《Journal of nonparametric statistics》2012,24(3):239-253

We apply the saddlepoint approximation of Gatto and Ronchetti (1996) to the multivariate R-estimator in the linear regression model. We derive confidence intervals from the saddlepoint approximation, following the bias-corrected method of Efron (1987). Our numerical examples show the approximations of marginal densities and confidence intervals to be accurate.  相似文献   

    

《Journal of nonparametric statistics》2012,24(3):279-293

This investigation proposes consistent nonparametric tests for the hypothesis that a distribution is symmetric about a known median, taken without loss of generality to be zero. These tests are based on the L L₂ no₂ norm and the celebrated kernel method of density estimation. The test statistics when appropriately centered and scaled are asymptotically normal under the null hypothesis. Generalization of the procedure to the case of testing symmetry of residuals in the linear regression model is given offering a more advantageous procedure to that of Fan and Gencay (1995). The procedure is also shown to apply to the case of testing “bivariate symmetry”, cf. Hollander (1971).  相似文献   

    

《Journal of nonparametric statistics》2012,24(2):149-166

In this paper, we focus on a fundamental reliability measure, the discrete-time intensity of the hitting time (DTIHT), which is the discrete analogue of the rate of occurrence of failures. The problem of evaluating and estimating the DTIHT is addressed for the first time for semi-Markov chains. First, a simple formula for the evaluation of the DTIHT is derived. Following the previous result, a statistical estimator of this plug-in type function is proposed. The main results given here are the asymptotic properties of this estimator, including the strong consistency and the asymptotic normality. Second, the DTIHT is investigated for hidden Markov renewal chains. Following its evaluation, a statistical estimator is suggested whose asymptotic properties are studied. Finally, we give some numerical examples for illustration purposes. The derived models and results can be used to typical reliability problems encountered in different scientific disciplines.  相似文献   

    

《Journal of nonparametric statistics》2012,24(4):923-937

This work provides a new nonparametric test with a flavour of the classical Mann–Whitney test for the isotonic change-point problem on correlated data with short-range dependence. The test statistic has a normal null limiting distribution and asymptotic test power 1 under the local alternative. Numerical study indicates that it has a similar or slightly better performance than the oracle form of the existing tests on independent data and works very well on moderate-sized correlated data where the existing tests usually fail. Its application to the global temperature data is presented.  相似文献   

    

《Journal of nonparametric statistics》2012,24(2):197-212

A two-sample sign test is developed for ranked set samples. It is shown that the testing procedure is distribution free but requires evaluation of the incomplete beta function. Efficiency and type I error, in general, depend on the measured observations and the ratio of cycle sizes. It is shown that there is a substantial gain in the efficiency of the test even when there are ranking errors. On the other hand, the type I error is inflated for imperfect ranking. The proposed test is superior to the two-sample Mann-Whitney-Wilcoxon ranked set sample test when the underlying probability model has heavy and long tail distribution, and the number of quantified observations in each cycle is small. We provide a simple way to implement the procedure.  相似文献   

    

《Journal of nonparametric statistics》2012,24(2):183-196

A new nonparametric test for simple linear regression that is resistant to gross errors is introduced for testing the null hypothesis H ₀α = α₀ β = β₀ against all alternatives. Using test resistances, the proposed test is shown to be more resistant to gross errors than the Brown-Mood and the Lancaster-Quade tests. Next, an alternative point extimate for the slope is proposed. It is shown that the proposed estimator attains the highest possible breakdown point. Finally, these findings are illustrated by an example.  相似文献   

    

《Journal of nonparametric statistics》2012,24(2):279-289

This paper is concerned with the sign test under unbalanced ranked-set sampling (URSS), which constitutes a generalization of the usual ranked-set sampling (RSS). The null distribution properties of the URSS sign test are discussed. Accordingly, a URSS sign test optimized on the basis of the asymptotic relative efficiency criterion is introduced. The proposed test is compared with the RSS analog by means of both asymptotic relative efficiency properties as well as small-sample Monte Carlo power simulations. The results strongly encourage the use of the optimized URSS sign test.  相似文献   

    

《Journal of Statistical Computation and Simulation》2012,82(3):189-211

This article presents tests for neglected non-linearity based on order statistics. The tests rely on the estimation of parametric and non-parametric models. The parametric model imposes linearity and is estimated using least squares and, in turn, quantile regressions. The non-parametric model is estimated by implementing nearest neighbor on induced order observations. When we implement the quantile regression estimates, we analyze robust parametric and robust non-parametric results. This avoids faulty inference caused by the lack of robustness of the least squares estimator and allows us to avoid any distributional assumption. The proposed tests are easier to compute than the existing tests based on series expansions. Simulations and examples analyze their behavior and their robustness in the presence of outliers.  相似文献   

    

《Journal of nonparametric statistics》2012,24(4):485-500

A generalization of the Cramer-vonMises L2 distance is proposed. It gives rise to a class of goodness-of-fit statistics that is difficult to analyze using traditional techniques based on empirical distributions but can easily be modified to yield null and non null limiting normal distributions. The family index may be used to maximize the power of the test for a specific alternative hypothesis. The procedure presented here is shown to work for Watson's modification for circular data and also when testing symmetry about the zero. The problem of testing two-samples is also presented. All procedures presented here are distributions-free and can be used equally for univariate or multivariate data.  相似文献   

    

《Journal of nonparametric statistics》2012,24(2):177-191

Using subspaces to describe the nonparametric null hypotheses introduced in Akritas and Arnold [Fully nonparametric hypotheses for factorial designs I: multivariate repeated measures designs, J. Amer. Statist. Assoc. 89 (1994), pp. 336–343.], leads to a natural extension of the models and the class of nonparametric hypotheses considered there. Nonparametric versions of all saturated or unsaturated parametric models for factorial designs, as well as nonparametric versions of all parametric hypotheses considered in such contexts, are included in the new formulation. To test these new hypotheses we introduce a new family of (mid-)rank statistics. The new statistics are modelled after the weighted F-statistics and are appropriate for (possibly) unbalanced designs with independent observations that can be heteroscedastic. Being rank versions of likelihood ratio statistics, the proposed statistics apply in situations where the Wald-type rank statistics of Akritas, Arnold and Brunner [Nonparametric hypotheses and rank statistics for unbalanced factorial designs, J. Amer. Statist. Assoc. 92 (1997), pp. 258–265.] have not been extended and are at least as efficient in the cases where both apply. We show that the new rank statistics converge in distribution to central chi-squared distributions under their respective null hypotheses. Finding the asymptotic distribution of statistics without a closed form expression requires a novel approach, which we introduce. A simulation study compares the achieved level and power of the new statistics with a number of competing procedures.  相似文献