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This paper considers linear regression models when neither the response variable nor the covariates can be directly observed, but are measured with multiplicative distortion measurement errors. The distortion functions for this kind of measurement errors are modelled under a general identifiability condition. For parameter estimation, we propose two calibration procedures: the conditional mean calibration based least squares estimation and the varying coefficient based estimation. The asymptotic normal confidence intervals and empirical likelihood confidence intervals are also proposed. Simulation studies are conducted to compare the proposed calibration procedures and a real example is analysed to illustrate its practical usage. [ABSTRACT FROM AUTHOR]

Multiple permutation testing is a test method combining the idea of permutation and multiple testing. It first employs the permutation testing to calculate p-values for single tests, and then determines the result based on criteria of multiple testing. To well control type I error rate, the classical method needs a large number of permutation samples for calculating p-values. When the dimension of data, m, is high, the permutation procedure is very time consuming. This paper proposes a components-combined algorithm for the type I error rate control. The new algorithm only requires a small and fixed number of permutation samples for any dimension of data and can achieve the same approximation accuracy of p-values as the classical method. Therefore, it reduces the computational amount of multiple permutation testing procedures from to . The algorithm is then applied to several testing problems and the power performance is examined by simulations and comparisons with existing methods. [ABSTRACT FROM AUTHOR]

Negative binomial group distribution was proposed in the literature which was motivated by inverse sampling when considering group inspection: products are inspected group by group, and the number of non-conforming items of a group is recorded only until the inspection of the whole group is finished. The non-conforming probabilitypof the population is thus the parameter of interest. In this paper, the confidence interval construction for this parameter is investigated. The common normal approximation and exact method are applied. To overcome the drawbacks of these commonly used methods, a composite method that is based on the confidence intervals of the negative binomial distribution is proposed, which benefits from the relationship between negative binomial distribution and negative binomial group distribution. Simulation studies are carried out to examine the performances of our methods. A real data example is also presented to illustrate the application of our method. [ABSTRACT FROM PUBLISHER]

In multiple hypothesis test, an important problem is estimating the proportion of true null hypotheses. Existing methods are mainly based on thep-values of the single tests. In this paper, we propose two new estimations for this proportion. One is a natural extension of the commonly used methods based onp-values and the other is based on a mixed distribution. Simulations show that the first method is comparable with existing methods and performs better under some cases. And the method based on a mixed distribution can get accurate estimators even if the variance of data is large or the difference between the null hypothesis and alternative hypothesis is very small. [ABSTRACT FROM PUBLISHER]

Multiple test based on familywise error rate is a popular problem in statistical inference as testing the null hypothesisH0=H1∩H2∩···∩Hnis true versus the alternative that at least one hypothesis inH1,H2, … ,Hnis false. Classical tests include the Bonferroni test and the Simes test. So far, the most efficient methods for this problem are known as the combinedp-value tests, such as the Fisher's product test, the truncated product method, the rank truncated product test, the adaptive rank truncated product (ARTP) method and Zhang et al.’s [A combinedp-value test for multiple hypothesis testing. J Stat Plan Inference. 2013;143:764–770] test that extends the ARTP method. Our method is based on Zhang et al.’s [A combinedp-value test for multiple hypothesis testing. J Stat Plan Inference. 2013;143:764–770] test and modifies it by using different critical percentile parameter τjfor the statisticwith eachj=1, … ,n. Simulation studies show that the sizes of our test are stable at the significance level and the powers are superior to commonly used methods. [ABSTRACT FROM PUBLISHER]

Birnbaum–Saunders (BS) distribution is widely used in reliability applications to model failure times. For several samples from possible different BS distributions, to prevent wrong conclusions in any further analysis, it is of importance to accompany a formal comparison for characteristic quantities of the distributions, including mean, quantile and reliability function difference. To this end, two test statistics, which are respectively based on the exact generalizedp-value approach and the Delta method, are proposed and their behaviours are investigated. Simulation studies are carried out to examine the size and power performance of the newly proposed statistics. An interesting phenomenon is that in the finite sample simulations we conduct, the Delta method-based test almost uniformly outperforms the generalizedp-value-based test although its sampling null distribution is simulated by Monte Carlo method. This might suggest that the sampling null distribution of the Delta method-based test statistic would have a fast convergence to its limit. The tests are also applied to analyse a real example on the fatigue life of 6061-T6 aluminium coupons for illustration. [ABSTRACT FROM AUTHOR]

One of the most basic and important problems in statistical inference is the construction of the confidence interval (CI). In this paper, we propose a novel CI for a binomial proportion by modifying the midpoint of the score interval. The proposed modified interval can solve the ‘downward spikes’ problem of the score interval without enlarging the interval length. Simulation studies are carried out to illustrate the performance of the modified interval. With regard to the criterions of coverage probability, mean absolute error and expected length, our method is competitive among the several commonly used methods for constructing a CI. A real data example is also presented to show the application of our method. [ABSTRACT FROM AUTHOR]

As a nonparametric randomness test, the positive and negative runs test is widely used in practice due to the simplicity of its procedures. The test can lose efficiency if the alternative distribution is symmetrical at 0.5. In addition, the test can only be applied to test the randomness of a sequence from the uniform distribution. In this paper, we introduce an adaptive positive and negative runs test method to maximize the power function by choosing the optimal cut point. Also, the test is extended to check the randomness of a sequence generated from any other given distributions. Furthermore, we derive the exact distribution and obtain the asymptotical critical values of the proposed test statistics. Compared with the existed test, the efficiency of the proposed adaptive positive and negative runs test is competitive through simulation study. [ABSTRACT FROM AUTHOR]