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Millions of measuring instruments are verified each year before being placed on the markets worldwide. In the EU, such initial conformity assessments are regulated by the Measuring Instruments Directive (MID). The MID modules F and F1 on product verification allow for statistical acceptance sampling, whereby only random subsets of instruments need to be inspected. This article re-interprets the acceptance sampling conditions formulated by the MID. The new interpretation is contrasted with the one advanced in WELMEC guide 8.10, and three advantages have become apparent. First, an economic advantage of the new interpretation is a producers' risk bounded from above, such that measuring instruments with sufficient quality are accepted with a guaranteed probability of no less than 95%. Second, a conceptual advantage is that the new MID interpretation fits into the well known, formal framework of statistical hypothesis testing. Thirdly, the new interpretation applies unambiguously to finite-sized lots, even very small ones. We conclude that the new interpretation is to be preferred and suggest re-formulating the statistical sampling conditions in the MID. Re-interpreting the MID conditions implies that currently available sampling plans are either not admissible or not optimal. We derive a new acceptance sampling scheme and recommend its application. for this article are available online. [ABSTRACT FROM AUTHOR]

Objectives: To assess: (1) the presence of any carry-over effect between interventions; (2) the immediate effects of inferior shoulder mobilization on shoulder and scapular muscle activity; and (3) to compare muscle activity response between the control and mobilization conditions. Repeated measures, cross-over, pre-post intervention study with sample of convenience. Methods: Twenty-two asymptomatic individuals performed 10 repetitions of shoulder abduction before and after the control and mobilization, with a dosage of three sets of 30-s duration, with grade-IV. The order of intervention was randomized. Surface electromyography was used for recording activity of upper and lower trapezius; anterior, middle and posterior deltoids; supraspinatus; infraspinatus; and serratus anterior. Repeated measures mixed-model analysis of variance was used to assess immediate changes in muscle activity levels following inferior shoulder mobilization. Statistical parametric mapping (SPM) was used for comparing muscle activity waveforms between control and mobilization conditions throughout the range of motion. Results: No systematic changes in muscle activity levels were found between: (1) baseline and follow-up for each condition, at the concentric and eccentric phases of shoulder abduction; (2) control and mobilization conditions during the concentric and eccentric phases of shoulder abduction. SPM results suggested no differences in muscle activity pattern between conditions. Conclusions: Inferior shoulder mobilization did not produce immediate effects on shoulder and scapular muscle activity. It is possible that the dose used was insufficient to generate an immediate neuromuscular response to the mobilization. [ABSTRACT FROM AUTHOR]

Objective:The study objective was to measure the rates of inclusion of populations at risk of advanced melanoma in a pilot targeted screening project involving general practitioners. Design:This cross-sectional database study compared the inclusion rates of patients who signed inclusion in a targeted screening project with those of patients who did not, during a period in which both groups of patients consulted investigators. Setting:Data were extracted from the national healthcare insurance records in western France from 11 April to 30 October 2011. Patients:Patients, older than 18, considered for the data extraction had consulted one of the 78 participating GPs during the study period, and were affiliated with the national healthcare insurance. Main outcome measures:Inclusion in the screening was the main outcome measure. Patients at risk of advanced melanoma were characterized by male gender, age over 50, low income, rural residence, farmer, and presence of chronic disease. Results:A total of 57,279 patients consulted GPs during the inclusion period and 2711 (4.73%) were included in the targeted screening. Populations at risk of advanced melanoma were less included: men (OR = 0.67; 95%CI [0.61–0.73];p < 0.001), older than 50 (OR = 0.67; 95%CI [0.60–0.74];p < 0.001), low income (OR = 0.65; 95%CI [0.55–0.77];p < 0.001), farmer (OR = 0.23; 95%CI [0.17–0.30];p < 0.001) and presence of a chronic disease (OR = 0.87; 95%CI [0.77–0.98];p < 0.028). Conclusion:This study demonstrated inequalities in the inclusion of patients in a melanoma screening. Patients at risk of advanced cancer were screened less often. Further studies should focus on GPs ability to identify and screen these patients.KEY POINTSAdvanced melanoma is more frequently diagnosed in men, older patients and socioeconomically disadvantaged populations, which leads to survival inequalities.• Despite the involvement of general practitioners, the implementation of targeted melanoma screening did not avoid inclusion inequalities.• Men, older patients, patients suffering from chronic diseases, and low-income patients were less likely to benefit from screening.• The display of a conventional or an alarmist poster in the waiting room did not statistically reduce these inclusion inequalities. [ABSTRACT FROM PUBLISHER]

In this article, the authors discuss Eric B. Laber and Susan A. Murphy's study on nonregular framework. Laber and Murphy use nonregular framework in the examination of a test error behavior for a wide class of linear classifiers and introduced an adaptive confidence intervals. They added that the study on nonregular framework inspired them to propose a family of adaptive classifiers.

During a few years around the turn of the millennium, a series of local hospitals in Philadelphia closed their obstetrics units, with the consequence that many mothers-to-be arrived unexpectedly at the city's large, regional teaching hospitals whose obstetrics units remained open. Nothing comparable happened in other United States cities, where there were only sporadic changes in the availability of obstetrics units. What effect did these closures have on mothers and their newborns? We study this question by comparing Philadelphia before and after the closures to a control Philadelphia constructed from elsewhere in Pennsylvania, California, and Missouri, matching mothers for 59 observed covariates including year of birth. The analysis focuses on the period 1995-1996, when there were no closures, and the period 1997-1999 when five hospitals abruptly closed their obstetrics units. Using a new sensitivity analysis for difference-in-differences with binary outcomes, we examine the possibility that Philadelphia mothers differed from control mothers in terms of some covariate not measured, and perhaps the distribution of that unobserved covariate changed in a different way in Philadelphia and control-Philadelphia in the years before and after the closures. We illustrate two recently proposed techniques for the design and analysis of observational studies, namely split samples and evidence factors. To boost insensitivity to unmeasured bias, we drew a small random planning sample of about 26,000 mothers in 13,000 pairs and used them to frame hypotheses that promised to be less sensitive to bias; then these hypotheses were tested on the large, independent complementary analysis sample of nearly 240,000 mothers in 120,000 pairs. The splitting was successful twice over: (i) it successfully identified an interesting and moderately insensitive conclusion, (ii) by comparison of the planning and analysis samples, it is clearly seen to have avoided a exaggerated claim of insensitivity to unmeasured bias that might have occurred by focusing on the least sensitive of many findings. Also, we identified two approximate evidence factors and one test for unmeasured bias: (i) factor 1 compared Philadelphia to control before and after the closures, (ii) factor 2 focused on the years 1997-1999 of abrupt closures and compared zip codes with closures to zip codes without closures, (iii) and the test for bias focused on the years 1995-1996 prior to closures and compared zip codes which would have closures in 1997-1999 to zip codes without closures in 1997-1999-any ostensible effect found in that last comparison is surely bias from the characteristics of Philadelphia zip codes in which closures took place. Approximate evidence factors provide nearly independent tests of a null hypothesis such that the evidence in each factor would be unaffected by certain biases that would invalidate the other factor. [ABSTRACT FROM AUTHOR]

The extremal index parameter θ characterizes the degree of local dependence in the extremes of a stationary time series and has important applications in a number of areas, such as hydrology, telecommunications, finance, and environmental studies. In this study, a novel estimator for θ based on the asymptotic scaling of block-maxima and resampling is introduced. It is shown to be consistent and asymptotically normal for a large class of rn-dependent time series. Further, a procedure for the automatic selection of its tuning parameter is developed and different types of confidence intervals that prove useful in practice proposed. The performance of the estimator is examined through simulations, which show its highly competitive behavior. Finally, the estimator is applied to three real datasets of daily crude oil prices, daily returns of the S&P 500 stock index, and high-frequency, intraday traded volumes of a stock. These applications demonstrate additional diagnostic features of statistical plots based on the new estimator. Supplementary materials including an appendix with complete proofs, the crude oil dataset, and an R-script implementing the estimators are available online. [ABSTRACT FROM AUTHOR]

The assumption of approximate normality of a pivotal used for constructing confidence intervals or tests often is violated by a substantial correlation between the point estimator at hand and the estimator of its variance. This can be caused by underlying skewness of data, generating both bias and skewness of the pivotal and leading to, for example, confidence intervals with poorer coverage properties, especially for one-sided intervals. We present in a general setting a simple, yet effective procedure that takes into account this correlation and leads to alternative adjusted intervals with more appealing coverage properties. We provide examples, including a simulation study. [ABSTRACT FROM AUTHOR]

Frequentist confidence intervals for population ranks and their statistical justifications are not well established, even though there is a great need for such procedures in practice. How do we assign confidence bounds for the ranks of health care facilities, schools, and financial institutions based on data that do not clearly separate the performance of different entities apart? The commonly used bootstrap-based frequentist confidence intervals and Bayesian intervals for population ranks may not achieve the intended coverage probability in the frequentist sense, especially in the presence of unknown ties or "near ties" among the populations to be ranked. Given random samples from k populations, we propose confidence bounds for population ranking parameters and develop rigorous frequentist theory and nonstandard bootstrap inference for population ranks, which allow ties and near ties. In the process, a notion of modified population rank is introduced that appears quite suitable for dealing with the population ranking problem. The proposed methodology and theoretical results are illustrated through simulations and a real dataset from a health research study involving 79 Veterans Health Administration (VHA) facilities. The results are extended to general risk adjustment models. [ABSTRACT FROM AUTHOR]

Statistical experiments, more commonly referred to as Monte Carlo or simulation studies, are used to study the behavior of statistical methods and measures under controlled situations. Whereas recent computing and methodological advances have permitted increased efficiency in the simulation process, known as variance reduction, such experiments remain limited by their finite nature and hence are subject to uncertainty; when a simulation is run more than once, different results are obtained. However, virtually no emphasis has been placed on reporting the uncertainty, referred to here as Monte Carlo error, associated with simulation results in the published literature, or on justifying the number of replications used. These deserve broader consideration. Here we present a series of simple and practical methods for estimating Monte Carlo error as well as determining the number of replications required to achieve a desired level of accuracy. The issues and methods are demonstrated with two simple examples, one evaluating operating characteristics of the maximum likelihood estimator for the parameters in logistic regression and the other in the context of using the bootstrap to obtain 95% confidence intervals. The results suggest that in many settings, Monte Carlo error may be more substantial than traditionally thought. [ABSTRACT FROM AUTHOR]

The use of equivalence testing in scientific research is increasing beyond its traditional role in the drug approval process. Largely due to its ease of use and recommendations from the U.S. Food and Drug Administration guidance, the most common statistical method for testing equivalence is the two one- sided tests (TOST) procedure. Like classical point-null hypothesis testing, TOST is subject to multiplicity concerns as more comparisons are made. Here we give a condition that bounds the familywise error rate (FWER) using TOST and leads to a simple solution for controlling the FWER. Specifically, we demonstrate that if all pairwise comparisons of k independent groups are being evaluated for equivalence, then simply scaling the nominal type I error rate down by (k - 1) is sufficient to maintain the FWER at the desired value or less. The resulting rule is much less conservative than the equally simple Bonferroni correction. An example of equivalence testing in a non- drug development setting is given. [ABSTRACT FROM AUTHOR]

This article reviews literature on confidence intervals for p, assuming (Bernoulli) single, double, and multistage sampling. Methods used to produce approximate single-sampling confidence intervals extend to double sampling as well. A new Wilson approximate confidence interval procedure for double sampling is compared with existing procedures in terms of general interval properties, such as interval invariance, and performance (in terms of actual coverage probability and expected length) for double-sampling plans from the literature. [ABSTRACT FROM AUTHOR]

The pretest-posttest study design is commonly used in medical and social science research to assess the effect of a treatment or an intervention. Recently, interest has been rising in developing inference procedures that improve efficiency while relaxing assumptions used in the pretest-posttest data analysis, especially when the posttest measurement might be missing. In this article we propose a semiparametric estimation procedure based on empirical likelihood (EL) that incorporates the common baseline covariate information to improve efficiency. The proposed method also yields an asymptotically unbiased estimate of the response distribution. Thus functions of the response distribution, such as the median, can be estimated straightforwardly, and the EL method can provide a more appealing estimate of the treatment effect for skewed data. We show that, compared with existing methods, the proposed EL estimator has appealing theoretical properties, especially when the working model for the underlying relationship between the pretest and posttest measurements is misspecified. A series of simulation studies demonstrates that the EL-based estimator outperforms its competitors when the working model is misspecified and the data are missing at random. We illustrate the methods by analyzing data from an AIDS clinical trial (ACTG 175). [ABSTRACT FROM AUTHOR]

A new nonparametric method is described to estimate the distribution of mass within spherical galaxies. The problem of estimating the mass, M(r), within radius ris converted into a problem of estimating a regression function nonparametrically, subject to shape restrictions. We represent the restrictions by the interception of quadratic cones and use the second-order cone programming to estimate the unknown parameters. We establish asymptotic results that are used to construct confidence intervals on M(r). We apply the technique to new kinematic data for four dwarf galaxies. Results indicate that dark matter dominates the stellar kinematics of these systems at ail radii. [ABSTRACT FROM AUTHOR]

This article makes two contributions. First, we outline a simple simulation-based framework for constructing conditional distributions for multifactor and multidimensional diffusion processes, for the case where the functional form of the conditional density is unknown. The distributions can be used, for example, to form predictive confidence intervals for time period t + τ, given information up to period t. Second, we use the simulation-based approach to construct a test for the correct specification of a diffusion process. The suggested test is in the spirit of the conditional Kolmogorov test of Andrews. However, in the present context the null conditional distribution is unknown and is replaced by its simulated counterpart. The limiting distribution of the test statistic is not nuisance parameter-free. In light of this, asymptotically valid critical values are obtained via appropriate use of the block bootstrap. The suggested test has power against a larger class of alternatives than tests that are constructed using marginal distributions/densities. The findings of a small Monte Carlo experiment underscore the good finite sample properties of the proposed test, and an empirical illustration underscores the ease with which the proposed simulation and testing methodology can be applied. [ABSTRACT FROM AUTHOR]

Although it is well known that modem methods of computing confidence intervals (CIs) based on likelihood or simulation have important advantages, normal approximation confidence interval procedures (NACPs) are still widely used, especially in the analysis of censored data. This is because CIs from NACPs are easy to compute and easy to explain. But when the sample size is not large or when there is heavy censoring, the performance of NACPs can be poor. A transformation can be applied to keep CI endpoints from falling outside the parameter space and improve performance, but the degree of improvement (if any) depends on the chosen function. To obtain CIs for distribution probabilities, some seemingly useful transformation functions will cause the estimated variance to blow up in the tails of the distribution and can lead to nonsensical confidence intervals. This article compares different NACPs for distribution probabilities. Our results suggest that an NACP based on a studentized statistic, which we call the z procedure, has desirable properties compared with alternative NACPs. [ABSTRACT FROM AUTHOR]

In this article, we consider the problem of constructing confidence intervals for a population median when the underlying population is discrete. We describe seven methods of assigning confidence levels to order statistic based confidence intervals, all of which are easy to implement. A simulation study shows that, with discrete populations, it is possible to obtain consistently more accurate confidence levels and shorter intervals compared to the ones reported by the classical method which is implemented in commercial software. More precisely, the best results are obtained by inverting a two-tailed sign test that properly takes into account tied observations. Some real data examples illustrate the use of these confidence intervals. [ABSTRACT FROM AUTHOR]

This article revisits the problem of determining sample size for interval estimation of a binomial proportion. It is motivated by the author's experience as an expert witness in a legal case. The legal case involves a class action suit against a large service provider for alleged over-collection of special service fees. We discuss how: (1) focusing on relative error of the binomial outcome instead of absolute error of the Bernoulli probability p can have a dramatic effect on sample size recommendations, and (2) a year-by-year analysis may differ from a single-year analysis. We also discuss the challenges in presenting such statistical results to nonstatisticians, and propose simplifications to enhance communicability. [ABSTRACT FROM AUTHOR]

In this article we show how to predict small-area means and obtain valid mean squared error estimators and confidence intervals when the areas represented in the sample are sampled with unequal probabilities possibly related to the true (unknown) area means and the sampling of units within the selected areas is with probabilities possibly related to the outcome values. Ignoring the effects of the sampling process on the distribution of the observed outcomes in such cases may bias the inference very severely. Classical design-based inference that uses the randomization distribution of probability-weighted estimators cannot be applied for predicting the means of nonsampled areas. We propose simple test statistics for testing the informativeness of the selection of areas and sampling of units within the selected areas. We illustrate the proposed procedures by a simulation study and a real application of estimating mean body mass index in U.S. counties, using data from the Third National Health and Nutrition Examination Survey. [ABSTRACT FROM AUTHOR]

Suppose that we are interested in establishing simple but reliable rules for predicting future t-year survivors through censored regression models. In this article we present inference procedures for evaluating such binary classification rules based on various prediction precision measures quantified by the overall misclassification rate, sensitivity and specificity, and positive and negative predictive values. Specifically, under various working models, we derive consistent estimators for the above measures through substitution and cross-validation estimation procedures. Furthermore, we provide large-sample approximations to the distributions of these nonsmooth estimators without assuming that the working model is correctly specified. Confidence intervals, for example, for the difference of the precision measures between two competing rules can then be constructed. All of the proposals are illustrated with real examples, and their finite-sample properties are evaluated through a simulation study. [ABSTRACT FROM AUTHOR]

In a randomized experiment comparing two treatments, there is interference between units if applying the treatment to one unit may affect other units. Interference implies that treatment effects are not comparisons of two potential responses that a unit may exhibit, one under treatment and the other under control, but instead are inherently more complex. Interference is common in social settings where people communicate, compete, or spread disease; in studies that treat one part of an organism using a symmetrical pall as control; in studies that apply different treatments to the same organism at different times; and in many other situations. Available statistical tools are limited. For instance. Fisher's sharp null hypothesis of no treatment effect implicitly entails no interference, and so his randomization test may be used to test no effect, but conventional ways of inverting the test to obtain confidence intervals, say for an additive effect, are not applicable with interference. Another commonly used approach assumes that interference is of a simple parametric form confined to units that are near one another in time or space: this is useful when applicable but is of little use when interference may be widespread and of uncertain form. Exact, nonparametric methods are developed for inverting randomization tests to obtain confidence intervals for magnitudes of effect assuming nothing at all about the structure of the interference between units. The limitations of these methods are discussed. To illustrate the general approach, two simple methods and two simple empirical examples are discussed. Extension to randomization based covariance adjustment is briefly described. [ABSTRACT FROM AUTHOR]

Simple random sampling is the foundation for almost every method taught in introductory statistics classes. Many students, however, have difficulty understanding the difference between simple random sampling and cluster sampling and determining whether the assumption of simple random sampling is met, We can find evidence of this difficulty in research articles reporting statistical findings: many analyze the data using simple random sampling assumptions even though a cluster sample was actually taken. We review several statistics texts' treatment of sampling assumptions for confidence intervals and hypothesis tests. We then propose activities that could be used in the classroom to help students gain a better understanding of the concepts of simple random sampling and confidence intervals. [ABSTRACT FROM AUTHOR]

A new collection of procedures is developed for the analysis of two-sample, ranked-set samples, providing an alternative to the Bohn-Wolfe procedure. These procedures split the data based on the ranks in the ranked-set sample and lead to tests for the centers of distributions, confidence intervals, and point estimators. The advantages of the new tests are that they require essentially no assumptions about the mechanism by which rankings are imperfect, that they maintain their level whether rankings are perfect or imperfect, that they lead to generalizations of the Bohn-Wolfe procedure that can be used to increase power in the case of perfect rankings, and that they allow one to analyze both balanced and unbalanced ranked-set samples. A new class of imperfect ranking models is proposed, and the performance of the procedure is investigated under these models. When rankings are random, a theorem is presented which characterizes efficient data splits. Because random rankings are equivalent to iid samples, this theorem applies to a wide class of statistics and has implications for a variety of computationally intensive methods. [ABSTRACT FROM AUTHOR]

In recent work we introduced a general, a weak, and a strong partitioning principles for the construction of multiple decision procedures as multiple testing or selection procedures. Partitioning principles can be viewed as natural extensions of the closure principle and sometimes yield more powerful decision procedures. In this article we consider the problem of establishing equivalence with the best with respect to k treatment means, where equivalence is defined in terms of a threshold value δ > 0. We reformulate the original selection problem as a multiple testing problem and develop various step-down and step-up procedures by applying the closure principle and partitioning principles. The new step-down procedure is shown to provide a uniform improvement over procedures currently in use. Moreover, we propose some projection methods that yield confidence intervals being compatible with stepwise tests and selection procedures. [ABSTRACT FROM AUTHOR]

We give a large-sample analysis of the minimal coverage probability of the usual confidence intervals for regression parameters when the underlying model is chosen by a "conservative" (or "overconsistent") model selection procedure. We derive an upper bound for the large-sample limit minimal coverage probability of such intervals that applies to a large class of model selection procedures including the Akaike information criterion as well as various pretesting procedures. This upper bound can be used as a safeguard to identify situations where the actual coverage probability can be far below the nominal level. We illustrate that the (asymptotic) upper bound can be statistically meaningful even in rather small samples. [ABSTRACT FROM AUTHOR]

In this article we study a general class of goodness-of-fit tests for a parametric conditional mean of a linear or nonlinear time series model. Among the properties of the proposed tests are that they are suitable when the conditioning set is infinite-dimensional; that they are consistent against a broad class of alternatives, including Pitman's local alternatives converging at the parametric rate ≪~l/2, with n the sample size; and that they do not need to choose a lag order depending on the sample size or to smooth the data. It turns out that the asymptotic null distributions of the tests depend on the data generating process, so a new bootstrap procedure is proposed and theoretically justified. The proposed bootstrap tests are robust to higher-order dependence, particularly to conditional heteroscedasticity of unknown form. A simulation study compares the finite-sample performance of the proposed and competing tests and shows that our tests can play a valuable role in time series modeling. Finally, an application to an economic price series highlights the merits of our approach. [ABSTRACT FROM AUTHOR]

Sample size determination methods are considered for hypothesis testing about location parameters of two continuous distributions using independent random samples and the Mann-Whitney-Wilcoxon (MWW) test, for a specified shift, size, and power. These methods are based on the so-called "Noether's formula," derived from a normal approximation to the power of the MWW test, and a pilot sample from each of the distributions. Compared with alternate methods, including the one using bootstrap similar to that of Hamilton and Collings (1991) the new methods are shown to be at least as good in terms of accuracy and substantially more efficient in terms of speed and variability. The simpler method, using linearly smoothed empirical cdf's of the pilot samples and requiring no bootstrapping, is recommended for practical use. Extensions and adaptations for obtaining an upper confidence bound on the sample size and to general linear rank tests are indicated. [ABSTRACT FROM AUTHOR]

A new approach to constructing nonparametric tests for the general two-sample problem is proposed. This approach not only generates traditional tests (including the two-sample Kolmogorov-Smirnov, Cramérvon Mises, and Anderson-Darling tests), but also produces new powerful tests based on the likelihood ratio. Although conventional two-sample tests are sensitive to the difference in location, most of them lack power to detect changes in scale and shape. The new tests are location-, scale-, and shape-sensitive, so they are robust against variation in distribution. [ABSTRACT FROM AUTHOR]

This article presents an estimator for the regression coefficient vector in the Cox proportional hazards model with covariate error. The estimator is obtained by maximizing a likelihood-type function similar to the Cox partial likelihood. The likelihood function involves the cumulative baseline hazard function, for which a simple estimator is substituted. The method is capable of handling general covariate error structures; it is not restricted to the independent additive error model. It can be applied to studies with either an external or internal validation sample, and also to studies with replicate measurements of the surrogate covariate. The estimator is shown to be consistent and asymptotically normal, and an estimate of the asymptotic covariance matrix is derived. Some extensions to general transformation survival models are indicated. Simulation studies are presented for a setup with a single error-prone binary covariate and a setup with a single error-prone normally distributed covariate. These simulation studies show that the method typically produces estimates with low bias and confidence intervals with accurate coverage rates. Efficiency results relative to fully parametric maximum likelihood are also presented. The method is applied to data from the Framingham Heart Study. [ABSTRACT FROM AUTHOR]

An oft-cited advantage of empirical likelihood is that the confidence intervals that are produced by this nonparametric technique are not necessarily symmetric. Rather, they reflect the nature of the underlying data and hence give a more representative way of reaching inferences about the functional of interest. However, this advantage can easily become a disadvantage if the resultant intervals are unduly influenced by one of the data points. This article proposes simple methods for evaluating the effect of single points on empirical likelihood confidence intervals. In addition to suggesting diagnostics for detecting important observations, we examine the use of bootstrap and of jackknife influence functions to assess the extremity of suspect points. [ABSTRACT FROM AUTHOR]

Reliability demonstration tests require demonstrating, with some level of confidence, that reliability exceeds a given standard. Demonstration tests can be expensive and time-consuming. Careful planning of sample size and test length is essential. This article develops exact theoretical methods, based on pivotal quantities and confidence intervals, to aid in proper sample size selection and determining how long the test should be run (in terms of how many units must fail before the test's end) for demonstration tests with failure-censored (type II censored) data from log-location-scale (and the corresponding location-scale) distributions. The methods have been implemented in S-PLUS for the lognormal, Weibull, and log-logistic distributions to allow users to develop graphs depicting probability of successful demonstration as a function of actual reliability, a target reliability, sample size, and number of units failing for an assumed distribution. [ABSTRACT FROM AUTHOR]

When comparing two variables with nonnormal distributions, application of the Wilcoxon-Mann-Whitney test (WMW) is a common choice. However, it is only valid to test the null hypothesis stating equality of the distributions. Sometimes the hypothesis of interest is H0: P(X < Y) = P(X > Y) against P(X < Y) ≠ P(X > Y), called stochastic equality and in- equality. Here we propose a bootstrap test for this problem. Results of an extensive simulation study based on empirical distributions suggest that the new test is valid for a wide range of problems in parasitology and psychology, and the loss of power as compared to WMW is rather small in those cases when both tests are applicable. [ABSTRACT FROM AUTHOR]

Confidence intervals for discrete distributions are often evaluated only by coverage and expected length. We discuss two additional criteria, p-confidence and p-bias. The choice of these criteria is motivated by the interpretation of a confidence interval as being the set of parameter values not rejected by a hypothesis test. Using these additional criteria we compare a number of equal-tailed confidence intervals for the binomial distribution. It is shown that methods that produce superior intervals, as measured by coverage and length, need not perform well in terms of p-confidence and p-bias. Cox's measuring device example is discussed to motivate the need for criteria beyond coverage and length. [ABSTRACT FROM AUTHOR]

Maximum likelihood (ML) inference for the class of homogeneous linear predictor (HLP) models for contingency tables is described. HLP models constrain the expected table counts m through L(m) = X/3, where the link L is allowed to be a many-to-one, nonlinear function. Generalized log-linear, association trend, marginal cumulative probit, and conditional marginal homogeneity models are given as specific examples. ML fit results, which include point estimates, goodness-of-fit statistics, and asymptotic-based approximate distributions, are described and compared for equivalent HLP models. The results are valid for a wide variety of sampling plans including combinations of product multinomial and Poisson sampling. An important practical implication of this article is that the implementation of ML fitting and theory is straightforward, and an attractive alternative to weighted least squares estimation, for HLP models. [ABSTRACT FROM AUTHOR]

We describe a sequential importance sampling (SIS) procedure for analyzing two-way zero-one or contingency tables with fixed marginal sums. An essential feature of the new method is that it samples the columns of the table progressively according to certain special distributions. Our method produces Monte Carlo samples that are remarkably close to the uniform distribution, enabling one to approximate closely the null distributions of various test statistics about these tables. Our method compares favorably with other existing Monte Carlo- based algorithms, and sometimes is a few orders of magnitude more efficient. In particular, compared with Markov chain Monte Carlo (MCMC)-based approaches, our importance sampling method not only is more efficient in terms of absolute running time and frees one from pondering over the mixing issue, but also provides an easy and accurate estimate of the total number of tables with fixed marginal sums, which is far more difficult for an MCMC method to achieve. [ABSTRACT FROM AUTHOR]

We consider the problem of setting a confidence interval or bound for a linear combination of variance components related to a multivariate normal distribution, which includes important applications such as comparing variance components and testing the bioequivalence between two drug products. The lack of an exact confidence interval for a general linear combination of variance components spurred the development of a modified large-sample (MLS) method that was shown to be superior to many other approximation methods. But existing MLS method requires the use of independent estimators of variance components. Using a chi-squared representation of a quadratic form of a multivariate normal vector, we extend the MLS method to situations in which estimators of variance components are dependent. Using Edgeworth and Cornish-Fisher expansions, we explicitly derive the second-order asymptotic coverage error of the MLS confidence bound. Our results show that the MLS confidence bound is not second-order accurate in general, but is much better than the confidence bound based on normal approximation and is nearly second-order accurate in some special cases. Our results also show how to construct an MLS confidence bound that is second-order accurate. As an application, we discuss the use of the MLS method in assessing population bioequivalence, with some simulation results and an example. [ABSTRACT FROM AUTHOR]

A common experimental design for the problem of comparing two means from a normal distribution assumes knowledge of the ratio of the population variances. The optimal sampling ratio is proportional to the square root of this quantity. This article demonstrates that a misspecification of the ratio of the population variances can cause a substantial loss in power of the corresponding tests. As a robust alternative, a maximin approach is used to construct designs, which are efficient, whenever the experimenter is able to specify a specific region for the ratio of the population variances. The advantages of the robust designs for inference in the Behrens-Fisher problem are illustrated in a simulation study and an application to the design of experiment for bioassay is presented. [ABSTRACT FROM AUTHOR]

We develop a flexible model-based procedure for clustering functional data. The technique can be applied to all types of curve data but is particularly useful when individuals are observed at a sparse set of time points. In addition to producing final cluster assignments, the procedure generates predictions and confidence intervals for missing portions of curves. Our approach also provides many useful tools for evaluating the resulting models. Clustering can be assessed visually via low-dimensional representations of the curves, and the regions of greatest separation between clusters can be determined using a discriminant function. Finally, we extend the model to handle multiple functional and finite-dimensional covariates and show how it can be applied to standard finite-dimensional clustering problems involving missing data. [ABSTRACT FROM AUTHOR]

Saddlepoint approximations are developed for the distributions of Satterthwaite F--type statistics that arise in ANOVA with balanced random-effects models. Such statistics are commonly used in variance component testing and confidence interval construction, because exact F pivotals usually do not exist. The approximations are shown to he uniform in their right tails, and the limiting relative errors for distribution approximations are determined. Based on these approxi- mations, a new method is devised for confidence interval construction of variance component ratios. Simulations show that the method has superior coverage accuracy over existing methods. Prepivoting of the proposed method, using the double-parametric bootstrap, is implemented and shows further coverage improvement. The double bootstrap is most efficiently implemented by using the saddlepoint approximation in lieu of the inner layer of resampling: therefore, only a single outer layer of resampling is required. [ABSTRACT FROM AUTHOR]

This article focuses on hypothesis testing from p values to Bayes factors. Testing hypotheses involves deciding on the plausibility of two or more hypothetical statistical models based on some data. It may be that there are two hypothesis on equal footing. In 1908, W. S. Gossett derived the distribution of the Student t statistic and used it to test null hypotheses about one mean and the difference of two means. His approach is used widely today. First, choose test statistic. Next, calculate its p value, which is the probability, assuming that the null hypothesis is true, that one would obtain a value of the test statistic as or more extreme than that obtained from the data. Finally, interpret this value as the probability that the null hypothesis is true. Of course, the p value is not the probability that the null hypothesis is true, but small values do cause one to doubt the null hypothesis. The general techniques have been applied in so many innovative ways. In Bayesian hypothesis testing, some common complaints included that the p value is not the probability that the null hypothesis is true. Another is that the p value is not very useful when sample sizes are large. The Bayesian approach to hypothesis testing answers complaints at a cost of requiring a prior distribution on the parameter.

Inference using the iterated-bootstrap method proposed by Hall is appealing for cases in which the percentile method needs to be used but the nominal level of a confidence interval has to be adjusted. One natural application is for generalized Gini indices of income inequality. When applying these theoretical inequality measures directly to sample data for the purpose of statistical inference, economists must come up with some measure of sampling variation. This is particularly the case when the index estimates are compared over time to infer information on the changes of social welfare and inequality. Although there are difficulties in the existing inferential procedures, a more intuitive approach is to use the iterated-bootstrap method. [ABSTRACT FROM AUTHOR]

The problem of whether stock returns can be predicted from dividend yields is discussed. I apply a new statistical method for finding reliable confidence intervals for regression parameters in the context of dependent and possibly heteroscedastic data, called subsampling. The method works under very weak conditions and avoids the pitfalls of having to choose a structural model to fit to observed data. Appropriate simulation studies suggest that it has better small-sample properties than the generalized method of moments, which is also model free and works under weak conditions. Applying the subsampling method to three datasets, I do not find convincing evidence for the predictability of stock returns. [ABSTRACT FROM AUTHOR]

Presents information on a study which present a range of test using a two-stage sampling procedure for testing the hypothesis that normal means are falling into a practical indifferent zone. Details on the evaluation of the level and power; Numerical solution; Data collection and analysis.

We consider the estimation of a distribution function when observations from this distribution are contaminated by measurement error. The unknown distribution is modeled as a mixture of a finite number of known distributions. Model parameters can be estimated and confidence intervals constructed using well-known likelihood theory. We show that it is also possible to apply this approach to estimation of a unimodal distribution. An application is presented using data from a dietary survey. Simulation results are given to indicate the performance of the estimators and the confidence interval procedures. [ABSTRACT FROM AUTHOR]

In clinical trials and other settings, confidence intervals for survival probabilities at a fixed point in time are often required. Typically, such intervals are constructed on the cumulative hazard scale; the quantiles required for computing these intervals are generally obtained using a first-order normal theory approximation. The appropriateness of such intervals for small sample sizes or under moderate to heavy censoring is suspect. We demonstrate that significant improvement is possible for randomly censored data using the nonparametric bootstrap. In particular. using Edgeworth expansion, it is shown that the percentile-t and Ba bootstrap methodologies based on the studentized Nelson-Aalen estimator yield second-order-correct confidence limits for the cumulative hazard function at a fixed lime point. An explicit formula for the correction term of the Edgeworth expansion is found. Easy-to-compute estimators for the components of the correction term are also found :ind lead to simple analytical corrections that avoid the need for resampling. Numerical results based on simulated data are given to support the theoretical results. The bootstrap is used to obtain confidence intervals for 1-year and median survival in a published Eastern Cooperative Oncology Group study of Taxol and non-small-cell lung cancer. [ABSTRACT FROM AUTHOR]

A new theory is developed for nonparametric analyses of r × k contingency tables, where the columns correspond to k ordered categories. The work is motivated by concern that conventional nonparametric theory yields inferences concerning the given categories, but results are often interpreted as if for a continuum. Asymptotic distributions are derived under random cut-points models for the Mann-Whitney (-Wilcoxon) U statistic. A model is recommended under which the exact moments of U are simple functions of k and the two sample sizes. For two more general models, the asymptotic variance is given for k ≤ 12 and k = 20, 30. Tables of empirical critical values show that the recommended model yields P values very close to P values under the general models. [ABSTRACT FROM AUTHOR]

In this article we propose some new notions of limiting P values for hypothesis testing. The limiting P value (LP) here not only provides the usual attractive interpretation of a P value as the strength in support of the null hypothesis coming from the observed data, but also has several advantages. First, it allows us to resample directly from the empirical distribution (in the bootstrap implementations), rather than from the estimated population distribution satisfying the null constraints. Second, it serves as a test statistic and as a P value simultaneously, and thus enables us to obtain test results directly without having to construct an explicit test statistic and then establish or approximate its sampling distribution. These are the two steps generally required in a standard testing procedure. Using bootstrap and the concept of data depth, we have provided LP's for a broad class of testing problems where the parameters of interest can be either finite or infinite dimensional. Some computer simulation results show the generality and the computational feasibility of our approach. [ABSTRACT FROM AUTHOR]

We present a procedure for finding simultaneous confidence intervals for the expectations μ = (μj, )jn=1 of a set of independent random variables, identically distributed up to their location parameters, that yields intervals less likely to contain zero than the standard simultaneous confidence intervals for many μ ≠ 0. The procedure is defined implicitly by inverting a nonequivariant hypothesis test with a hyperrectangular acceptance region whose orientation depends on the unsigned ranks of the components of μ, then projecting the convex hull of the resulting confidence region onto the coordinate axes. The projection to obtain simultaneous confidence intervals implicitly involves solving n! sets of linear inequalities In n variables, but the optima are attained among a set of at most n2 such sets and can be found by a simple algorithm. The procedure also works when the statistics are exchangeable but not independent and can be extended to cases where the inference is based on statistics for μ that are independent but not necessarily identically distributed, provided that there are known functions of μ that are location parameters for the statistics. In the general case, however, it appears that all n! sets of linear inequalities must be examined to find the confidence intervals. [ABSTRACT FROM AUTHOR]

Exact simultaneous one-sided confidence intervals for contrasts in normal means are discussed. The set C of contrast vectors considered is of one of two forms: Either it is a cone whose coordinates are monotone for a partial ordering defined on the coordinate index set {1,. . . , m} or it is the polar of such a cone. It is shown that the intervals obtained are inverted from test statistics that may be used for testing the null hypothesis that the mean vector μ lies in the dual (or negative polar) cone of Κ, against the alternative that μ is not in the dual of Κ. Corresponding conservative two-sided intervals are also discussed. The structure of such cones is considered and results concerning dual norms for such cones are obtained. Illustrations for simple ordering, simple-tree, and umbrella orderings are discussed. [ABSTRACT FROM AUTHOR]

In a nonrandom sample or a nonrandomized comparison of treated and control groups, methods are developed for displaying the sensitivity of confidence intervals for population quantiles to the magnitude of the departure from random selection. Quantiles of a single distribution and for a shift in two distributions are both discussed. These confidence intervals are based on a new inequality for the distribution of the number of successes in a nonrandom sample or nonrandomized comparison. The inequality has additional applications. In particular, it greatly accelerates the computations in a sensitivity analysis for the Mantel-Haenszel statistic in a 2 × 2 × S contingency table. Examples include a nonrandom collection of blood samples from a town with comparatively high levels of radon gas, an observational study of chromosome damage from mercury, and a study of the drug allopurinol as a cause of skin rash. The proof of the inequality makes use of Savage's lattice for ranks and Holley's inequality, which gives sufficient conditions for stochastic ordering in a lattice. [ABSTRACT FROM AUTHOR]

Confidence intervals for the survival function and the cumulative hazard function are considered. These confidence intervals are based on an inversion of the likelihood ratio statistic. To do this, two extensions of the likelihood, each of which yields meaningful likelihood ratio hypothesis tests and subsequent confidence intervals, are considered. The choice of the best extension is difficult. In the failure time setting, the binomial extension is best in constructing confidence intervals concerning the survival function and the Poisson extension is best in constructing confidence intervals concerning the cumulative hazard. Simulations indicate that these two methods perform as well as or better than competitors based on the asymptotic normality of the estimator. [ABSTRACT FROM AUTHOR]