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Abstract: We derive the asymptotical distributions of two-sample -statistics and two-sample empirical -quantiles in the case of weakly dependent data. Our results apply to observations that can be represented as functionals of absolutely regular processes, including e.g. many classical time series models as well as data from chaotic dynamical systems. Based on these theoretical results we propose a new robust nonparametric test for the two-sample location problem, which is constructed from the median of pairwise differences between the two samples. We inspect the properties of the test in the case of weakly dependent data and compare the performance with classical tests such as the -test and Wilcoxon’s two-sample rank test with corrections for dependencies. Simulations indicate that the new test offers better power than the Wilcoxon test in case of skewed and heavy tailed distributions, when at least one of the two samples is not very large. The test is then applied for detecting shifts of location in some weakly dependent time series, which are contaminated by outliers. [Copyright &y& Elsevier]

Abstract: We consider the problem of testing whether the common mean of a single -vector of multivariate normal random variables with known variance and unknown common correlation is zero. We derive the standardized likelihood ratio test for known and explore different ways of proceeding with unknown. We evaluate the performance of the standardized statistic where is replaced with an estimate of and determine the critical value that controls the type I error rate for the least favorable in [0,1]. The constant increases with and this procedure has pathological behavior if depends on and converges to zero at a certain rate. As an alternate approach, we replace with the upper limit of a confidence interval chosen so that for all . We determine so that the type I error rate is exactly controlled for all in [0,1]. We also investigate a simpler approach where we bound the type I error rate. The former method performs well for all while the less powerful bound method may be a useful in some settings as a simple approach. The proposed tests can be used in different applications, including within-cluster resampling and combining exchangeable -values. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the problem of testing for variance changes in the linear autoregressive processes including AR() processes when there are autoregressive parameter shifts. In performing a test, we employ the conventional residual CUSUM of squares test (RCUSQ) statistic. The RCUSQ test is based on the subsampling method introduced by Jach and Kokoszka (2004) to eliminate the influence caused by autoregressive parameter shifts. It is shown that under regularity conditions, the test statistic behaves asymptotically the function of a standard Brownian bridge. We establish the asymptotic validity of this method and assess its performance both theoretically and numerically. [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]

Abstract: Item nonresponse occurs frequently in sample surveys and other applications. Imputation is commonly used to fill in the missing item values in a random sample . Fractional linear regression imputation, based on the model with independent zero mean errors , is used to create one or more imputed values in the data file for each missing item , where , is observed completely. Asymptotic normality of the imputed estimators of the mean , distribution function for a given y, and qth quantile is established, assuming that Y is missing at random (MAR) given X. This result is used to obtain normal approximation (NA)-based confidence intervals on and . In the case of , a Bahadur-type representation and Woodruff-type confidence intervals are also obtained. Empirical likelihood (EL) ratios are also obtained and shown to be asymptotically scaled variables. This result is used to obtain asymptotically correct EL-based confidence intervals on and . Results of a simulation study on the finite sample performance of NA-based and EL-based confidence intervals are reported. [Copyright &y& Elsevier]

Abstract: Simultaneous confidence intervals for multinomial proportions are useful in many areas of science. Since 1964, approximate simultaneous confidence intervals have been proposed for multinomial proportions. Although at each point in the parameter space, these confidence sets have asymptotic coverage probability, the exact confidence coefficients of these simultaneous confidence intervals for a fixed sample size are unknown before. In this paper, we propose a procedure for calculating exact confidence coefficients for simultaneous confidence intervals of multinomial proportions for any fixed sample size. With this methodology, exact confidence coefficients can be clearly derived, and the point at which the infimum of the coverage probability occurs can be clearly identified. [Copyright &y& Elsevier]

Abstract: Let be a -valued random vector where the conditional distribution of given is a Poisson distribution with mean . We estimate by a local polynomial kernel estimate defined by maximizing a localized log-likelihood function. We use this estimate of to estimate the conditional distribution of given by a corresponding Poisson distribution and to construct confidence intervals of level of given . Under mild regularity conditions on and on the distribution of we show strong convergence of the integrated distance between Poisson distribution and its estimate. We also demonstrate that the corresponding confidence interval has asymptotically (i.e., for sample size tending to infinity) level , and that the probability that the length of this confidence interval deviates from the optimal length by more than one converges to zero with the number of samples tending to infinity. [Copyright &y& Elsevier]

Abstract: This paper addresses the problem of estimating the monotone boundary of a nonconvex set in a full nonparametric and multivariate setup. This is particularly useful in the context of productivity analysis where the efficient frontier is the locus of optimal production scenarios. Then efficiency scores are defined by the distance of a firm from this efficient boundary. In this setup, the free disposal hull (FDH) estimator has been extensively used due to its flexibility and because it allows nonconvex attainable production sets. However, the nonsmoothness and discontinuities of the FDH is a drawback for conducting inference in finite samples. In particular, it is shown that the bootstrap of the FDH has poor performances and so is not useful in practice. Our estimator, the LFDH, is a linearized version of the FDH, obtained by linear interpolation of appropriate FDH-efficient vertices. It offers a continuous, smooth version of the FDH. We provide an algorithm for computing the estimator, and we establish its asymptotic properties. We also provide an easy way to approximate its asymptotic sampling distribution. The latter could offer bias-corrected estimator and confidence intervals of the efficiency scores. In a Monte Carlo study, we show that these approximations work well even in moderate sample sizes and that our LFDH estimator outperforms, both in bias and in MSE, the original FDH estimator. [Copyright &y& Elsevier]