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Fusion is the linking of two survey datasets by pairing up similar respondents and joining their data records, in order to be able to cross-analyse outputs from one survey with those from the other. Invariably, the two surveys are pre-existing rather than being designed specifically for the fusion, and their samples of respondents differ both in design and size. Depending on the particular method of fusion used, the size of the fused dataset may be the same as one of the surveys or different to both. An unresolved issue is: what is the effective sample size of the fused dataset -- that is, the size of a hypothetical single-source sample that would deliver equal variances and standard errors to the fusion? This paper addresses this question and provides three main findings. First, it is shown that the assumption of conditional independence, crucial for good fusion, also facilitates analysis and comparison of effective sample sizes and variances. Second, across the range of fusion methods and outputs examined, the effective sample size is shown to be a weighted geometric mean of the two source sample sizes and therefore lies between them; and for designers of fusion the simple (unweighted) geometric mean may be taken as a representative figure. Third, while limited validation of the geometric mean result has been performed so far, the generality of the conditions under which it was derived implies that it should have wide validity across different fusion methodologies. Knowledge of the effective sample size in turn provides several benefits: it is a tool for designers of fusion to deliver outputs of required precision, and a tool for users to compute the standard error of outputs; this in turn permits calculation of confidence intervals and significance tests. [ABSTRACT FROM AUTHOR]

Information for evaluating the statistical significance of stepwise regression models developed with a forward selection procedure is presented. Cumulative distributions of the adjusted coefficient of determination (R²) under the null hypothesis of no relationship between the dependent variable and m potential independent variables are derived from a Monté Carlo simulation study. The study design included sample sizes of 25, 50, and 100, available independent variables of 10, 20, and 40, and three criteria for including variables in the regression model. The results reveal that the biases involved in testing statistical significance by two well-known rules are very large, thus demonstrating the desirability of using the Monté Carlo cumulative R² distributions developed by the authors. Although the results were derived under the assumption of uncorrelated predictors, the authors show that the results continue to be useful for the correlated predictor case. [ABSTRACT FROM AUTHOR]

The ranked set sampling (RSS) method is more efficient than the commonly used simple random sampling (SRS) method. In this paper, some new goodness-of-fit tests based on the sample entropy and empirical distribution function for the Laplace distribution using ranked set sampling (RSS) are suggested. The newly suggested tests based on RSS are compared with their simple random sampling (SRS) competitors. The critical values of the corresponding test statistic are computed for each method and the powers of the tests are obtained based on different alternatives. Simulation results indicate that RSS tests are more powerful than their SRS counterparts. [ABSTRACT FROM AUTHOR]

A common situation in biology is where we have count data and wish to explore whether there is an association between two categorical variables, each with two levels (a 2 × 2 contingency table). The size of the association can be measured using the odds ratio, with a confidence interval for this measure enclosing unity suggesting no evidence of an association. However, there is no universally agreed method for calculating such a confidence interval., Here, we provide a review of some commonly used and recently suggested methods., Of all of the methods currently available, the unconditional approach based on the score statistic was consistently closest to the nominal type I error level in our investigations, and this is the method we generally recommend. This method also offers good agreement with P-values from null hypothesis testing using the method of Fisher-Boschloo., However, some scientists may prefer the recently developed minlike or Blaker methods, which offered better agreement with P-values calculated using Fisher's Exact test or Blaker's Exact test, respectively., Lastly, where calculation without use of a computer is required, we recommend the Woolf method with Haldane- Anscombe correction. [ABSTRACT FROM AUTHOR]

Power method polynomial transformations are commonly used for simulating continuous nonnormal distributions with specified moments. However, conventional moment-based estimators can (a) be substantially biased, (b) have high variance, or (c) be influenced by outliers. In view of these concerns, a characterization of power method transformations by L-moments is introduced. Specifically, systems of equations are derived for determining coefficients for specified L-moment ratios, which are associated with standard normal and standard logistic-based polynomials of order five and three. Boundaries for L-moment ratios are also derived, and closed-formed formulae are provided for determining if a power method distribution has a valid probability density function. It is demonstrated that L-moment estimators are nearly unbiased and have relatively small variance in the context of the powermethod. Examples of fitting powermethod distributions to theoretical and empirical distributions based on the method of L-moments are also provided. [ABSTRACT FROM AUTHOR]

The article discusses the study on the use of inferential confidence intervals (ICIs) to evaluate independent proportions for statistical difference, indeterminacy, equivalence, and trivial difference. It notes that the reduction factor used to adjust descriptive confidence intervals (DCIs) was corrected in order to create ICIs, along with the introduction of trivial statistical difference. Hybrid confidence intervals on ICI and DCI limits as replacements for error bars were also discussed.

This paper considers inference for parameters defined by moment inequalities and equalities. The parameters need not be identified. For a specified class of test statistics, this paper establishes the uniform asymptotic validity of subsampling, m out of n bootstrap, and "plug-in asymptotic" tests and confidence intervals for such parameters. Establishing uniform asymptotic validity is crucial in moment inequality problems because the pointwise asymptotic distributions of the test statistics of interest have discontinuities as functions of the true distribution that generates the observations. The size results are quite general because they hold without specifying the particular form of the moment conditions--only 2+δ moments finite are required. The results allow for independent and identically distributed (i.i.d.) and dependent observations and for preliminary consistent estimation of identified parameters. [ABSTRACT FROM AUTHOR]

In this paper, we use smoothed empirical likelihood methods to construct confidence intervals for hazard and density functions under right censorship. Some empirical log-likelihood ratios for the hazard and density functions are obtained and their asymptotic limits are derived. Approximate confidence intervals based on these methods are constructed. Simulation studies are used to compare the empirical likelihood methods and the normal approximation methods in terms of coverage accuracy. It is found that the empirical likelihood methods provide better inference. [ABSTRACT FROM AUTHOR]

Conventional bootstrap- t intervals for density functions based on kernel density estimators exhibit poor coverages due to failure of the bootstrap to estimate the bias correctly. The problem can be resolved by either estimating the bias explicitly or undersmoothing the kernel density estimate to undermine its bias asymptotically. The resulting bias-corrected intervals have an optimal coverage error of order arbitrarily close to second order for a sufficiently smooth density function. We investigated the effects on coverage error of both bias-corrected intervals when the nominal coverage level is calibrated by the iterated bootstrap. In either case, an asymptotic reduction of coverage error is possible provided that the bias terms are handled using an extra round of smoothed bootstrapping. Under appropriate smoothness conditions, the optimal coverage error of the iterated bootstrap- t intervals has order arbitrarily close to third order. Examples of both simulated and real data are reported to illustrate the iterated bootstrap procedures. [ABSTRACT FROM AUTHOR]

The two-stage design is popular in epidemiology studies and clinical trials due to its cost effectiveness. Typically, the first stage sample contains cheaper and possibly biased information, while the second stage validation sample consists of a subset of subjects with accurate and complete information. In this paper, we study estimation of a survival function with right-censored survival data from a two-stage design. A non-parametric estimator is derived by combining data from both stages. We also study its large sample properties and derive pointwise and simultaneous confidence intervals for the survival function. The proposed estimator effectively reduces the variance and finite-sample bias of the Kaplan–Meier estimator solely based on the second stage validation sample. Finally, we apply our method to a real data set from a medical device postmarketing surveillance study. [ABSTRACT FROM AUTHOR]

Data that are skewed and contain a relatively high proportion of zeros can often be modelled using a delta-lognormal distribution. We consider three methods of calculating a 95% confidence interval for the mean of this distribution, and use simulation to compare the methods, across a range of realistic scenarios. The best method, in terms of coverage, is that based on the profile-likelihood. This gives error rates that are within 1% (lower limit) or 3% (upper limit) of the nominal level, unless the sample size is small and the level of skewness is moderate to high. Our results will also apply to the delta-lognormal linear model, when we wish to calculate a confidence interval for the expected value of the response variable, given the value of one or more explanatory variables. We illustrate the three methods using data on red cod densities, taken from a fisheries trawl survey in New Zealand. [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]

Much research has been devoted to modelling strategies for longitudinal data with missingness, recently especially within the missingness not at random context. In this paper, the relatively unexplored but practically highly relevant domain of non-monotone missingness with multivariate ordinal responses is broached. For this, a dedicated version of the multivariate Dale model is formulated. Furthermore, we also assess the sensitivity of these models to their assumptions, by using the technique of global influence. [ABSTRACT FROM AUTHOR]

For sample sizes from 5 to 100, the bias of the scale parameter was investigated for probability estimators, P = ( i − a)/( n + b), which yield unbiased estimates of the shape parameter. A class of unbiased estimators for both the shape and scale parameters was developed for each sample size. In addition, the percentage points of the distribution of unbiased estimate of the shape parameter were determined for all sample sizes. The distribution of the scale parameter was found to be normal by using the Anderson-Darling goodness-of-fit test. How the results can be used to establish confidence intervals on both the shape and scale parameters are demonstrated in the paper. [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]

The article focuses on correcting a significance test for clustering. Neglecting the effect of clustering and analyzing the data as if each treatment group were a simple random sample are common mistakes in the analysis of cluster randomized trials. These mistakes may in turn lead to an overstatement of the accuracy of results and anticonservative suppositions regarding precision and statistical importance of treatment effects. The article offers a correction to the t statistic that would be calculated if clustering were incorrectly ignored. The correction made is a multiplicative factor that depends on the total sample size, cluster size and intraclass correlation ρ.

In experiments involving many variables, investigators typically use multiple comparisons procedures to determine differences that are unlikely to be the result of chance. However, investigators rarely consider how the magnitude of the greatest observed effect sizes may have been subject to bias resulting from multiple testing. These questions of bias become important to the extent investigators focus on the magnitude of the observed effects. As an example, such bias can lead to problems in attempting to validate results, if a biased effect size is used to power a follow-up study. An associated important consequence is that confidence intervals constructed using standard distributions may be badly biased. A bootstrap approach is used to estimate and adjust for the bias in the effect sizes of those variables showing strongest differences. This bias is not always present; some principles showing what factors may lead to greater bias are given and a proof of the convergence of the bootstrap distribution is provided. [ABSTRACT FROM AUTHOR]

Complex-valued Gaussian distributions occur frequently in signal processing. We derive a simple statistic, independent of any complex-valued correlation, for testing for the equality of variances using a sample drawn from such a bivariate distribution. The percentage points of the distribution are easy to compute. The power of the test is determined and shown to be high even for very small sample sizes when the variables are highly correlated. The new test is used to determine whether the spectral power associated with an ultralow-frequency wave in the solar magnetic field is equal at two different observing spacecraft. [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 this paper we present a survey of recent progress on the distribution of B-free numbers in short intervals and some of its applications. [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]

Background & Aims: The aim of this study was to evaluate the usefulness of short-term infliximab combined with azathioprine (AZA) or 6-mercaptopurine (6-MP) in steroid-dependent Crohn’s disease patients. Methods: Patients with active disease despite prednisone given for more than 6 months were eligible and were stratified as follows: the failure stratum consisted of patients receiving AZA/6-MP at a stable dose for more than 6 months, and the naive stratum consisted of patients not treated previously with AZA/6-MP. Patients were randomized to infliximab 5 mg/kg or placebo at weeks 0, 2, and 6. All patients were treated with AZA/6-MP maintained at a stable dose throughout the 52 weeks of the study. The primary end point was remission off steroids at week 24. Results: Among the 113 enrolled patients (55 in the failure stratum), 57 were assigned to infliximab. At week 24, the success rate (intent-to-treat analysis) was higher in the infliximab group than in the placebo group (57% vs 29%; P = .003); at weeks 12 and 52, the corresponding rates were 75% vs 38% (P < .001) and 40% vs 22% (P = .04), respectively. In each stratum, the success rate was significantly higher in the infliximab group at weeks 12 and 24, and a trend was found at week 52. In the failure stratum, only 27% of the patients in the infliximab group were still in remission off steroids, compared with 52% in the naive stratum. Steroid resistance was less common and the cumulative dose of prednisone was lower in the infliximab group. Conclusions: Infliximab plus AZA/6-MP is more effective than AZA/6-MP alone in steroid-dependent Crohn’s disease patients. [Copyright &y& Elsevier]

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]

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]

This article extends recent results [Scand. J. Statist. 28 (2001) 699] about exact non-parametric inferences based on order statistics with progressive type-II censoring. The extension lies in that non-parametric inferences are now covered where the dependence between involved order statistics cannot be circumvented. These inferences include: (a) tolerance intervals containing at least a specified proportion of the parent distribution, (b) prediction intervals containing at least a specified number of observations in a future sample, and (c) outer and/or inner confidence intervals for a quantile interval of the parent distribution. The inferences are valid for any parent distribution with continuous distribution function. The key result shows how the probability of an event involving k dependent order statistics that are observable/uncensored with progressive type-II censoring can be represented as a mixture with known weights of corresponding probabilities involving k dependent ordinary order statistics. Further applications/developments concerning exact Kolmogorov-type confidence regions are indicated. [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]

Normal theory procedures for calculating upper confidence limits (UCL) on the risk function for continuous responses work well when the data come from a normal distribution. However, if the data come from an alternative distribution, the application of the normal theory procedures may lead serious over- or under-coverage depending upon the alternative distribution. In this paper we conduct simulation studies to investigate the sensitivity of three normal theory UCL procedures to departures from normality. Data from several gamma, reciprocal gamma, and lognormal distributions are considered. The normal theory procedures are applied to both the raw data and the log-transformed data. [ABSTRACT FROM AUTHOR]

In this paper, a goodness-of-fit test for the latent class model is presented. The test uses only the limited information in the second-order marginal distributions from a set of k dichotomous variables, and it is intended for use when k is large and the sample size, n, is moderate or small. In that situation, a 2[sup k] contingency table formed by the full cross-classification of k variables will be sparse in the sense that a high proportion of cell frequencies will be equal to zero or 1, and the chi-square approximation for traditional goodness-of-fit statistics such as the likelihood ratio will not be valid. The second-order marginal frequencies, which correspond to the bivariate distributions, are rarely sparse even when the joint frequencies have a high proportion of zero cells. Results from Monte Carlo experiments are presented that compare the rates of Type I and Type II errors for the proposed test to the rates for traditional goodness-of-fit tests. Results show that under commonly encountered conditions, a test of fit based on the limited information in the second-order marginals has a Type II error rate that is no higher than the error rate found for full-information test statistics, and that the test statistic given in this paper does not suffer from ill effects of sparseness in the joint frequencies. [ABSTRACT FROM AUTHOR]

Dans cet article on considère le probleme de comparer et de tester des relations d'ordre entre des fonctions de percentiles liées aux durées de vie résiduelles. On introduit des représentations du type R-R et on développe une approche générate pour ce problème. [ABSTRACT FROM AUTHOR]

Cet article s'applique à ľanalyse de données de dénombrement résultant de phénomènes de jumelage. Les paires formées par le jumelage ďé1éments 'semblables' sont cependant exclues. Plusieurs modèles sont proposés et analysés. On s'attache surtout à développer des méthodes aptes à déceler les paires qui se manifestent plus (ou moins) souvent que ne le voudrait le hasard. [ABSTRACT FROM AUTHOR]

The article presents a study that deals with a distribution theory for likelihood-ratio statistics for the comparison of several treatments with a control. The study assumes that the sample sizes on the treatments are equal while the sample size on the control as large. It presents the results of a study comparing a one-sided t-test, the likelihood-ratio test, and Dunnett's one-sided test.

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 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]

Johnson proposed some modified t tests to assess the mean of asymmetrical distributions. The tests were suggested for any parent distribution ranging from the normal to a distribution as asymmetric as an exponential distribution for sample sizes as small as 13. In many practical situations the skewness of the parent distribution can be greater than those studied by Johnson and the sample sizes can be quite small, possibly as small as 10, due to the cost of the sampling procedures. In these cases Johnson's test can be quite inaccurate. Sutton suggested a composite test to improve Johnson's upper-tailed t test. In this article a new test procedure is proposed for the upper-tailed test for the mean of positively skewed distributions, which requires only a little more effort than Johnson's test. A Monte Carlo study investigates the new procedure's properties for a variety of positively skewed distributions with small sample sizes. It is shown that the new test procedure is more accurate and more powerful than both Johnson's modified t test and Sutton's composite test. [ABSTRACT FROM AUTHOR]

We propose a new method for constructing parametric confidence intervals for quantiles of an unknown distribution. These confidence intervals are constructed so that the joint probability that all intervals simultaneously contain their respective percentiles is at least a preset value. Thus we may also use the set of either upper or lower confidence limits to define an upper (or lower) bound distribution function, which we call an upper (or lower) tolerance distribution because this distribution may also be used to construct tolerance intervals for the unknown distribution. We derive tolerance distributions with exact coverage probability for iid samples from distributions in the location-scale family. Tolerance distributions can also be used for best- and worst-case analyses, as we illustrate by considering bounds on the distribution of the time interval between the onset of infectiousness and development of detectable antibody in individuals newly infected with the human immunodeficiency virus (HIV), the virus that causes acquired immune deficiency syndrome (AIDS). [ABSTRACT FROM AUTHOR]

We analyze the choice of the truncation lag in the context of the Said-Dickey test for the presence of a unit root in a general autoregressive moving average model. It is shown that a deterministic relationship between the truncation lag and the sample size is dominated by data-dependent rules that take sample information into account. In particular, we study data-dependent rules that are not constrained to satisfy the lower bound condition imposed by Said-Dickey. Akaike's information criterion falls into this category. The analytical properties of the truncation lag selected according to a class of information criteria are compared to those based on sequential testing for the significance of coefficients on additional lags. The asymptotic properties of the unit root test under various methods for selecting the truncation lag are analyzed, and simulations arc used to show their distinctive behavior in finite samples. Our results favor methods based on sequential tests over those based on information criteria, because the former show less size distortions and have comparable power. [ABSTRACT FROM AUTHOR]

This article introduces a resampling procedure called the stationary bootstrap as a means of calculating standard errors of estimators and constructing confidence regions for parameters based on weakly dependent stationary observations Previously, a technique based on resampling blocks of consecutive observations was introduced to construct confidence intervals for a parameter of the in-dimensional joint distribution of in consecutive observations where in is fixed This procedure has been generalized by constructing a "blocks of blocks" resampling scheme that yields asymptotically valid procedures even for a multivariate parameter of the whole (i.e., infinite-dimensional) joint distribution of the stationary sequence of observations These methods share the construction of resampling blocks of observations to form a pseudo-time series, so that the statistic of interest may be recalculated based on the resampled data set But in the context of applying the method to stationary data, it is natural to require the resampled pseudo-time series to be stationary (conditional on the original data) as well Although the aforementioned procedures lack this property, the stationary procedure developed here is indeed stationary and possesses other desirable properties The stationary procedure is based on resampling blocks of random length. where the length of each block its a geometric distribution In this article, fundamental consistency and weak convergence properties of the stationary resampling scheme are developed. [ABSTRACT FROM AUTHOR]

We study bootstrap confidence intervals for three types of parameters in Cox's proportional hazards model: the regression parameter, the survival function at fixed time points, and the median survival time at fixed values of a covariate. Several types of bootstrap confidence intervals are studied, and the type of interval is determined by two factors. One factor is the method of drawing the bootstrap sample. We consider three such methods: (1) ordinary resampling from the empirical cumulative distribution function, (2) resampling conditional on the covariates, and (3) resampling conditional on the covariates and the censoring pattern. Another factor is the method of forming the confidence interval from a given sample; the methods considered are the percentile, hybrid, and bootstrap-t. All the methods of forming confidence intervals are compared to each other and to the standard asymptotic method via a Monte Carlo study. The data sets for this Monte Carlo study are simulated conditionally on the covariates and the censoring pattern, the situation appropriate for the third method of resampling. One conclusion drawn from the Monte Carlo study is that the asymptotic method is best for the regression parameter, but not for the survival function or the median survival time. Conclusions about the bootstrap methods include the surprising result that, overall, the second method of drawing the samples outperforms the third method. Also, there is an interaction effect between the two factors, method of drawing the sample and method of forming the interval, especially for estimation of the regression parameter. Finally, the bootstrap-t intervals are consistently outperformed by at least one of the two more rudimentary types of bootstrap interval. [ABSTRACT FROM AUTHOR]

Clearly, Efron's article has been stimulating for me, as I am sure it will be for JASA's readers, and I look forward to his responses to my five major points. First, the distinction between valid estimates of variability of intervals and valid confidence intervals for well-defined estimates is critically important, and I firmly believe that valid confidence intervals should continue to be defined to require consistency for a well-defined scientific estimate. Second, if the operating characteristics of a procedure, whether derived using Bayesian distributions or nonparametric reasoning, vary critically with distributional settings, such as the true missing-data mechanism, then the procedure cannot be said to be "distribution free." Third, imputers and users of data bases often have different responsibilities and capabilities, and methods appropriate for a single analyst might not be appropriate with shared data bases. Fourth, critical assumptions used to create imputations should not be hidden but rather should be explicitly stated and communicated. And fifth, multiple imputation is neither logically nor historically an outgrowth of either EM or data augmentation. I hope my discussion of these issues is stimulating for Efron and JASA's readers and look forward to further commentary. [ABSTRACT FROM AUTHOR]

This article discusses importance sampling as an alternative to conventional Monte Carlo sampling for estimating exact significance levels in a broad class of two-sample tests, including all of the linear rank tests (with or without censoring), homogeneity tests based on the chi-squared, hypergeometric, and likelihood ratio statistics, the Mantel-Haenszel trend test, and Zelen's test for a common odds ratio in several 2 x 2 contingency tables. Inference is based on randomly selecting 2 x k contingency tables from a reference set of all such tables with fixed marginals. Through a network algorithm, the tables are selected in proportion to their importance for reducing the variance of the estimated Monte Carlo p-value. Spectacular gains, up to four orders of magnitude, are achieved relative to conventional Monte Carlo sampling. The technique is illustrated on four real data sets. [ABSTRACT FROM AUTHOR]

When applied to frequency tables with small expected cell counts, Pearson chi-squared test statistics may be asymptotically inconsistent even in cases in which a satisfactory chi-squared approximation exists for the distribution under the null hypothesis. This problem is particularly important in cases in which the number of cells is large and the expected cell counts are quite variable. To illustrate this bias of the chi-squared test, this article considers the Pearson chi-squared test of the hypothesis that the cell probabilities for a multinomial frequency table have specified values. In this case, the expected value and variance of the Pearson chi-square may be evaluated under both the null and alternative hypotheses. When the number of cells is large, normal approximations and discrete Edgeworth expansions may also be used to assess the size and power of the Pearson chi-squared test. These analyses show that unless all cell probabilities are equal, it is possible to select a significance level and cell probabilities under the alternative hypothesis such that the power is less than the size of the test. As shown by exact calculations, the difference may be substantial even in cases in which all expected cell sizes are at least 5 under the null hypothesis. The use of moments shows that given any minimum expected cell size under the null hypothesis and given any significance level, it is possible to make the power arbitrarily close to 0 by the selection of a large enough number of cells in the table and suitable cell probabilities for the null and alternative hypotheses. The normal approximations for the distribution of the Pearson chi-squared statistic permit the size of this bias to be assessed in.. [ABSTRACT FROM AUTHOR]

A problem frequently encountered in the practice of statistics is the comparison of several treatments with a control or standard. We consider an experimental situation where prior knowledge indicates that all of the treatments are at least as effective as the control and the problem is to determine if any are significantly better than the control. A number of statistical procedures have been proposed for this situation, of which the best known is Dunnett's (1955) multiple comparison procedure. Dunnett's test rejects equality of the treatments and the control for a large value of the maximum contrast of the data vector with several vectors that are located "symmetrically" within the alternative region. We study a large class of such tests, which includes Dunnett's test as a particular case. One of these tests, which is based on the maximum contrast of the data vector with several orthogonal vectors, is very easy to implement and has an uncomplicated, good, and fairly uniform power function over the entire alternative region. In fact, a small Monte Carlo power study suggests that this orthogonal contrast test is approximately "maximin" within this class of tests. Moreover, the simplicity of the power function of the orthogonal contrast test enables the experimenter to determine sample sizes for designed experiments with specific power characteristics. Such sample size determinations can be difficult, if not impossible, using other procedures. Abelson and Tukey (1963) suggested tests for a large class of restricted problems that are based on contrasts of the data vector with a single vector that is "centrally" located within the alternative region. These single contrast tests have the advantage that their distributions under the null hypotheses (a t distribution) and under the alternative (a... [ABSTRACT FROM AUTHOR]

Opinion polls often give an indication of sampling error based on the standard conservative confidence intervals for a single binomial proportion. We give a lower bound for the simultaneous coverage probability when such intervals are applied to all of the proportions in a poll. This bound is equal to 1 - 2 alpha for small values of a. The same result is shown to apply to the standard confidence intervals for changes in proportions between surveys. [ABSTRACT FROM AUTHOR]

In the two-sample problem under random censorship we consider the uncensored observations and the censored ones as two separate groups. For each group a suitable rank statistic is obtained, and these two are then combined to a final one. This idea, which was first employed in Akritas (1983), is shown here to produce tests that (a) closely resemble the ordinary rank tests for the uncensored case and do not require the calculation of the Kaplan-Meier estimator, (b) are comparatively easy to apply and to understand, and (c) allow results on asymptotic normality to follow simply from standard results for the uncensored case. It is shown that the loss due to using two separate rankings rather than one complete ranking is asymptotically negligible. The optimal score function for each of the two separate rank statistics is seen to depend on the censoring distribution. Whereas in Akritas (1983) no assumption on the form of the censoring distribution was made (unrestricted adaptation), here we pursue restricted adaptation that results in simple score functions. In particular, motivated by the model of Koziol and Green (1976), we assume that the censoring distribution is a suitable function of the survival distribution. An example related to the Wilcoxon test is used for illustration. The effect of restricted adaptation on the efficiency of the test is examined by both exact efficiency calculations and simulation results. [ABSTRACT FROM AUTHOR]

The techniques of exploratory data analysis include a resistant rule for identifying possible outliers in univariate data. Using the lower and upper fourths, F[sub L] and F[sub U] (approximate quartiles), it labels as "outside" any observations below F[sub L] - 1.5(F[sub U] - F[sub L]) or above F[sub U] + 1.5( F[sub U] - F[sub L]). For example, in the ordered sample -5, -2, 0, l, 8, F[sub L] = -2 and F[sub U] = 1, so any observation below -6.5 or above 5.5 is outside. Thus the rule labels 8 as outside. Some related rules also use cutoffs of the form F[sub L] -k(F[sub U] - F[sub L]) and F[sub U] + k(F[sub U] - F[sub L]). This approach avoids the need to specify the number of possible outliers in advance; as long as they are not too numerous, any outliers do not affect the location of the cutoffs. To describe the performance of these rules, we define the some-outside rate per sample as the probability that a sample will contain one or more outside observations. Its complement is the all-inside rate per sample. We also define the outside rate per observation as the average fraction of outside observations. For Gaussian data the population all-inside rate per sample (0) and the population outside rate per observation (.7%) substantially understate the corresponding small-sample values. Simulation studies using Gaussian samples with n between 5 and 300 yield detailed information on the resistant rules. The main resistant rule (k = 1.5) has an all-inside rate per sample between 67% and 86% for 5 less than or equal to n less than or equal to 20, and corresponding estimates of its outside rate per observation range from 8.6% to 1.7%. Both characteristics vary with n in ways that lead to good empirical approximations. Because of the way in which the fourths are defined, the sample sizes separate into four classes, according to whether dividing n by 4 leaves a remainder of 0, 1, 2, or 3. Within these... [ABSTRACT FROM AUTHOR]

For samples of equal size, the p values of Bartlett's, Cochran's, and Hartley's tests for the equality of several variances, obtained under the normality assumption, are shown to underestimate the true p values when the parent distribution is a normal or a chi[sup 2] scale mixture or when there is within-sample dependence. The proof uses elements of majorization theory. When the sample sizes are not equal, a partial extension is obtained for the two-sample case. [ABSTRACT FROM AUTHOR]