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This paper studies the problem of simultaneously testing that each of k samples, coming from k count variables, were all generated by Poisson laws. The means of those populations may differ. The proposed procedure is designed for large k, which can be bigger than the sample sizes. First, a test is proposed for the case of independent samples, and then the obtained results are extended to dependent data. In each case, the asymptotic distribution of the test statistic is stated under the null hypothesis as well as under alternatives, which allows to study the consistency of the test. Specifically, it is shown that the test statistic is asymptotically free distributed under the null hypothesis. The finite sample performance of the test is studied via simulation. A real data set application is included. [ABSTRACT FROM AUTHOR]

This paper introduces a nonparametric bootstrap method for estimating the causal effects of public policy under the circumstances of imperfect compliance and overlap. It focuses on business investment subsidies in Sardinia by comparing firms eligible for the 1999 subsidies to those not, amid issues of imperfect compliance and overlapping programs. Bootstrap confidence intervals (CI) are proposed for the average effect of treatment on the sub-population of compliers. The obtained CIs are consistent across nominal levels and robust against data nonnormality; they show coverages of credible intervals close to nominal, suggesting effectiveness for assessing causal effects. Compared to other methods, the results of the new combination of a specific estimator for incompliance and the bootstrap align with those of more modern approaches such as Bayesian Additive Regression Trees and Causal forest. [ABSTRACT FROM AUTHOR]

It has been shown in the literature that judgment post stratification (JPS) sampling design often leads to more efficient statistical inference than what is possible to obtain in simple random sampling (SRS) design of comparable size. Since the JPS is a cost-efficient sampling design, a large enough sample size may not be available to use normal theory of the estimators. In this paper, we describe two bootstrap methods for JPS sampling scheme, one of which has been already used in the literature without studying its consistency and the other is new. We also show that both bootstrap approaches are consistent. We then investigate the use of the bootstrap methods for constructing confidence intervals for the population mean and compare them with the confidence interval of the population mean obtained via normal approximation (NA) method using Monte Carlo simulation. It is found that for the asymmetric distributions, one of the bootstrap methods we describe in the paper often leads to a closer coverage probability (CP) to the nominal level than NA method. Finally, a real dataset is analysed for illustration. [ABSTRACT FROM AUTHOR]

Given finite i.i.d. samples in a Hilbert space with zero mean and trace-class covariance operator Σ , the problem of recovering the spectral projectors of Σ naturally arises in many applications. In this paper, we consider the problem of finding distributional approximations of the spectral projectors of the empirical covariance operator Σ ^ , and offer a dimension-free framework where the complexity is characterized by the so-called relative rank of Σ . In this setting, novel quantitative limit theorems and bootstrap approximations are presented subject to mild conditions in terms of moments and spectral decay. In many cases, these even improve upon existing results in a Gaussian setting. [ABSTRACT FROM AUTHOR]

This paper proposes a new test for the comparison of conditional quantile curves when the outcome of interest, typically a duration, is subject to right censoring. The test can be applied both in the case of two independent samples and for paired data, and can be used for the comparison of quantiles at a fixed quantile level, a finite set of levels or a range of quantile levels. The asymptotic distribution of the proposed test statistics is obtained both under the null hypothesis and under local alternatives. We describe a bootstrap procedure in order to approximate the critical values and present the results of a simulation study, in which the performance of the tests for small and moderate sample sizes is studied and compared with the behavior of alternative tests. Finally, we apply the proposed tests on a data set concerning diabetic retinopathy. [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]

A common assumption in non-parametric regression models is the independence of the covariate and the error. Some procedures have been suggested for testing that hypothesis. This paper considers a test, whose test statistic compares estimators of the joint and the product of the marginal characteristic functions of the covariate and the error. It is proposed to approximate the null distribution of such statistic by means of a weighted bootstrap estimator. The resulting test is able to detect any fixed alternative as well as local alternatives converging to the null at the rate n − 1 / 2 , n denoting the sample size. The finite sample performance of this approximation is assessed by means of a simulation study, where it is also compared with other estimators. This study reveals that, from a computational point of view, the proposed approximation is very efficient. Two real data set applications are also included. [ABSTRACT FROM AUTHOR]

This paper deals with the semi-functional partial linear regression model Y=XTβ+m(χ)+ε under α-mixing conditions. β∈Rp and m(·) denote an unknown vector and an unknown smooth real-valued operator, respectively. The covariates X and χ are valued in Rp and some infinite-dimensional space, respectively, and the random error ε verifies E(ε|X,χ)=0. Naïve and wild bootstrap procedures are proposed to approximate the distribution of kernel-based estimators of β and m(χ), and their asymptotic validities are obtained. A simulation study shows the behavior (on finite sample sizes) of the proposed bootstrap methodology when applied to construct confidence intervals, while an application to real data concerning electricity market illustrates its usefulness in practice. [ABSTRACT FROM AUTHOR]

In missing data analysis, the assumption of the missing data mechanism is crucial. Under different assumptions, different statistical methods have to be developed accordingly; however, in reality this kind of assumption is usually unverifiable. Therefore a less stringent, and hence more flexible, assumption is preferred. In this paper, we consider a generally applicable missing data mechanism. Under this general missing data mechanism, we introduce the conditional likelihood and its approximate version as the base for estimating the unknown parameter of interest. Since this approximate conditional likelihood uses the completely observed samples only, it may result in large estimation bias, which could deteriorate the statistical inference and also jeopardise other statistical procedure. To tackle this problem, we propose to use some resampling techniques to reduce the estimation bias. We consider both the Jackknife and the Bootstrap in our paper. We compare their asymptotic biases through a higher order expansion up to. We also derive some results for the mean squared error (MSE) in terms of estimation accuracy. We conduct comprehensive simulation studies under different situations to illustrate our proposed method. We also apply our method to a prostate cancer data analysis. [ABSTRACT FROM AUTHOR]

Consider a semiparametric transformation model of the form $$\varLambda _{\theta }(Y)$$ $$= m(X) + \varepsilon $$ , where $$Y$$ is a univariate dependent variable, $$X$$ is a $$d$$ -dimensional covariate, and $$\varepsilon $$ is independent of $$X$$ and has mean zero. We assume that $$\{ \varLambda _{\theta } : \theta \in \varTheta \}$$ is a parametric family of strictly increasing functions, while $$m$$ is an unknown regression function. The goal of the paper is to develop tests for the null hypothesis that $$m(\cdot )$$ belongs to a certain parametric family of regression functions. We propose a Kolmogorov-Smirnov and a Cramér-von Mises type test statistic, which measure the distance between the distribution of $$\varepsilon $$ estimated under the null hypothesis and the distribution of $$\varepsilon $$ without making use of this null hypothesis. The estimated distributions are based on a profile likelihood estimator of $$\theta $$ and a local polynomial estimator of $$m(\cdot )$$ . The limiting distributions of these two test statistics are established under the null hypothesis and under a local alternative. We use a bootstrap procedure to approximate the critical values of the test statistics under the null hypothesis. Finally, a simulation study is carried out to illustrate the performance of our testing procedures, and we apply our tests to data on the scattering of sunlight in the atmosphere. [ABSTRACT FROM AUTHOR]

This paper considers a sparse spiked covariance matrix model in the high-dimensional setting and studies the minimax estimation of the covariance matrix and the principal subspace as well as the minimax rank detection. The optimal rate of convergence for estimating the spiked covariance matrix under the spectral norm is established, which requires significantly different techniques from those for estimating other structured covariance matrices such as bandable or sparse covariance matrices. We also establish the minimax rate under the spectral norm for estimating the principal subspace, the primary object of interest in principal component analysis. In addition, the optimal rate for the rank detection boundary is obtained. This result also resolves the gap in a recent paper by Berthet and Rigollet (Ann Stat 41(4):1780-1815, ) where the special case of rank one is considered. [ABSTRACT FROM AUTHOR]

When permutation methods are used in practice, often a limited number of random permutations are used to decrease the computational burden. However, most theoretical literature assumes that the whole permutation group is used, and methods based on random permutations tend to be seen as approximate. There exists a very limited amount of literature on exact testing with random permutations, and only recently a thorough proof of exactness was given. In this paper, we provide an alternative proof, viewing the test as a “conditional Monte Carlo test” as it has been called in the literature. We also provide extensions of the result. Importantly, our results can be used to prove properties of various multiple testing procedures based on random permutations. [ABSTRACT FROM AUTHOR]

This paper studies the estimation of the characteristic function of a finite population. Specifically, the weak convergence of the finite population empirical characteristic process is studied. Under suitable assumptions, it has the same limit as the empirical characteristic process for independent, identically distributed data from a random variable, up to a multiplicative constant depending on the sampling design. Applications of the obtained results for the two-sample problem, testing for independence and testing for symmetry are given. [ABSTRACT FROM AUTHOR]

This paper is devoted to the estimation of partial derivatives of multivariate density functions. In this regard, nonparametric linear wavelet-based estimators are introduced, showing their attractive properties from the theoretical point of view. In particular, we prove the strong uniform consistency properties of these estimators, over compact subsets of R d , with the determination of the corresponding convergence rates. Then, we establish the asymptotic normality of these estimators. As a main contribution, we relax some standard dependence conditions; our results hold under a weak dependence condition allowing the consideration of mixing, association, Gaussian sequences and Bernoulli shifts. [ABSTRACT FROM AUTHOR]

The paper considers model-based inference for finite population parameters under informative sampling, when the draws of the different units are not independent and the joint selection probability is modeled using a copula. We extend the "sample likelihood" approach to the case of dependent draws and provide the expression of the likelihood given the selected sample, called here "selection likelihood". We show how to derive maximum likelihood estimators of the model parameters based on the resulting selection likelihood. Further, we find optimal predictors of individual values and of finite population parameters under the proposed informative selection models. In an experiment based on the 1988 U.S. National Maternal and Infant Health Survey, results indicate that, for small sample size, the proposed selection likelihood method reduces systematically the bias and standard errors of the estimators obtained from the sample likelihood based on independent draws and become the same for large sample size. It reduces considerably the bias due to informativeness and gives more efficient estimators than the pseudo likelihood (or quasi-likelihood) approach based on weighting the sample estimating equations by the survey weights. [ABSTRACT FROM AUTHOR]

The comparison of two samples is a problem very frequently encountered in practice. There is active interest in researching for tests that are powerful also when the data are not compatible with the assumptions of normality and equal variances – as it is common in many fields – while controlling their type-one error rate. The Yuen test is a familiar method based on trimmed means. There is no agreement in the literature about the preferable rate of trimming. This paper has two aims: to study the power of many Yuen tests with different trimming rates and propose a bootstrap test based on the combination of Yuen tests with different trimming rates. It is shown that the various Yuen tests have very different power for different distributions because the best rate of trimming depends on distribution tailweight. Conversely, the combined test is powerful irrespective to the underlying distribution. [ABSTRACT FROM AUTHOR]

Fiducial inference is applied to nonparametric g-modeling in the discrete case. We propose a computationally efficient algorithm to sample from the fiducial distribution and use the generated samples to construct point estimates and confidence intervals. We study the theoretical properties of the fiducial distribution and perform extensive simulations in various scenarios. The proposed approach gives rise to good statistical performance in terms of the mean squared error of point estimators and coverage of confidence intervals. Furthermore, we apply the proposed fiducial method to estimate the probability of each satellite site being malignant using gastric adenocarcinoma data with 844 patients. [ABSTRACT FROM AUTHOR]

The two-sample problem usually tests for a difference in location. However, there are many situations, for example in biomedicine, where jointly testing for difference in location and variability may be more appropriate. Moreover, heavy-tailed data, outliers and small-sample sizes are common in biomedicine and in other fields. These considerations make the use of nonparametric methods more appealing than parametric ones. The aim of the paper is to contribute to the literature about nonparametric simultaneous location and scale testing. More precisely, several existing tests are generalized and unified, and a new class of tests based on the Mahalanobis distance between the percentile modified test statistics for location and scale differences is introduced. The asymptotic distributions of the test statistics are obtained, and small-sample size behaviour of the tests is studied and compared to other tests via Monte Carlo simulations. It is shown that the proposed class of tests performs well when there are differences in both location and variability. A practical application is presented. [ABSTRACT FROM AUTHOR]

Let X 1 , ... , X n be i.i.d. sample in R p with zero mean and the covariance matrix Σ . The problem of recovering the projector onto an eigenspace of Σ from these observations naturally arises in many applications. Recent technique from Koltchinskii and Lounici (Ann Stat 45(1):121–157, 2017) helps to study the asymptotic distribution of the distance in the Frobenius norm P r - P ^ r 2 between the true projector P r on the subspace of the rth eigenvalue and its empirical counterpart P ^ r in terms of the effective rank of Σ . This paper offers a bootstrap procedure for building sharp confidence sets for the true projector P r from the given data. This procedure does not rely on the asymptotic distribution of P r - P ^ r 2 and its moments. It could be applied for small or moderate sample size n and large dimension p. The main result states the validity of the proposed procedure for Gaussian samples with an explicit error bound for the error of bootstrap approximation. This bound involves some new sharp results on Gaussian comparison and Gaussian anti-concentration in high-dimensional spaces. Numeric results confirm a good performance of the method in realistic examples. [ABSTRACT FROM AUTHOR]

In this paper the Jackknife estimate of covariance of two Kaplan–Meier integrals with covariates is introduced. Its strong consistency is established under mild conditions. Several applications of the estimator are discussed. [ABSTRACT FROM AUTHOR]

This paper develops a bootstrap hypothesis test for the existence of finite moments of a random variable, which is nonparametric and applicable to both independent and dependent data. The test is based on a property in bootstrap asymptotic theory, in which themout ofnbootstrap sample mean is asymptotically normal when the variance of the observations is finite. Consistency of the test is established. Monte Carlo simulations are conducted to illustrate the finite sample performance and compare it with alternative methods available in the literature. Applications to financial data are performed for illustration. [ABSTRACT FROM PUBLISHER]

We provide a new testing procedure to detect serial dependence in time series. Our method is based solely on the ordinal structure of the data. We explicitly allow for ties in the data windows we consider. Consequently, we use generalised ordinal patterns, that is, Cayley permutations. Unlike in the classical case, the pattern distribution is not uniform under the null hypothesis of serial independence. In our new framework, the underlying distribution has to be taken into account and we overcome this problem by a bootstrap procedure. The applicability of our method is supported by a simulation study and two real-world data examples. [ABSTRACT FROM AUTHOR]

In this paper, we propose several new goodness-of-fit tests for normality based on the distance between the observed sample and the predictive sample drawn from the posterior predictive distribution. Note that the predictive sample is stochastic for a set of given sample observations, the distance being consequently random. To circumvent the randomness, we choose the conditional expectation and qth quantile as the test statistics. Two statistics are related to the well-known Shapiro-Francia test, and their asymptotic distributions are derived. The simulation study shows that the new tests are able to better discriminate between the normal distribution and heavy-tailed distributions or mixed normal distributions. Against those alternatives, the new tests are more powerful than existing tests including the Anderson-Darling test and the Shapiro-Wilk test, which are two of the best tests of normality in the literature. [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]

Although there have been fairly recent advances regarding inference for three-dimensional rotation data, there are still many areas of interest yet to be explored. One such area involves comparing the rotational symmetry of 3-D rotations. In this paper, nonparametric inference is used to test if F = F , where F is the degree of rotational symmetry of distribution i, through a permutation test. The validity of the developed permutation test is examined through a simulation study and the test is applied to a small example in biomechanics. [ABSTRACT FROM AUTHOR]

Length-biased data are a particular case of weighted data, which arise in many situations: biomedicine, quality control or epidemiology among others. In this paper we study the theoretical properties of kernel density estimation in the context of length-biased data, proposing two consistent bootstrap methods that we use for bandwidth selection. Apart from the bootstrap bandwidth selectors we suggest a rule-of-thumb. These bandwidth selection proposals are compared with a least-squares cross-validation method. A simulation study is accomplished to understand the behaviour of the procedures in finite samples. [ABSTRACT FROM AUTHOR]

When interval-grouped data are available, the classical Parzen-Rosenblatt kernel density estimator has to be modified to get a computable and useful approach in this context. The new nonparametric grouped data estimator needs of the choice of a smoothing parameter. In this paper, two different bandwidth selectors for this estimator are analyzed. A plug-in bandwidth selector is proposed and its relative rate of convergence obtained. Additionally, a bootstrap algorithm to select the bandwidth in this framework is designed. This method is easy to implement and does not require Monte Carlo. Both proposals are compared through simulations in different scenarios. It is observed that when the sample size is medium or large and grouping is not heavy, both bandwidth selection methods have a similar and good performance. However, when the sample size is large and under heavy grouping scenarios, the bootstrap bandwidth selector leads to better results. [ABSTRACT FROM AUTHOR]

Various statistical tests have been developed for testing the equality of means in matched pairs with missing values. However, most existing methods are commonly based on certain distributional assumptions such as normality, 0-symmetry or homoscedasticity of the data. The aim of this paper is to develop a statistical test that is robust against deviations from such assumptions and also leads to valid inference in case of heteroscedasticity or skewed distributions. This is achieved by applying a clever randomization approach to handle missing data. The resulting test procedure is not only shown to be asymptotically correct but is also finitely exact if the distribution of the data is invariant with respect to the considered randomization group. Its small sample performance is further studied in an extensive simulation study and compared to existing methods. Finally, an illustrative data example is analysed. [ABSTRACT FROM AUTHOR]