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Johns (1988), Davison (1988), and Do and Hall (1991) used importance sampling for calculating bootstrap distributions of one-dimensional statistics. Realizing that their methods can not be extended easily to multi-dimensional statistics, Fuh and Hu (2004) proposed an exponential tilting formula for statistics of multi-dimension, which is optimal in the sense that the asymptotic variance is minimized for estimating tail probabilities of asymptotically normal statistics. For one-dimensional statistics, Hu and Su (2008) proposed a multi-step variance minimization approach that can be viewed as a generalization of the two-step variance minimization approach proposed by Do and Hall (1991). In this article, we generalize the approach of Hu and Su (2008) to multi-dimensional statistics, which applies to general statistics and does not resort to asymptotics. Empirical results on a real survival data set show that the proposed algorithm provides significant computational efficiency gains. [ABSTRACT FROM AUTHOR]

This paper by using data envelopment analysis (DEA) and statistical inference evaluates the citation performance of 229 economic journals. The paper categorizes the journals into four main categories (A-D) based on their efficiency levels. The results are then compared to the 27 'core economic journals' as introduced by Diamond (Curr Contents 21(1):4-11, ). The results reveal that after more than 20 years Diamonds' list of 'core economic journals' is still valid. Finally, for the first time the paper uses data from four well-known databases (SSCI, Scopus, RePEc, Econlit) and two quality ranking reports (Kiel Institute internals ranking and ABS quality ranking report) in a DEA setting and in order to derive the ranking of 229 economic journals. The ten economic journals with the highest citation performance are Journal of Political Economy, Econometrica, Quarterly Journal of Economics, Journal of Financial Economics, Journal of Economic Literature, American Economic Review, Review of Economic Studies, Journal of Econometrics, Journal of Finance, Brookings Papers on Economic Activity. [ABSTRACT FROM AUTHOR]

The goal of this paper is to describe the quality of different two-sample bootstrap and permutation tests for comparing variances. It is thereby inter alia shown that studentized resampling versions of the classical F-ratio test are asymptotically effective in a general nonparametric setting. This means that there is asymptotic no loss of power under contiguous alternatives. Moreover it is indicated that these tests are asymptotically consistent for fixed alternatives. [ABSTRACT FROM AUTHOR]

This article deals with the availability behavior of a repairable system in which standby switched to primary is subject to breakdowns. The time-to-failure of the four primary and two standby units are assumed to be exponentially and generally distributed. In addtion, the repair time of service station follow four common distributions: exponential (EXP), Gamma (G), Uniform (U), and Mixture (M). We use a recursive method, and the supplementary variable technique to develop the steady-state availability, Av. The estimator [image omitted] is strongly consistent and asymptotically normal. The interval estimations of Av are constructed by five bootstrap approaches: standard bootstrap confidence interval (SB), the percentile bootstrap confidence interval (PB), the bias-corrected percentile bootstrap confidence interval (BCPB), the bias-corrected and accelerated confidence interval (BCa), and bootstrap pivot confidence interval (BP). Finally, some simulation computations are conducted in order to describe the performances of [image omitted] on various interval estimation by calculating the coverage percentage and the average length of intervals. [ABSTRACT FROM AUTHOR]

In the area of sufficient dimension reduction, two structural conditions are often assumed: the linearity condition that is close to assuming ellipticity of underlying distribution of predictors, and the constant variance condition that nears multivariate normality assumption of predictors. Imposing these conditions are considered as necessary trade-off for overcoming the 'curse of dimensionality'. However, it is very hard to check whether these conditions hold or not. When these conditions are violated, some methods such as marginal transformation and re-weighting are suggested so that data fulfill them approximately. In this article, we assume an independence condition between the projected predictors and their orthogonal complements which can ensure the commonly used inverse regression methods to identify the central subspace of interest. The independence condition can be checked by the gridded chi-square test. Thus, we extend the scope of many inverse regression methods and broaden their applicability in the literature. Simulation studies and an application to the car price data are presented for illustration. [ABSTRACT FROM AUTHOR]

As is common in case-control studies, treatments have an influence not only on mean values, but also on variance or distributional aspects. That is why several statistics, each one suitable for a specific aspect, are usually assessed (Salmaso and Solari, 2005). According to Farkas (1947, p. 185), different tests of significance are appropriate to test different features of the same null hypothesis (Lehmann, 1993), thus leading to the Multi-Aspect (MA) testing issue (Pesarin and Salmaso, 2010). When dealing with paired data, usually inferences concern differences between the means. However, there are some circumstances in which it is of interest to test for differences between the variances (McCulloch, 1987). Here, we present a nonparametric permutation solution to this problem. Our goal is to develop MA techniques for paired data, thus finding powerful tests, such that both differences in mean and in variance are separately identified. The inferential procedures proposed in the paper and assessed throughout a simulation study are then applied to a real case study in rhinoseptoplasty surgery. [ABSTRACT FROM AUTHOR]

Abstract: The paper reconsiders the autoregressive aided periodogram bootstrap (AAPB) which has been suggested in Kreiss and Paparoditis (2003) . Their idea was to combine a time domain parametric and a frequency domain nonparametric bootstrap to mimic not only a part but as much as possible the complete covariance structure of the underlying time series. We extend the AAPB in two directions. Our procedure explicitly leads to bootstrap observations in the time domain and it is applicable to multivariate linear processes, but agrees exactly with the AAPB in the univariate case, when applied to functionals of the periodogram. The asymptotic theory developed shows validity of the multiple hybrid bootstrap procedure for the sample mean, kernel spectral density estimates and, with less generality, for autocovariances. [ABSTRACT FROM AUTHOR]

Abstract: In the multiple testing context, a challenging problem is the estimation of the proportion of true null hypotheses. A large number of estimators of this quantity rely on identifiability assumptions that either appear to be violated on real data, or can be at least relaxed. The proposed estimator results from density estimation by histograms, and cross-validation. Several consistency results are derived under independence. A new (plug-in) multiple testing procedure (MTP) is also described, based on the Benjamini and Hochberg procedure (BH-procedure) and the proposed estimator. This procedure is asymptotically optimal, provides the asymptotic desired false discovery rate (FDR) control, and is more powerful than the BH-procedure. The non-asymptotic behavior of is finally assessed through several simulation experiments. It outperforms numerous existing estimators in usual settings, and remains accurate with “U-shape” densities where other estimators usually fail. It does not exhibit any strong sensitivity to dependence. With m block-structured dependent data, it stays reliable up to a within block correlation , when m/50 blocks are used. [Copyright &y& Elsevier]

SubBag is a technique by combining bagging and random subspace methods to generate ensemble classifiers with good generalization capability. In practice, a hyperparameter K of SubBag-the number of randomly selected features to create each base classifier-should be specified beforehand. In this article, we propose to employ the out-of-bag instances to determine the optimal value of K in SubBag. The experiments conducted with some UCI real-world data sets show that the proposed method can make SubBag achieve the optimal performance in nearly all the considered cases. Meanwhile, it occupied less computational sources than cross validation procedure. [ABSTRACT FROM AUTHOR]

Abstract: Generalised varying-coefficient models (GVC) are very important models. There are a considerable number of literature addressing these models. However, most of the existing literature are devoted to the estimation procedure. In this paper, we systematically investigate the statistical inference for GVC, which includes confidence band as well as hypothesis test. We establish the asymptotic distribution of the maximum discrepancy between the estimated functional coefficient and the true functional coefficient. We compare different approaches for the construction of confidence band and hypothesis test. Finally, the proposed statistical inference methods are used to analyse the data from China about contraceptive use there, which leads to some interesting findings. [Copyright &y& Elsevier]

Abstract: In this paper we consider the estimation of the error distribution in a heteroscedastic nonparametric regression model with multivariate covariates. As estimator we consider the empirical distribution function of residuals, which are obtained from multivariate local polynomial fits of the regression and variance functions, respectively. Weak convergence of the empirical residual process to a Gaussian process is proved. We also consider various applications for testing model assumptions in nonparametric multiple regression. The model tests obtained are able to detect local alternatives that converge to zero at an -rate, independent of the covariate dimension. We consider in detail a test for additivity of the regression function. [Copyright &y& Elsevier]

Several variations of monotone nonparametric regression have been developed over the past 30 years. One approach is to first apply nonparametric regression to data and then monotone smooth the initial estimates to “iron out” violations to the assumed order. Here, such estimators are considered, where local polynomial regression is first used, followed by either least squares isotonic regression or a monotone method using simple averages. The primary focus of this work is to evaluate different types of confidence intervals for these monotone nonparametric regression estimators through Monte Carlo simulation. Most of the confidence intervals use bootstrap or jackknife procedures. Estimation of a response variable as a function of two continuous predictor variables is considered, where the estimation is performed at the observed values of the predictors (instead of on a grid). The methods are then applied to data involving subjects that worked at plants that use beryllium metal who have developed chronic beryllium disease. [ABSTRACT FROM AUTHOR]

In this study, we use the wavelet analysis to construct a test statistic to test for the existence of a trend in the series. We also propose a new approach for testing the presence of trend based on the periodogram of the data. Since we are also interested in the presence of a long-memory process among the data, we study the properties of our test statistics under different degrees of dependency. We compare the results when using the band periodogram test and the wavelet test with results obtained by applying the ordinary least squares (OLS) method under the same conditions. [ABSTRACT FROM AUTHOR]

In this article, we use two efficient approaches to deal with the difficulty in computing the intractable integrals when implementing Gibbs sampling in the nonlinear mixed effects model (NLMM) based on Dirichlet processes (DP). In the first approach, we compute the Laplace's approximation to the integral for its high accuracy, low cost, and ease of implementation. The second approach uses the no-gaps algorithm of MacEachern and Muller (1998) to perform Gibbs sampling without evaluating the difficult integral. We apply both approaches to real problems and simulations. Results show that both approaches perform well in density estimation and prediction and are superior to the parametric analysis in that they can detect important model features, such as skewness, long tails, and multimodality, whereas the parametric analysis cannot. [ABSTRACT FROM AUTHOR]

Abstract: The problem of subsampling in two-sample and -sample settings is addressed where both the data and the statistics of interest take values in general spaces. We focus on the case where each sample is a stationary time series, and construct subsampling confidence intervals and hypothesis tests with asymptotic validity. Some examples are also given, and the problem of optimal block size choice is discussed. [Copyright &y& Elsevier]

Statistical practitioners frequently wish to know whether a variable is symmetrically distributed. There are a number of different tests available but the most commonly used one is perhaps that based on the standardized third central moment, as defined by Pearson and Fisher in the early 1900's. While this traditional skewness measure uniquely determines the symmetry of a variable within the Pearson family, it does not uniquely determine symmetry for a general distribution. In this article, we propose a modified version of the classical skewness test which is easy to conduct and consistent against a wide family of asymmetric distributions. [ABSTRACT FROM AUTHOR]

The history of regression analysis when response and explanatory variables are subject to error dates back to Eisenhart (1939) and Wald (1940). Now the subject is discussed in the robust regression framework involving “leverage” points in addition to the traditional “outliers,” e.g., see Rousseeuw and Leroy (1987). In this article, we develop two variations of co-ordinatewise Winsorized-bootstrapped approach and study their properties using empirical methods and illustrative examples. The new methods are seen to provide significant improvement when the data are in a neighborhood of multivariate normal population without significant loss in the performance when the multivariate normal model holds. [ABSTRACT FROM AUTHOR]

In this paper, through an information-theoretic approach, we construct estimations and confidence intervals of Z-functionals involving finite population and with the presence of auxiliary information. In particular, we give a method of estimating the variance of finite population with known mean. The modified estimates and confidence intervals for Z-functionals can adequately use the auxiliary information, at least not worse than what the standard ones do. A simulation study is presented to assess the performance of the modified estimates for the finite sample case. [ABSTRACT FROM AUTHOR]

Methods for computing a confidence interval for the difference between two Pearson correlations are compared when dealing with nonnormality and heteroscedasticity. Variations of a method derived by Zou performed relatively well in simulations for the dependent case. For the independent case, the Wilcox--Muska method performed best. [ABSTRACT FROM AUTHOR]

Abstract: For testing the problem of regions in the space of distribution functions, this paper considers approaches to modify the bootstrap probability to be a second-order accurate -value based on the familiar bias correction and acceleration method. It is shown that Shimodaira''s [2004a. Approximately unbiased tests of regions using multistep-multiscale bootstrap resampling. Ann. Statist. 32, 2616–2641] twostep-multiscale bootstrap method works even in the problem of regions in functional space. In this paper the bias correction quantity is estimated by his onestep-multiscale bootstrap method. Instead of using the twostep-multiscale bootstrap method, the acceleration constant is estimated by a newly proposed jackknife method which requires first-level bootstrap resamplings only. Some numerical examples are illustrated, in which an application to testing significance in model selection is included. [Copyright &y& Elsevier]

A classic problem is comparing Pearson's correlation corresponding to two independent groups. The article examines a generalization where the goal is to compare the groups based on a robust variation of explanatory power used in conjunction with a particular nonparametric regression method that allows curvature. If the nonparametric regression estimator is replaced by the ordinary least squares estimator, and if explanatory power is measured with the usual variance, and if the regression line is straight, the approach used here reduces to comparing Pearson's correlation. For reasons summarized in the article, Cleveland's (1979) lowess estimator is used. It is found that a modified percentile bootstrap method controls Type I error probabilities reasonably well in simulations. Even when the regression line is straight, the power of the method compares well to a variation that fits a (straight) robust regression line to the data. And even under normality, using Pearson's correlation was found to provide little or no advantage in terms of power. [ABSTRACT FROM AUTHOR]

Richter and McCann (2007) presented a median-based multiple comparison procedure for assessing evidence of group location differences. The sampling distribution was based on the permutation distribution of the maximum median difference among all pairs, and provides strong control of the FWE. This idea is extended to develop a step-down procedure for comparing group locations. The new step-down procedure exploits logical dependencies between pairwise hypotheses and provides greater power than the single-step procedure, while still maintaining strong FWE control. The new procedure can also be a more powerful alternative to existing methods based on means, especially for heavy-tailed distributions. [ABSTRACT FROM AUTHOR]

Abstract: We propose a new test for independence of error and covariate in a nonparametric regression model. The test statistic is based on a kernel estimator for the -distance between the conditional distribution and the unconditional distribution of the covariates. In contrast to tests so far available in literature, the test can be applied in the important case of multivariate covariates. It can also be adjusted for models with heteroscedastic variance. Asymptotic normality of the test statistic is shown. Simulation results and a real data example are presented. [Copyright &y& Elsevier]

Abstract: The Möbius transformation of probability cells in a multi-way contingency table is used to partition the Pearson chi-square test of mutual independence into A-dependence statistics. A similar partition is proposed for a universal and consistent test of serial independence in a stationary sequence of a categorical variable. The partition proposed can be adapted whether using estimated or theoretical marginal probabilities. With the aim of detecting a dependence of high order in a long sequence, A-dependence terms of the partition measuring increasing lagged dependences can be combined in a Box–Pierce type test of serial independence. A real data analysis of a nucleotides sequence using the Box–Pierce type test is provided. [Copyright &y& Elsevier]

We study the asymptotic distribution of the L 1 regression estimator under general conditions with matrix norming and possibly non i.i.d. errors. We then introduce an appropriate bootstrap procedure to estimate the distribution of this estimator and study its asymptotic properties. It is shown that this bootstrap is consistent under suitable conditions and in other situations the bootstrap limit is a random distribution. [ABSTRACT FROM AUTHOR]

Abstract: We investigate the asymptotic behavior of a nonparametric M-estimator of a regression function for stationary dependent processes, where the explanatory variables take values in some abstract functional space. Under some regularity conditions, we give the weak and strong consistency of the estimator as well as its asymptotic normality. We also give two examples of functional processes that satisfy the mixing conditions assumed in this paper. Furthermore, a simulated example is presented to examine the finite sample performance of the proposed estimator. [Copyright &y& Elsevier]

Motivated by applications in call center management, we propose a framework based on empirical process techniques for inference about waiting time and patience distributions in multiserver queues with abandonment. The framework rigorises heuristics based on survival analysis of independent and identically distributed observations by allowing correlated waiting times. Assuming a regenerative structure of offered waiting times, we establish asymptotic properties of estimators of limiting distribution functions and derived functionals. We discuss construction of bootstrap confidence intervals and statistical tests, including a simple bootstrap two-sample test for comparing patience distributions. A small simulation study and a real data example are presented. [ABSTRACT FROM AUTHOR]

We study an at-most-one-change time-series model with an abrupt change in the mean and dependent errors that fulfil certain mixing conditions. We obtain confidence intervals for the unknown change-point via bootstrapping methods. Precisely, we use a block bootstrap of the estimated centred error sequence. Then, we reconstruct a sequence with a change in the mean using the same estimators as before. The difference between the change-point estimator of the resampled sequence and the one of the original sequence can be used as an approximation of the difference between the real change-point and its estimator. This enables us to construct confidence intervals using the empirical distribution of the resampled time series. A simulation study shows that the resampled confidence intervals are usually closer to their target levels and at the same time smaller than the asymptotic intervals. [ABSTRACT FROM AUTHOR]

Abstract: We develop statistical inferential tools for estimating and comparing conditional tail expectation (CTE) functions, which are of considerable interest in actuarial science. In particular, we construct estimators for the CTE functions, develop the necessary asymptotic theory for the estimators, and then use the theory for constructing confidence intervals and bands for the functions. Both parametric and non-parametric approaches are explored. Simulation studies illustrate the performance of estimators in various situations. Results are obtained under minimal assumptions, and the general Vervaat process plays a crucial role in achieving these goals. [Copyright &y& Elsevier]

Abstract: Diagnostic checking for multivariate parametric models is investigated in this article. A nonparametric Monte Carlo Test (NMCT) procedure is proposed. This Monte Carlo approximation is easy to implement and can automatically make any test procedure scale-invariant even when the test statistic is not scale-invariant. With it we do not need plug-in estimation of the asymptotic covariance matrix that is used to normalize test statistic and then the power performance can be enhanced. The consistency of NMCT approximation is proved. For comparison, we also extend the score type test to one-dimensional cases. NMCT can also be applied to diverse problems such as a classical problem for which we test whether or not certain covariables in linear model has significant impact for response. Although the Wilks lambda, a likelihood ratio test, is a proven powerful test, NMCT outperforms it especially in non-normal cases. Simulations are carried out and an application to a real data set is illustrated. [Copyright &y& Elsevier]

Parametric model-based regression imputation is commonly applied to missing-data problems, but is sensitive to misspecification of the imputation model. Little and An (2004) proposed a semiparametric approach called penalized spline propensity prediction (PSPP), where the variable with missing values is modeled by a penalized spline (P-Spline) of the response propensity score, which is logit of the estimated probability of being missing given the observed variables. Variables other than the response propensity are included parametrically in the imputation model. However they only considered point estimation based on single imputation with PSPP. We consider here three approaches to standard errors estimation incorporating the uncertainty due to non response: (a) standard errors based on the asymptotic variance of the PSPP estimator, ignoring sampling error in estimating the response propensity; (b) standard errors based on the bootstrap method; and (c) multiple imputation-based standard errors using draws from the joint posterior predictive distribution of missing values under the PSPP model. Simulation studies suggest that the bootstrap and multiple imputation approaches yield good inferences under a range of simulation conditions, with multiple imputation showing some evidence of closer to nominal confidence interval coverage when the sample size is small. [ABSTRACT FROM AUTHOR]

Variance of parameter estimate in Cox’s proportional hazards model is based on asymptotic variance. When sample size is small, variance can be estimated by bootstrap method. However, if censoring rate in a survival data set is high, bootstrap method may fail to work properly. This is because bootstrap samples may be even more heavily censored due to repeated sampling of the censored observations. This paper proposes a random weighting method for variance estimation and confidence interval estimation for proportional hazards model. This method, unlike the bootstrap method, does not lead to more severe censoring than the original sample does. Its large sample properties are studied and the consistency and asymptotic normality are proved under mild conditions. Simulation studies show that the random weighting method is not as sensitive to heavy censoring as bootstrap method is and can produce good variance estimates or confidence intervals. [ABSTRACT FROM AUTHOR]

Abstract: For estimating a rare event via the multivariate extreme value theory, the so-called tail dependence function has to be investigated (see [L. de Haan, J. de Ronde, Sea and wind: Multivariate extremes at work, Extremes 1 (1998) 7–45]). A simple, but effective estimator for the tail dependence function is the tail empirical distribution function, see [X. Huang, Statistics of Bivariate Extreme Values, Ph.D. Thesis, Tinbergen Institute Research Series, 1992] or [R. Schmidt, U. Stadtmüller, Nonparametric estimation of tail dependence, Scand. J. Stat. 33 (2006) 307–335]. In this paper, we first derive a bootstrap approximation for a tail dependence function with an approximation rate via the construction approach developed by [K. Chen, S.H. Lo, On a mapping approach to investigating the bootstrap accuracy, Probab. Theory Relat. Fields 107 (1997) 197–217], and then apply it to construct a confidence band for the tail dependence function. A simulation study is conducted to assess the accuracy of the bootstrap approach. [Copyright &y& Elsevier]

This article considers a simple procedure for assessing whether a weakly dependent univariate stochastic process is time-reversible. Our approach is based on a simple index of the deviation from zero of the median of the one-dimensional marginal law of differenced data. An attractive feature of the method is that it requires no moment assumptions. Instead of relying on Gaussian asymptotic approximations, we consider using subsampling and resampling methods to construct confidence intervals for the time-reversibility parameter, and show that such inference procedures are asymptotically valid under a mild mixing condition. The small-sample properties of the proposed procedures are examined by means of Monte Carlo experiments and an application to real-world data is also presented. [ABSTRACT FROM AUTHOR]

Abstract: The problem of building bootstrap confidence intervals for small probabilities with count data is addressed. The law of the independent observations is assumed to be a mixture of a given family of power series distributions. The mixing distribution is estimated by nonparametric maximum likelihood and the corresponding mixture is used for resampling. We build percentile-t and Efron percentile bootstrap confidence intervals for the probabilities and we prove their consistency in probability. The new theoretical results are supported by simulation experiments for Poisson and geometric mixtures. We compare percentile-t and Efron percentile bootstrap intervals with eight other bootstrap or asymptotic theory based intervals. It appears that Efron percentile bootstrap intervals outperform the competitors in terms of coverage probability and length. [Copyright &y& Elsevier]

Abstract: We develop two methods to construct confidence bands for the receiver operating characteristic (ROC) curve without estimating the densities of the underlying distributions. The first method is based on the smoothed bootstrap while the second method uses the Bonferroni inequality. As an illustration, we provide confidence bands for the ROC curve using data on Duchanne Muscular Dystrophy. [Copyright &y& Elsevier]

A number of parametric and non-parametric linear trend tests for time series are evaluated in terms of test size and power, using also resampling techniques to form the empirical distribution of the test statistics under the null hypothesis of no linear trend. For resampling, both bootstrap and surrogate data are considered. Monte Carlo simulations were done for several types of residuals (uncorrelated and correlated with normal and nonnormal distributions) and a range of small magnitudes of the trend coefficient. In particular for AR(1) and ARMA(1, 1) residual processes, we investigate the discrimination of strong autocorrelation from linear trend with respect to the sample size. The correct test size is obtained for larger data sizes as autocorrelation increases and only when a randomization test that accounts for autocorrelation is used. The overall results show that the type I and II errors of the trend tests are reduced with the use of resampled data. Following the guidelines suggested by the simulation results, we could find significant linear trend in the data of land air temperature and sea surface temperature. [ABSTRACT FROM AUTHOR]

Robust tests are proposed for unrestricted and ordered alternatives in the multi-sample problem without assuming homogeneity of scales and/or symmetry of the underlying distributions. The methodology consists of bootstrapping appropriately centered Mann–Whitney statistics. Data sets from Physics and Psychology illustrate the methodology. [Copyright &y& Elsevier]

Hollander (1970) proposed a distribution-free signed rank test for testing parallelism of two regression lines. Hollander's test requires that the number of pairs of data in the two datasets must be equal and even. This requirement of the test is met by discarding observation pairs randomly from one or both datasets as needed. In this article, we propose that instead of discarding the observation pairs randomly, we add observation pairs randomly in one or both datasets as needed to meet the requirement of Hollander's test. By using simulation technique we show that the new test is a significant improvement over the original test of Hollander since the new test is consistently more powerful than the original test and provides narrower confidence intervals for the difference of the two slopes of the regression lines. [ABSTRACT FROM AUTHOR]

Abstract: A nonparametric test of the mutual independence between many numerical random vectors is proposed. This test is based on a characterization of mutual independence defined from probabilities of half-spaces in a combinatorial formula of Möbius. As such, it is a natural generalization of tests of independence between univariate random variables using the empirical distribution function. If the number of vectors is p and there are n observations, the test is defined from a collection of processes , where A is a subset of of cardinality , which are asymptotically independent and Gaussian. Without the assumption that each vector is one-dimensional with a continuous cumulative distribution function, any test of independence cannot be distribution free. The critical values of the proposed test are thus computed with the bootstrap which is shown to be consistent. Another similar test, with the same asymptotic properties, for the serial independence of a multivariate stationary sequence is also proposed. The proposed test works when some or all of the marginal distributions are singular with respect to Lebesgue measure. Moreover, in singular cases described in Section 4, the test inherits useful invariance properties from the general affine invariance property. [Copyright &y& Elsevier]

Abstract: Many applications aim to learn a high dimensional parameter of a data generating distribution based on a sample of independent and identically distributed observations. For example, the goal might be to estimate the conditional mean of an outcome given a list of input variables. In this prediction context, bootstrap aggregating (bagging) has been introduced as a method to reduce the variance of a given estimator at little cost to bias. Bagging involves applying an estimator to multiple bootstrap samples and averaging the result across bootstrap samples. In order to address the curse of dimensionality, a common practice has been to apply bagging to estimators which themselves use cross-validation, thereby using cross-validation within a bootstrap sample to select fine-tuning parameters trading off bias and variance of the bootstrap sample-specific candidate estimators. In this article we point out that in order to achieve the correct bias variance trade-off for the parameter of interest, one should apply the cross-validation selector externally to candidate bagged estimators indexed by these fine-tuning parameters. We use three simulations to compare the new cross-validated bagging method with bagging of cross-validated estimators and bagging of non-cross-validated estimators. [Copyright &y& Elsevier]

Abstract: This paper establishes the weak convergence of a class of marked empirical processes of possibly non-stationary and/or non-ergodic multivariate time series sequences under martingale conditions. The assumptions involved are similar to those in Brown''s martingale central limit theorem. In particular, no mixing conditions are imposed. As an application, we propose a test statistic for the martingale hypothesis and we derive its asymptotic null distribution. Finally, a Monte Carlo study shows that the asymptotic results provide good approximations for small and moderate sample sizes. An application to the S&P 500 is also considered. [Copyright &y& Elsevier]

We investigate the second order accuracy of the M out of N bootstrap for a Studentized trimmed mean using the Edgeworth expansion derived in a previous paper. Some simulations, which support our theoretical results, are also given. The effect of extrapolation in conjunction with the M out of N bootstrap for Studentized trimmed means is briefly discussed. As an auxiliary result we obtain a Bahadur’s type representation for an M out of N bootstrap quantile. Our results supplement previous work on (Studentized) trimmed means by Hall and Padmanabhan [13], Bickel and Sakov [7], and Gribkova and Helmers [11]. [ABSTRACT FROM AUTHOR]