approximate tolerance limits for zipf mandelbrot distributions abstract zipf mandelbrot distributions are commonly used to model natural phenomena where the frequency of an event s occurrence is inversely proportional to its rank based on that frequency of occurrence this discrete distribution typically exhibits a large number of rare events however it may be of interest to obtain reasonable limits that bound the majority of the number of different events we propose the use of statistical tolerance limits as a way to quantify such a bound the tolerance limits are constructed using wald confidence limits for the zipf mandelbrot parameters and are shown through a simulation study to have coverage probabilities near the nominal levels we also calculate zipf mandelbrot tolerance limits for two real datasets and discuss the associated computer code developed for the r programming language

on the removal of skewness by transformation summary we suggest empirical transformations for removing most of the skewness of an asymmetric statistic these transformations may be used as the basis for accurate confidence procedures or hypothesis tests and can be employed in conjunction with either a normal approximation or the bootstrap our approach differs from those of other researchers in that the transformation is monotone and invertible in this paper we suggest elementary but general transformations for eliminating skewness from the distribution of a studentized statistic the transformations are monotone and have simple explicit inversion formulae and so are readily applied to confidence interval problems when the transformations are used in conjunction with the bootstrap they can produce confidence intervals with particularly low levels of coverage error that confidence intervals for symmetric statistics have lower coverage error than their counterparts in the case of asymmetry may be deduced from edgeworth expansions the first term in an expansion of size n 1 2 where n is the sample size describes the error in the usual normal approximation and is due entirely to skewness if it can be eliminated for example by transformation then the normal approxima tion will be in error by only o n 1 thus our method involves transforming one statistic into another where the distribution is virtually symmetric applying the normal approximation or the bootstrap to the new statistic and then regaining the asymmetry of the original problem by inverse transformation at the same time retain ing the high coverage accuracy conferred by applying confidence interval procedures to a symmetric statistic

lusin s theorem on fuzzy measure spaces in this paper we show that weakly null additive fuzzy measures on metric spaces possess regularity lusin s theorem which is well known in classical measure theory is generalized to fuzzy measure space by using the regularity and weakly null additivity a version of egoroff s theorem for the fuzzy measure defined on metric spaces is given an application of lusin s theorem to approximation in the mean of measurable function on fuzzy measure spaces is presented

the alexandroff theorem for riesz space valued non additive measures the alexandroff theorem for a compact non additive measure with values in a riesz space is still valid for the following two cases one is the case that the measure is autocontinuous and the riesz space has the weak asymptotic egoroff property and the other is the case that the measure is uniformly autocontinuous and the riesz space is weakly distributive a close connection between regularity and continuity of non additive measures is also given

confidence intervals for the 50 per cent response dose confidence intervals for the 50 per cent response dose are usually computed using either the delta method or fieller s procedure recently confidence intervals computed by inverting the asymptotic likelihood ratio test have also been recommended there is some controversy as to which of these methods should be used by means of an extensive simulation study we examine these methods as well as confidence intervals obtained by the approximate bootstrap confidence abc procedure and an adjusted form of the likelihood ratio based confidence intervals

improved pivotal methods for constructing confidence regions with directional data abstract the importance of pivoting is well established in the context of nonparametric confidence regions it ensures enhanced coverage accuracy however pivoting for directional data cannot be achieved simply by rescaling a somewhat cumbersome pivotal method which involves passing first into a space of higher dimension has been developed by fisher and hall for samples of unit vectors although that method has some advantages over nonpivotal techniques it does suffer from certain drawbacks in particular the operation of passing to a higher dimension here we suggest alternative pivotal approaches the implementation of which does not require us to increase the intrinsic dimension of the data and which in practice seem to achieve greater coverage accuracy these methods are of two types new pivotal bootstrap techniques and techniques that exploit the implicit pivotalness of the empirical likelihood algorithm unlike the method proposed by fisher and hall these methods are also applicable to axia

on lusin s theorem for non additive measures that take values in an ordered topological vector space abstract lusin s theorem was established for real valued monotone measures under an equivalent condition to egoroff s theorem recently in this paper we show that the same result remains valid for non additive measures that take values in an ordered topological vector space we apply our result to several ordered topological vector spaces

some asymptotic theory for the bootstrap efron s bootstrap method of distribution approximation is shown to be asymptotically valid in a large number of situations including t statistics the empirical and quantile processes and von mises functionals some counter examples are also given to show that the approximation does not always succeed

estimating mean concentrations under transformation for environmental data with detection limits the reporting procedures for potentially toxic pollutants are complicated by the fact that concentrations are measured using small samples that include a number of observations lying below some detection limit furthermore there is often a small number of high concentrations observed in combination with a substantial number of low concentrations this results in small nonnormally distributed censored samples this article presents maximum likelihood estimators for the mean of a population based on censored samples that can be transformed to normality the method estimates the optimal power transformation in the box cox family by searching the censored data likelihood maximum likelihood estimators for the mean in the transformed scale are calculated via the expectation maximization algorithm estimates for the mean in the original scale are functions of the estimated mean and variance in the transformed population confidence intervals are computed using the delta method and the nonparametric percentil

prediction and tolerance intervals with transformation and or weighting we consider estimation of quantiles and construction of prediction and tolerance intervals for a new response following a possibly nonlinear regression fit with transformation and or weighting we consider the case of normally distributed errors and to a lesser extent the nonparametric case in which the error distribution is unknown quantile estimation here follows standard theory although we introduce a simple computational device for likelihood ratio testing and confidence intervals prediction and tolerance intervals are somewhat more difficult to obtain we show that the effect of estimating parameters when constructing tolerance intervals can be expected to be greater than the effect in the prediction problem improved prediction and tolerance intervals are constructed based on resampling techniques in the tolerance interval case a simple analytical correction is introduced we apply these methods to the prediction of automobile stopping distances and salmon production using respectively a he

improvements of jackknife confidence limit methods summary edgeworth expansion is applied to studentized parameter estimates when the standard error has been computed by a jackknife method adjustments to the usual jackknife confidence limit formulae are obtained this approach is contrasted with a bootstrap approach in numerical illustrations for estimation of a ratio jackknife methods are nonparametric methods for estimating the bias and standard error of an estimate t approximate confidence limits for the estimand can be found by using a large sample normal approximation for t somewhat curiously little is known about possible improvements to the normal approximation in this context although improvements based on edgeworth expansions are familiar in other problems in this paper we show that edgeworth expansion methods can be applied in the jackknife context numerical results for a particular application raise the possibility that the resulting improvements of jackknife methods can be matched by a suitable use of bootstrap methods efron 1982

on a sufficient condition of lusin s theorem for non additive measures that take values in an ordered topological vector space classical lusin s theorem is extended for real valued fuzzy measures under the weak null additivity condition recently in this paper we show similar results for non additive measures that take values in an ordered topological vector space firstly we prove lusin type theorem for weakly null additive borel measures that are continuous from above and possess an additional continuity property suggested by sun in 1994 secondly we state another one for weakly null additive fuzzy borel measures our results are applicable to several ordered topological vector spaces

a weighted bootstrap approach to bootstrap iteration the operation of resampling from a bootstrap resample encountered in applications of the double bootstrap may be viewed as resampling directly from the sample but using probability weights that are proportional to the numbers of times that sample values appear in the resample this suggests an approximate approach to double bootstrap monte carlo simulation where weighted bootstrap methods are used to circumvent much of the labour involved in compounded monte carlo approximation in the case of distribution estimation or equivalently confidence interval calibration the new method may be used to reduce the computational labour moreover the method produces the same order of magnitude of coverage error for confidence intervals or level error for hypothesis tests as a full application of the double bootstrap

subsampling for heteroskedastic time series abstract in this article a general theory for the construction of confidence intervals or regions in the context of heteroskedastic dependent data is presented the basic idea is to approximate the sampling distribution of a statistic based on the values of the statistic computed over smaller subsets of the data this method was first proposed by politis and romano 1994b for stationary observations we extend their results to heteroskedastic observations and prove a general asymptotic validity result under minimal conditions in contrast the usual bootstrap and moving blocks bootstrap are typically valid only for asymptotically linear statistics and their justification requires a case by case analysis our general asymptotic results are applied to a regression setting with dependent heteroskedastic errors

on egoroff s theorems on fuzzy measure spaces in this paper we show that egoroff s theorem which is well known in classical measure theory remains valid for a fuzzy measure without any additional condition previous results obtained by wang zhenyuan and others are improved egoroff s theorem on fuzzy measure spaces is formulated in full generality taylor s theorem which concerns convergence almost everywhere in classical measure theory is also extended to fuzzy measure spaces

continuity and compactness of the indirect product of two non additive measures let x and y be non empty sets e a field of subsets of x and f a field of subsets of y then every uniformly autocontinuous indirect product of two non additive measures m on e and n on f is continuous on the product field generated by e and f whenever m is continuous and n is compact a similar result holds for the compactness of indirect product measures

regularity and lusin s theorem for riesz space valued fuzzy measures a smoothness condition the multiple egoroff property is introduced and imposed on a riesz space to show that every weakly null additive riesz space valued fuzzy borel measure on any metric space is regular it is also proved that lusin s theorem remains valid for such riesz space valued non additive measures

convergence theorems for monotone measures in classical measure theory there are a number of convergence theorems such as the egorov the riesz and the lusin theorem among others we consider monotone measures i e monotone set functions vanishing in the empty set and defined on a measurable space and discuss how and to which extent classical convergence theorems can be carried over to this more general case

fixed b subsampling and the block bootstrap improved confidence sets based on p value calibration summary subsampling and block based bootstrap methods have been used in a wide range of inference problems for time series to accommodate the dependence these resampling methods involve a bandwidth parameter such as the subsampling window width and block size in the block based bootstrap in empirical work using different bandwidth parameters could lead to different inference results but traditional first order asymptotic theory does not capture the choice of the bandwidth we propose to adopt the fixed b approach as advocated by kiefer and vogelsang in the heteroscedasticity auto correlation robust testing context to account for the influence of the bandwidth on inference under the fixed b asymptotic framework we derive the asymptotic null distribution of the p values for subsampling and the moving block bootstrap and further propose a calibration of the traditional small b based confidence intervals regions or bands and tests our treatment is fairly general as it includes both finite dimensional parameters and infinite dimensional parameters such as the marginal distribution function simulation results show that the fixed b approach is more accurate than the traditional small b approach in terms of approximating the finite sample distribution and that the calibrated confidence sets tend to have smaller coverage errors than the uncalibrated counterparts

improvements on stability analysis and stabilisation of constant and variable gain second order sliding mode algorithms via exact convex representations a novel lyapunov based methodology for both stability analysis and stabilisation of second order sliding mode algorithms in the presence of exogenous disturbances is presented nowadays second ord

regularity and autocontinuity of set multifunctions in this paper we study different types of regularity for monotone uniformly autocontinuous set multifunctions defined on a ring of subsets of a locally compact hausdorff space t and taking values in the family of closed nonvoid sets of a real normed space x

asymptotic iterated bootstrap confidence intervals an iterated bootstrap confidence interval requires an additive correction to be made to the nominal coverage level of an uncorrected interval such correction is usually performed using a computationally intensive monte carlo simulation involving two nested levels of bootstrap sampling asymptotic expansions of the required correction and the iterated interval endpoints are used to provide two new computationally efficient methods for constructing an approximation to the iterated bootstrap confidence interval the first asymptotic interval replaces the need for a second level of bootstrap sampling with a series of preliminary analytic calculations which are readily automated and from which an approximation to the coverage correction is easily obtained the second interval directly approximates the endpoints of the iterated interval and yields for the first time the possibility of constructing an approximation to an iterated bootstrap confidence interval which does not require any resampling the theoretical properties of the two intervals are considered the computation required for their construction is detailed and has been coded in a fully automatic user friendly fortran program which may be obtained by anonymous ftp a simulation study which illustrates their effectiveness on three examples is presented

calibrating confidence coefficients abstract two approaches for dealing with the problem of poor coverage probabilities of certain standard confidence intervals are proposed the first is a recommendation that the actual coverage be estimated directly from the data and its value reported in addition to the nominal level this is achieved through a combination of computer simulation and density estimation the asymptotic validity of the procedure is proved for a number of common situations a classical example is the nonparametric estimation of the variance of a population using the normal theory interval here it is shown that the estimated coverage probability consistently estimates the true coverage probability if the population distribution possesses a finite sixth moment the second approach is more traditional it is a procedure for modifying an interval to yield improved coverage properties given a confidence interval its estimated coverage probability obtained in the first approach is used to alter the nominal level of the interval

lusin s theorem on monotone measure spaces in this paper a kind of regularity of monotone measures is shown by using the pseudometric generating property of set function for short p g p and an equivalence condition for egoroff s theorem lusin s theorem which is well known in classical measure theory is generalized to monotone measure spaces the continuity from above and below of set functions is not required in the discussions therefore the previous results obtained by jiang et al are generalized an approximation of measurable functions by continuous functions on monotone measure spaces is presented

pseudo atoms and darboux property for set multifunctions in this paper we introduce and study the concepts of pseudo atom and darboux property for set multifunctions we establish relationships between the darboux property and non atomicity in the multivalued case we also prove that the range of a multimeasure having the darboux property is a convex set

conditions for egoroff s theorem in non additive measure theory abstract this paper gives necessary and or sufficient conditions for egoroff s theorem in non additive measure theory a necessary and sufficient condition described without measurable functions two sufficient conditions and a necessary condition one of the two sufficient conditions is strong order total continuity continuity at measurable sets of measure zero with respect to net convergence and the other is strong order continuity sequential continuity at measurable sets of measure zero together with property s the necessary condition is strong order continuity in addition the paper shows the following continuity from above and below which is a known sufficient condition and the above mentioned two sufficient conditions are independent of each other the disjunction of these three sufficient conditions is not a necessary condition if the underlying set is at most countable then strong order continuity is necessary and sufficient and generally strong order continuity is not sufficient

on egoroff s theorems on finite monotone non additive measure space in this note we give four versions of egoroff s theorem in non additive measure theory by using condition e the pseudo condition e of set function and the duality relations between the conditions these conditions offered are not only sufficient but also necessary for the four kinds of egoroff s theorems

a lusin type theorem for regular monotone uniformly autocontinuous set multifunctions in this paper we continue our study concerning monotone uniformly autocontinuous regular set multifunctions as an application a lusin type theorem under a suitable type of measurability is obtained and several applications for finitely purely atomic multisubmeasures are proved

lusin s theorem for monotone set valued measures on topological spaces abstract on a topological space the inner regularity outer regularity and regularity of a monotone set valued measure are considered their properties are discussed based on these the versions of egoroff s theorem and lusin s theorem for monotone set valued measures on a topological space are shown respectively

a bootstrap causality test for covariance stationary processes abstract this paper examines a nonparametric test for granger causality for a vector covariance stationary linear process under possibly the presence of long range dependence we show that the test converges to a nondistribution free multivariate gaussian process say vec b indexed by 0 1 because contrary to the scalar situation it is not possible except in very specific cases to find a time transformation g such that vec b g is a vector with independent brownian motion components it implies that inferences based on vec b will be difficult to implement to circumvent this problem we propose to bootstrapping the test by two alternative although similar algorithms showing their validity and consistency

regularities of riesz space valued non additive measures with applications to convergence theorems for choquet integrals a deeper investigation of radonness and t smoothness properties of riesz space valued borel non additive measures is carried out to this end due to a lack of e argument in a riesz space the multiple egoroff property is introduced and enforced on the involved riesz space the established regularity properties of borel non additive measures are instrumental when formulating certain types of monotone convergence theorems for choquet integrals

prediction intervals for overdispersed binomial data with application to historical controls bioassays are highly standardized trials for assessing the impact of a chemical compound on a model organism in that context it is standard to compare several treatment groups with an untreated control if the same type of bioassay is carried out several times the amount of information about the historical controls rises with every new study this information can be applied to predict the outcome of one future control using a prediction interval since the observations are counts of success out of a given sample size like mortality or histopathological findings the data can be assumed to be binomial but may exhibit overdispersion caused by the variability between historical studies we describe two approaches that account for overdispersion asymptotic prediction intervals using the quasi binomial assumption and prediction intervals based on the quantiles of the beta binomial distribution both interval types were calibrated using bootstrap methods for an assessment of the intervals coverage probabilities a simulation study based on various numbers of historical studies and sample sizes as well as different binomial proportions and varying levels of overdispersion was run it could be shown that calibration can improve the coverage probabilities of both interval types the coverage probability of the calibrated intervals calculated based on at least 10 historical studies was satisfactory close to the nominal 95 in a last step the intervals were computed based on a real data set from the ntp homepage using historical controls from bioassays with the mice strain b6c3f1

identification of subgroups with differential treatment effects for longitudinal and multiresponse variables we describe and evaluate a regression tree algorithm for finding subgroups with differential treatments effects in randomized trials with multivariate outcomes the data may contain missing values in the outcomes and covariates and the treatment variable is not limited to two levels simulation results show that the regression tree models have unbiased variable selection and the estimates of subgroup treatment effects are approximately unbiased a bootstrap calibration technique is proposed for constructing confidence intervals for the treatment effects the method is illustrated with data from a longitudinal study comparing two diabetes drugs and a mammography screening trial comparing two treatments and a control copyright 2016 john wiley sons ltd

testing whether independent treatment groups have equal medians the paper suggests new methods for comparing the medians corresponding to independent treatment groups the procedures are based on the harrell davis estimator in conjunction with a slight modification and extension of the bootstrap calibration technique suggested by loh alternatives to the harrell davis estimator are briefly discussed for the special case of two treatment groups the proposed procedure always had more power than the fligner rust solution as well as the procedure examined by wilcox and charlin included is an illustration using real data that comparing medians rather than means can yield a substantially different conclusion as to whether two distributions differ in terms of some measure of central location

the egoroff property and the egoroff theorem in riesz space valued non additive measure theory the egoroff theorem remains valid for any riesz space valued non additive measure which is strong order continuous and possesses a form of continuity called property s in the literature whenever the riesz space has the egoroff property this version of the egoroff theorem is also valid for any non additive measure with the property of uniform autocontinuity strong order continuity and continuity from below by assuming only the weak s distributivity which is weaker than the egoroff property

the continuity and compactness of riesz space valued indirect product measures the purpose of the paper is to extend the classical marczewski and ryll nardzewski theorems for the continuity and compactness of measures to riesz space valued non additive measures

resampling inference with complex survey data abstract methods for standard errors and confidence intervals for nonlinear statistics such as ratios regression and correlation coefficients have been extensively studied for stratified multistage designs in which the clusters are sampled with replacement in particular the important special case of two sampled clusters per stratum these methods include the customary linearization or taylor method and resampling methods based on the jackknife and balanced repeated replication brr unlike the jackknife or the brr the linearization method is applicable to general sampling designs but it involves a separate variance formula for each nonlinear statistic thereby requiring additional programming efforts both the jackknife and the brr use a single variance formula for all nonlinear statistics but they are more computing intensive the resampling methods developed here retain these features of the jackknife and the brr yet permit extension to more complex designs involving sampling without replace

on the regularities of fuzzy set multifunctions with applications in variation extensions and fuzzy set valued integrability problems in this paper we continue our studies 6 7 concerning regularity in this sense we obtain extension results by preserving regularity and we establish basic properties and continuity properties for the variation of fuzzy set multifunctions this enables us to get relationships among different types of regularity and also to point out regularity properties of the fuzzy set valued integral 20

a note on the l_1 consistency of variable kernel estimates 1 introduction most consistent nonparametric density estimates have a built in smoothing parameter numerous schemes have been proposed see e g references found in rudemo 1982 or devroye and penrod 1984 for selecting the smoothing parameter as a function of the data only a process called automatization and for introducing locally adaptable smoothing parameters in this note we give conditions which insure that estimators of the form

the problem of regions in the problem of regions we wish to know which one of a discrete set of possibilities applies to a continuous parameter vector this problem arises in the following way we compute a descriptive statistic from a set of data notice an interesting feature and wish to assign a confidence level to that feature for example we compute a density estimate and notice that the estimate is bimodal what confidence can we assign to bimodality a natural way to measure confidence is via the bootstrap we compute our descriptive statistic on a large number of bootstrap data sets and record the proportion of times that the feature appears this seems like a plausible measure of confidence for the feature the paper studies the construction of such confidence values and examines to what extent they approximate frequentist p values and bayesian a posteriori probabilities we derive more accurate confidence levels using both frequentist and objective bayesian approaches the methods are illustrated with a number of examples including polynomial model selection and estimating the number of modes of a density

monte carlo study of three data based nonparametric probability density estimators abstract although the theoretical properties of modern nonparametric probability density estimators have been studied for 25 years there remains the practical problem of how to specify the amount of bias or smoothing in a density estimate based on a random sample in this paper we review and evaluate three recently developed data based algorithms that completely specify a density estimate from a random sample using monte carlo techniques we compare the statistical accuracy of these algorithms as measured by the integrated mean squared error in addition we examine the sensitivity of these algorithms to outliers and estimate computer time requirements one conclusion we draw is that the statistical accuracy of these data based algorithms seems comparable to levels predicted by theoretical models

jackknife bootstrap and other resampling methods in regression analysis motivated by a representation for the least squares estimator we propose a class of weighted jackknife variance estimators for the least squares estimator by deleting any fixed number of observations at a time they are unbiased for homoscedastic errors and a special case the delete one jackknife is almost unbiased for heteroscedastic errors the method is extended to cover nonlinear parameters regression m estimators nonlinear regression and generalized linear models interval estimators can be constructed from the jackknife histogram three bootstrap methods are considered two are shown to give biased variance estimators and one does not have the bias robustness property enjoyed by the weighted delete one jackknife a general method for resampling residuals is proposed it gives variance estimators that are bias robust several bias reducing estimators are proposed some simulation results are reported

bootstrap technology and applications bootstrap resampling methods have emerged as powerful tools for constructing inferential procedures in modern statistical data analysis although these methods depend on the availability of fast inexpensive computing they offer the potential for highly accurate methods of inference moreover they can even eliminate the need to impose a convenient statistical model that does not have a strong scientific basis in this article we review some bootstrap methods emphasizing applications through illustrations with some real data special attention is given to regression problems with dependent data and choosing tuning parameters for optimal performance

a set valued egoroff type theorem in this paper an egoroff type theorem for a fuzzy multimeasure defined on a s algebra of subsets of an abstract space and taking values in the family of all nonvoid closed subsets of a real normed space is established some necessary and or sufficient conditions under which egoroff s theorem is valid are also presented

subgroups from regression trees with adjustment for prognostic effects and postselection inference identification of subgroups with differential treatment effects in randomized trials is attracting much attention many methods use regression tree algorithms this article addresses 2 important questions arising from the subgroups how to ensure that treatment effects in subgroups are not confounded with effects of prognostic variables and how to determine the statistical significance of treatment effects in the subgroups we address the first question by selectively including linear prognostic effects in the subgroups in a regression tree model the second question is more difficult because it falls within the subject of postselection inference we use a bootstrap technique to calibrate normal theory t intervals so that their expected coverage probability averaged over all the subgroups in a fitted model approximates the desired confidence level it can also provide simultaneous confidence intervals for all subgroups the first solution is implemented in the guide algorithm and is applicable to data with missing covariate values 2 or more treatment arms and outcomes subject to right censoring bootstrap calibration is applicable to any subgroup identification method it is not restricted to regression tree models two real examples are used for illustration a diabetes trial where the outcomes are completely observed but some covariate values are missing and a breast cancer trial where the outcome is right censored

a new method for testing separate families of hypotheses abstract theoretical and empirical evidence are reported showing that the tests given in cox 1961 and williams 1970a b for the problem of testing separate families of hypotheses suffer from fundamental difficulties neither test is guaranteed to be asymptotically level a even for very smooth problems a new method proposed here as an alternative works adaptively by repeated application of the parametric bootstrap idea over slowly shrinking confidence regions theoretical properties of the method are derived and its finite sample behavior is studied in a number of examples

on the probable error of the ratio of two gamma means summary the two sample student s t interval can be derived by parametric bootstrap coverage calibration of the naive plug in interval that fails to account for the estimation of the common variance parameter the same technique results in an essentially exact confidence interval for the ratio of two means based on independent samples from gamma distributions the gamma problem is more difficult computationally because an exact pivot is not available however the computational burden of bootstrap calibration can be reduced to a routine level using the fact that the ratio of sample means is proportional to an exact f variate that is independent of the conditional maximum likelihood estimator of the shape parameter the density of the conditional estimator can be approximated with extreme accuracy using the p formula and a rejection sampler can be used to simulate from this approximate density this greatly simplifies bootstrap calibration in this context an alternative interval is obtained by inverting an exact test described by jensen 1986 simulation studies suggest that the two intervals have similar performance in terms of length and coverage in practice we recommend the bootstrap calibration method because it is much simpler to implement and is more versatile

the egoroff theorem for non additive measures in riesz spaces the egoroff theorem remains valid for any riesz space valued non additive measure which is continuous from above and below by assuming that the riesz space has the asymptotic egoroff property this property is satisfied for many concrete riesz spaces such as rs of all real functions on a non empty set s l0 0 1 of all lebesgue measurable functions and their ideals

qualms about bootstrap confidence intervals abstract the percentile method and bias corrected percentile method of efron 1981 1982 are discussed when these methods are used to construct nonparametric confidence intervals for the variance of a normal distribution the coverage probabilities are substantially below the nominal level for small to moderate samples this is due to the inapplicability of assumptions underlying the methods these assumptions are difficult or impossible to check in the complicated situations for which the bootstrap is intended therefore bootstrap confidence intervals should be used with caution in complex problems

set valued lusin type theorem for null null additive set multifunctions in a previous paper we presented a set valued egoroff type theorem for monotone set multifunctions in this paper a new version of this set valued egoroff type theorem is obtained it enables a set valued lusin type theorem for null null additive monotone continuous set multifunctions to be established several applications of this lusin type theorem are given pointing out some relationships among m measurability a measurability and totally measurability of real functions we also compare our new lusin type theorem with lusin s theorem previously obtained by the second author

the bootstrap and modern statistics 2000 the bootstrap and modern statistics journal of the american statistical association vol 95 no 452 pp 1293 1296

monte carlo approximation and the iterated bootstrap summary we discuss optimal choice of the numbers of resamples in the two stages of the iterated bootstrap when that technique is used to calibrate bootstrap confidence intervals if the numbers of resamples in the first and second stages are denoted by b and c respectively we show that it is optimal to take c to be approximately a constant multiple of b the value of the constant is derived and shown to depend only on the nominal coverage level of a confidence interval however it assumes different values in the cases of one and twosided intervals

confidence bands in non parametric errors in variables regression summary errors in variables regression is important in many areas of science and social science e g in economics where it is often a feature of hedonic models in environmental science where air quality indices are measured with error in biology where the vegetative mass of plants is frequently obscured by mismeasurement and in nutrition where reported fat intake is typically subject to substantial error to date in non parametric contexts the great majority of work has focused on methods for estimating the mean as a function with relatively little attention being paid to techniques for empirical assessment of the accuracy of the estimator we develop methodologies for constructing confidence bands our contributions include techniques for tuning parameter choice aimed at minimizing the coverage error of confidence bands

non atomicity for fuzzy and non fuzzy multivalued set functions in this paper we extend the concept of set valued fuzzy measures introduced and studied by guo and zhang 2004 on set valued fuzzy measures information sciences 160 2004 13 25 to the class of multivalued set functions taking values in the family of non empty closed subsets of a real normed space also we introduce the notions of atom and non atomicity of a multivalued set function and present some of their properties we also establish an extension result by preserving non atomicity for a fuzzy multisubmeasure multimeasure

constrained maximum likelihood exemplified by isotonic convex logistic regression abstract maximum likelihood estimates in problems in which the likelihood is smooth and the parameter space is defined by linear or smooth nonlinear inequality constraints can be obtained using available nonlinear optimization packages such as npsol this class of models includes generalized linear models with order restrictions convexity or smoothness constraints on the parameters smoothness constraints being in the form of bounds on finite differences of the regression function methods for such models are demonstrated by an analysis of data from four published studies of the incidence of down s syndrome in single year maternal age intervals constrained logistic regression of the incidence of down s syndrome on maternal age shows that the data are fitted well by a nondecreasing convex function p values for the likelihood ratio test of this model against alternatives are obtained by the parametric bootstrap and iterated parametric bootstrap the iterated bootstrap is used as a diagnostic tool it