type I error rates near the nominal rate and good power in detecting multidimensionality, although Type I error inflation is observed for larger sample sizes. Results suggest that a 50/50 split maximizes power and keeps the Type I error rate below the nominal level unless the test is short and the sample is large. A 75/25 split controls Type I error better for short tests and large samples.

In this article, we derive a locally best test for testing the mean of exponential distributions with interval-censored samples. This locally best test possesses certain optimality. It is of unbiasedness and equivalent to a likelihood ratio test in some circumstances, and it is also a Bayes test for some loss function. For the locally best test, the associated critical values and powers at a nominal level of significance are provided. For a large sample size case, asymptotic critical values and powers are also calculated and tabulated. Moreover, based on the locally best test, a curtailed test is proposed. This curtailed test is equivalent to the locally best test on the acceptance or rejection of the null hypothesis. A Monte Carlo simulation is carried out to illustrate the performance of the curtailed test compared with the locally best test. Numerical results show that the experimental duration time of the curtailed test is substantially smaller than that of the locally best test.

Two families of processes: pure jump processes and jump-diffusion processes are widely used in literatures. Recently, empirical findings demonstrate that the underlying processes of high frequency data sets are pure-jump processes of infinite variation in many situations. Statistical tests are also proposed to make the empirical findings theoretically grounded. In this paper, we extend the work of Jing et al. (2012) in two aspects: (1) the jump process in the null hypothesis and the alternative hypothesis could be different; (2) the null hypothesis covers more flexible processes which are more relevant in finance when considering models for asset prices or nominal interest rates. Theoretically, the test is proven to be very powerful and can control the type I error probabilities well under the nominal level.

In this article we examine sample size calculations for a binomial proportion based on the confidence interval width of the Agresti-Coull, Wald and Wilson Score intervals. We pointed out that the commonly used methods based on known and fixed standard errors cannot guarantee the desired confidence interval width given a hypothesized proportion. Therefore, a new adjusted sample size calculation method was introduced, which is based on the conditional expectation of the width of the confidence interval given the hypothesized proportion. With the reduced sample size, the coverage probability can still maintain at the nominal level and is very competitive to the converge probability for the original sample size.

We present approximations to the distribution of the weighted combination of independent and dependent p - values, . In case that independence of Pi 's is not assumed, it is argued that the quantity A is implic-itly dominated by positive definite quadratic forms that induce a chi-square distribution. This gives way to the approximation of the associated degrees of freedom using Satterthwaite (1946) or Patnaik (1949) method. An approximation by Brown (1975) is used to estimate the covariance between the log transformed P - values. The performance of the approximations is compared using simulations. For both the independent and dependent cases, the approximations are shown to yield probability values close to the nominal level, even for arbitrary weights, ωi ’s.

Recall, the proportion of relevant documents retrieved, is an important measure of effectiveness in information retrieval, particularly in the legal, patent, and medical domains. Where document sets are too large for exhaustive relevance assessment, recall can be estimated by assessing a random sample of documents; but an indication of the reliability of this estimate is also required. In this article, we examine several methods for estimating two-tailed recall confidence intervals. We find that the normal approximation in current use provides poor coverage in many circumstances, even when adjusted to correct its inappropriate symmetry. Analytic and Bayesian methods based on the ratio of binomials are generally more accurate, but are inaccurate on small populations. The method we recommend derives beta-binomial posteriors on retrieved and unretrieved yield, with fixed hyperparameters, and a Monte Carlo estimate of the posterior distribution of recall. We demonstrate that this method gives mean coverage at or near the nominal level, across several scenarios, while being balanced and stable. We offer advice on sampling design, including the allocation of assessments to the retrieved and unretrieved segments, and compare the proposed beta-binomial with the officially reported normal intervals for recent TREC Legal Track iterations., To appear in ACM Transactions on Information Systems

Rationale and Objectives Multireader imaging trials often use a factorial design, in which study patients undergo testing with all imaging modalities and readers interpret the results of all tests for all patients. A drawback of this design is the large number of interpretations required of each reader. Split-plot designs have been proposed as an alternative, in which one or a subset of readers interprets all images of a sample of patients, while other readers interpret the images of other samples of patients. In this paper, the authors compare three methods of analysis for the split-plot design. Materials and Methods Three statistical methods are presented: the Obuchowski-Rockette method modified for the split-plot design, a newly proposed marginal-mean analysis-of-variance approach, and an extension of the three-sample U -statistic method. A simulation study using the Roe-Metz model was performed to compare the type I error rate, power, and confidence interval coverage of the three test statistics. Results The type I error rates for all three methods are close to the nominal level but tend to be slightly conservative. The statistical power is nearly identical for the three methods. The coverage of 95% confidence intervals falls close to the nominal coverage for small and large sample sizes. Conclusions The split-plot multireader, multicase study design can be statistically efficient compared to the factorial design, reducing the number of interpretations required per reader. Three methods of analysis, shown to have nominal type I error rates, similar power, and nominal confidence interval coverage, are available for this study design.

We consider the one-way ANOVA problem of testing the equality of several normal means when the variances are not assumed to be equal. This is a generalization of the Behrens-Fisher problem, but even in this special case there is no exact test and the actual size of any test depends on the values of the nuisance parameters. Therefore, controlling the actual size of the test is of main concern. In this article, we first consider a test using the concept of generalized p-value. Extensive simulation studies show that the actual size of this test does not exceed the nominal level, for practically all values of the nuisance parameters, but the test is not too conservative either, in the sense that the actual size of the test can be very close to the nominal level for some values of the nuisance parameters. We then use this test to propose a simple F-test, which has similar properties but avoids the computations associated with generalized p-values. Because of its simplicity, both conceptually as well as computa...

Among statistical inferences, one of the main interests is drawing the inferences about the log-normal means since the log-normal distribution is a well-known candidate model for analyzing positive and right-skewed data. In the past, the researchers only focused on one or two log-normal populations or used the large sample theory or quadratic procedure to deal with several log-normal distributions. In this article, we focus on making inferences on several log-normal means based on the modification of the quadratic method, in which the researchers often used the vector of the generalized variables to deal with the means of the symmetric distributions. Simulation studies show that the quadratic method performs well only for symmetric distributions. However, the modified procedure fits both symmetric and skew distribution. The numerical results show that the proposed modified procedure can provide the confidence interval with coverage probabilities close to the nominal level and the hypothesis testing perfor...

Linear mixed-effects models are a powerful tool for the analysis of longitudinal data. The aim of this paper is to study model averaging for linear mixed-effects models. The asymptotic distribution of the frequentist model average estimator is derived, and a confidence interval procedure with an actual coverage probability that tends to the nominal level in large samples is developed. The two confidence intervals based on the model averaging and based on the full model are shown to be asymptotically equivalent. A simulation study shows good finite sample performance of the model average estimators.

The class of inflated beta regression models generalizes that of beta regressions [S.L.P. Ferrari and F. Cribari-Neto, Beta regression for modelling rates and proportions, J. Appl. Stat. 31 (2004), pp. 799–815] by incorporating a discrete component that allows practitioners to model data on rates and proportions with observations that equal an interval limit. For instance, one can model responses that assume values in (0, 1]. The likelihood ratio test tends to be quite oversized (liberal, anticonservative) in inflated beta regressions estimated with a small number of observations. Indeed, our numerical results show that its null rejection rate can be almost twice the nominal level. It is thus important to develop alternative testing strategies. This paper develops small-sample adjustments to the likelihood ratio and signed likelihood ratio test statistics in inflated beta regression models. The adjustments do not require orthogonality between the parameters of interest and the nuisance parameters and are ...

It is well known that the standard independent, identically distributed (iid) bootstrap of the mean is inconsistent in a location model with infinite variance (α-stable) innovations. This occurs because the bootstrap distribution of a normalised sum of infinite variance random variables tends to a random distribution. Consistent bootstrap algorithms based on subsampling methods have been proposed but have the drawback that they deliver much wider confidence sets than those generated by the iid bootstrap owing to the fact that they eliminate the dependence of the bootstrap distribution on the sample extremes. In this paper we propose sufficient conditions that allow a simple modification of the bootstrap (Wu, 1986) to be consistent (in a conditional sense) yet to also reproduce the narrower confidence sets of the iid bootstrap. Numerical results demonstrate that our proposed bootstrap method works very well in practice delivering coverage rates very close to the nominal level and significantly narrower con...

This article investigates three procedures on the multiple comparisons with a control in the presence of unequal error variances. The advantages of the proposed methods are illustrated through two examples. The performance of the proposed methods and other alternative methods is compared by simulation studies. The results show that the typical methods assuming equal variance will have inflated error rate and may lead to erroneous inference when the equal variance assumption fails. In addition, the simulation study shows that the proposed approaches always control the family-wise error rate at a specified nominal level α, while some established methods are liberal and have inflated error rate in some scenarios.

The Savannah River National Laboratory (SRNL) received one set of Solvent Hold Tank (SHT) samples (MCU-16-701, MCU-16-702 and MCU-16-703), pulled on 05/23/2016, and another set of SHT samples (MCU-16-710, MCU-16-711, and MCU-16-712) were pulled on 05/28/2016 after the solvent was superwashed with 300 mM sodium hydroxide for analysis. Samples MCU-16-701, MCU-16-702, and MCU-16-703 were combined into one sample (MCU-16-701-702-703) and samples MCU-16-710, MCU- 16-711, and MCU-16-712 were combined into one sample (MCU-16-710-711-712). Of the two composite samples MCU-16-710-711-712 represents the current chemical state of the solvent at MCU. All analytical conclusions are based on the chemical analysis of MCU-16-710-711-712. There were no chemical differences between MCU-16-701-702-703 and superwashed MCU-16-710-711-712. Analysis of the composited sample MCU-16-710-712-713 indicated the Isopar™L concentration is above its nominal level (102%). The modifier (CS-7SB) is 16% below its nominal concentration, while the TiDG and MaxCalix concentrations are at and above their nominal concentrations, respectively. The TiDG level has begun to decrease, and it is 7% below its nominal level as of May 28, 2016. Based on this current analysis, the levels of TiDG, Isopar™L, MaxCalix, and modifier are sufficient for continuing operation but are expected to decrease with time. Periodic characterization and trimming additions to themore » solvent are recommended.« less

Multiple testing of correlations arises in many applications including gene coexpression network analysis and brain connectivity analysis. In this article, we consider large-scale simultaneous testing for correlations in both the one-sample and two-sample settings. New multiple testing procedures are proposed and a bootstrap method is introduced for estimating the proportion of the nulls falsely rejected among all the true nulls. We investigate the properties of the proposed procedures both theoretically and numerically. It is shown that the procedures asymptotically control the overall false discovery rate and false discovery proportion at the nominal level. Simulation results show that the methods perform well numerically in terms of both the size and power of the test and it significantly outperforms two alternative methods. The two-sample procedure is also illustrated by an analysis of a prostate cancer dataset for the detection of changes in coexpression patterns between gene expression levels. Supplementary materials for this article are available online.

Savannah River National Laboratory (SRNL) received one set of Solvent Hold Tank (SHT) samples (MCU-16-348-349-350), pulled on 03/30/2016 for analysis. The samples were combined and analyzed for composition. Analysis of the composite sample MCU-16-348-349-350 indicated the IsoparTML concentration is above its nominal level (101%). The modifier (CS-7SB) and the TiDG concentrations are 9% and 55% below their nominal concentrations. This analysis confirms the solvent may require the addition of TiDG, and possibly of modifier. Based on the current monthly sample, the levels of TiDG, IsoparTML, MaxCalix, and modifier are sufficient for continuing operation but are expected to decrease with time. Periodic characterization and trimming additions to the solvent are recommended.