Asymptotic expansions in non-linear renewal theory

We obtain first order asymptotic expansions for the distribution of the excess of a standard normal random walk over a curved boundary and the error probabilities of some repeated significance tests. The key step in the analysis is an asymptotic expansion for the conditional probability that the random walk has not crossed the boundary before the N step, given that it is near the boundary after the n^th step.     

The union-intersection principle applied to the test of dimensionality

In the first section Anderson-Rao-Fujikoshi's test statistics for testing the hypothesis of dimensionality are reviewed and then Olkin-Tomsky's generalized union-intersection principle is applied to show that a new class of test statistics for testing the hypothesis of dimensionality are derived which includes the likelihood ratio test statistics, the trace test statistics and a version of ROY'S maximum root test statistics.     

NONPARAMETRIC TWO SAMPLE TESTS BASED ON AREA STATISTICS

ABSTRACT

Area statistics are sample versions of areas occurring in a probability plot of two distribution functions F and G. This paper presents a unified basis for five statistics of this type. They can be used for various testing problems in the framework of the two sample problem for independent observations, such as testing equality of distributions against inequality or testing stochastic dominance of distributions in one or either direction against nondominance. Though three of the statistics considered have already been suggested in literature, two of them are new and deserve our interest. The finite sample distributions of the statistics (under F=G) can be calculated via recursion formulae. Two tables with critical values of the new statistics are included. The asymptotic distribution of the properly normalized versions of the area statistics are functionals of the Brownian bridge. The distribution functions and quantiles thereof are obtained by Monte Carlo simulation. Finally, the power functions of the two new tests based on area statistics are compared to the power functions of the tests based on the corresponding supremum statistics, i.e., statistics of the Kolmogorov–Smirnov type.     

The periodogram regression:correction and comments

Ratios of periodogram and spectral density at different harmonic frequencies are independent if the frequency zero is approached slowly enough. This is an asymptotically relevant condition for the periodogram regression to work with fractionally integrated series. In finite samples, however, this theoretical condition should be ignored as we illustrate experimentally.     

Group sequential x2 statistic for testing the difference of two mean vectors in clinical trials

In this study we discuss the group sequential procedures for comparing two treatments based on multivariate observations in clinical trials. Also we suppose that a response vector on each of two treatments has a multivariate normal distribution with unknown covariance matrix. Then we propose a group sequential x² statistic in order to carry out repeated significance test for hypothesis of no difference between two population mean vectors. In order to realize the group sequential test where average sample number is reduced, we propose another modified group sequential x² statistic by extension of Jennison and Turnbull ( 1991 ). After construction of repeated confidence boundaries for making the repeated significance test, we compare two group sequential procedures based on two statistics regarding the average sample number and the power of the test in the simulations.     

Asymptotic expansions for sequential confidence levels in inverse linear regression

Non-linear renewal theory is used to derive second order asymptotic expansions for the coverage probability of a fixed-width sequential confidence interval for an unknown parameter xin the inverse linear regression model. These expansions are obtained for a two-stage sequential procedure, proposed by Perng and Tong (1974) for the construction of a confidence interval for x.     

Nonparametric and semiparametric estimation of the three way receiver operating characteristic surface

In many situations the diagnostic decision is not limited to a binary choice. Binary statistical tools such as receiver operating characteristic (ROC) curve and area under the ROC curve (AUC) need to be expanded to address three-category classification problem. Previous authors have suggest various ways to model the extension of AUC but not the ROC surface. Only simple parametric approaches are proposed for modeling the ROC measure under the assumption that test results all follow normal distributions. We study the estimation methods of three-dimensional ROC surfaces with nonparametric and semiparametric estimators. Asymptotical results are provided as a basis for statistical inference. Simulation studies are performed to assess the validity of our proposed methods in finite samples. We consider an Alzheimer's disease example from a clinical study in the US as an illustration. The nonparametric and semiparametric modelling approaches for the three way ROC analysis can be readily generalized to diagnostic problems with more than three classes.     

Nonparametric control charts based on runs and Wilcoxon-type rank-sum statistics

In this article, we introduce three new distribution-free Shewhart-type control charts that exploit run and Wilcoxon-type rank-sum statistics to detect possible shifts of a monitored process. Exact formulae for the alarm rate, the run length distribution, and the average run length (ARL) are all derived. A key advantage of these charts is that, due to their nonparametric nature, the false alarm rate (FAR) and in-control run length distribution is the same for all continuous process distributions. Tables are provided for the implementation of the charts for some typical FAR values. Furthermore, a numerical study carried out reveals that the new charts are quite flexible and efficient in detecting shifts to Lehmann-type out-of-control situations.     

The Semiparametric Normal Variance-Mean Mixture Model

We study the normal variance-mean mixture model from a semiparametric point of view, i.e. we let the mixing distribution belong to a non-parametric family. The main results are consistency of the non-parametric maximum likelihood estimator and construction of an asymptotically normal and efficient estimator for the Euclidian part of the parameter. We study the model according to the theory outlined in the monograph by Bickel et al. (1993) and apply a general result (based on the theory of empirical processes) for semiparametric models from van der Vaart (1996) to prove asymptotic normality and efficiency of the proposed estimator.     

五四新文化运动与欧洲文艺复兴运动比较

五四新文化运动与欧洲文艺复兴运动生成于不同时期,植根于不同土壤,二者既有一些共同之处,又有不少差异。对其进行比较,有助于加深我们对两个运动各自特性的认识。其共同点是：（一）对传统的批判与重建;（二）倡导文学革命;（三）抨击封建权威思想;（四）呼唤人性的复苏,倡导个人的解放。其不同点是：（一）背景不同;（二）影响力不同;（三）带来的后果不同。