Tests of ordered hypotheses in linkage in heredity

The asymptotic null distribution of the likelihood ratio test for two cases of ordered hypotheses in a particular genetic model is considered. A simple iterative process is proposed in order to get the restricted estimates. It is shown that both tests have asymptotically a chi-bar squared distribution and the same size. A simulation study is also conducted in order to compare the usual unrestricted test with the corresponding one of ordered hypotheses. Finally, the results are extended to some special cases.     

Two tests for multivariate normality based on the characteristic function

We present two tests for multivariate normality. The presented tests are based on the Lévy characterization of the normal distribution and on the BHEP tests. The tests are affine invariant and consistent. We obtain the asymptotic null distribution of the test statistics using some results about generalized one-sample U-statistics, which are of independent interest.      

Testing for Uniformity of the Residual Life Time Based on Dynamic Kullback-Leibler Information

In this article a goodness of fit test for distributional assumptions regarding the residual lifetime is proposed. The test is based on a Vasicek type sum log-spacings estimators of a dynamic version of Kullback-Leibler information. The specific distributional hypothesis considered is of the uniformity over [0,1]. However, the test can be used for testing any simple goodness of fit hypothesis. The asymptotic distribution of the test statistic together with a tabulation of the critical points for different sample sizes are given. Finally, the power function of the test is empirically studied in comparison with some competitors, and the test appears to be meritorious.     

A class of rank-based test for left-truncated and right-censored data

A class of rank-based tests is proposed for the two-sample problem with left-truncated and right-censored data. The class contains as special cases the extension of log-rank test and Gehan test. The asymptotic distribution theory of the test is presented. The small-sample performance of the test is investigated under a variety of situations by means of Mone Carlo simulations.     

Goodness-of-Fit Tests for the Inverse Gaussian Distribution Based on the Empirical Laplace Transform

This paper considers two flexible classes of omnibus goodness-of-fit tests for the inverse Gaussian distribution. The test statistics are weighted integrals over the squared modulus of some measure of deviation of the empirical distribution of given data from the family of inverse Gaussian laws, expressed by means of the empirical Laplace transform. Both classes of statistics are connected to the first nonzero component of Neyman's smooth test for the inverse Gaussian distribution. The tests, when implemented via the parametric bootstrap, maintain a nominal level of significance very closely. A large-scale simulation study shows that the new tests compare favorably with classical goodness-of-fit tests for the inverse Gaussian distribution, based on the empirical distribution function.     

Goodness-Of-Fit Tests Based on Estimated Expectations of Probability Integral Transformed Order Statistics

New goodness-of-fit tests, based on bootstrap estimated expectations of probability integral transformed order statistics, are derived for the location-scale model. The resulting test statistics are location and scale invariant, and are sensitive to discrepancies at the tails of the hypothesized distribution. The limiting null distributions of the test statistics are derived in terms of functionals of a certain Gaussian process, and the tests are shown to be consistent against a broad family of alternatives. Critical points for all sample sizes are provided for tests of normality. A simulation study shows that the proposed tests are more powerful than established tests such as Shapiro-Wilk, Cramér-von Mises and Anderson-Darling, for a wide range of alternative distributions.     

Nonparametric tests based on N-distances

This paper is devoted to goodness-of-fit and homogeneity tests based on N-distances. The work is a continuation of our research started in [2]. The power of the proposed criteria is compared with classical tests using Monte Carlo simulations. Different alternatives both in one-and multidimensional cases are investigated. Applications of N-distance statistics for testing hypotheses of symmetry (univariate case) and independence (bivariate case) are provided.     

The asymptotic power of rank tests under scale-al ternatives including contaminated distributions

Summary The alternative hypothesis of translated scale for the classical non-parametric hypothesis of equality of two distribution functions in the two-sample problem is extended to a scale-alternative including contamination. The asymptotic power of rank tests and the two-sampleF-test under contiguous sequences of the alternatives is derived and asymptotic relative efficiency of these rank tests with respect to theF-test is investigated. It is found that some of the rank tests have reasonably high asymptotic powers satisfied enough.     

几类改进的新的两步六阶Chebyshev-Halley方法

利用权函数法,给出非线性方程求根的Chebyshev-Halley方法的几类改进方法,证明方法六阶收敛到单根.Chebyshev-Halley方法的效率指数为1.442,改进后的两步方法的效率指数为1.565.最后给出数值试验,且与牛顿法,Chebyshev-Halley 方法及其它已知的方程求根方法做了比较.结果表明方法具有一定的优越性.     

On score-functions and goodness-of-fit tests for stochastic processes

The problems of the construction of asymptotically distribution free goodness-of-fit tests for two diffusion processes are considered. The null hypothesis is composite parametric. All tests are based on the score-function processes, where the unknown parameter is replaced by the maximum likelihood estimators. We show that a special change of time transforms the limit score-function processes into the Brownian bridge. This property allows us to construct asymptotically distribution-free tests for dynamical systems with small noise and ergodic diffusion processes. The proposed tests are in some sense universal. We discuss the possibilities of the construction of asymptotically distribution free tests for inhomogeneous Poisson processes and nonlinear AR time series.     

Optimal testing strategies in overlapped design process

Testing is an important activity in product development. Past studies, which are developed to determine the optimal scheduling of tests, often focused on single-stage testing of sequential design process. This paper presents an analytical model for the scheduling of tests in overlapped design process, where a downstream stage starts before the completion of upstream testing. We derive optimal stopping rules for upstream and downstream stages’ testing, together with the optimal time elapsed between beginning the upstream tests and beginning the downstream development. We find that the cost function is first convex then concave increasing with respect to upstream testing duration. A one-dimensional search algorithm is then proposed for finding the unique optimum that minimizes the overall cost. Moreover, the impact of different model parameters, such as the problem-solving capacity and opportunity cost, on the optimal solution is discussed. Finally, we compare the testing strategies in overlapped process with those in sequential process, and get some additional results. The methodology is illustrated with a case study at a handset design company.     

Permutation Tests for Reflected Symmetry

The paper presents a permutation procedure for testing reflected (or diagonal) symmetry of the distribution of a multivariate variable. The test statistics are based in empirical characteristic functions. The resulting permutation tests are strictly distribution free under the null hypothesis that the underlying variables are symmetrically distributed about a center. Furthermore, the permutation tests are strictly valid if the symmetric center is known and are asymptotic valid if the center is an unknown point. The equivalence, in the large sample sense, between the tests and their permutation counterparts are established. The power behavior of the tests and their permutation counterparts under local alternative are investigated. Some simulations with small sample sizes (?20) are conducted to demonstrate how the permutation tests works.     

基于主Hessian方向的中央均值子空间边际坐标检验

本文给出了基于两种相近的主Hessian方向方法的边际坐标检验. 这种检验方法能够非常有效的识别自变量对于回归均值中央子空间的贡献. 此外, 与利用切片逆回归和切片平均方差估计的检验方法不同的是, 本文中主Hessian方向的检验方法可以避免对切片数目的选择. 我们证明了检验统计量在原假设下的渐近分布, 并且通过模拟, 证实了检验的有效性.     

Estimation of systems with statistically-constrained inputs

This paper discusses the estimation of a class of discrete-time linear stochastic systems with statistically-constrained unknown inputs (UI), which can represent an arbitrary combination of a class of un-modeled dynamics, random UI with unknown covariance matrix and deterministic UI. In filter design, an upper bound filter is explored to compute, recursively and adaptively, the upper bounds of covariance matrices of the state prediction error, innovation and state estimate error. Furthermore, the minimum upper bound filter (MUBF) is obtained via online scalar parameter convex optimization in pursuit of the minimum upper bounds. Two examples, a system with multiple piecewise UIs and a continuous stirred tank reactor (CSTR), are used to illustrate the proposed MUBF scheme and verify its performance.     

Score tests for inverse Gaussian mixtures

The mixed inverse Gaussian given by Whitmore (biScand. J. Statist., 13 , 1986, 211–220) provides a convenient way for testing the goodness‐of‐fit of a pure inverse Gaussian distribution. The test is a one‐sided score test with the null hypothesis being the pure inverse Gaussian (i.e. the mixing parameter is zero) and the alternative a mixture. We devise a simple score test and study its finite sample properties. Monte Carlo results show that it compares favourably with the smooth test of Ducharme ( Test , 10 , 2001, 271‐290). In practical applications, when the pure inverse Gaussian distribution is rejected, one is interested in making inference about the general values of the mixing parameter. However, as it is well known that the inverse Gaussian mixture is a defective distribution; hence, the standard likelihood inference cannot be applied. We propose several alternatives and provide score tests for the mixing parameter. Finite sample properties of these tests are examined by Monte Carlo simulation. Copyright © 2010 John Wiley & Sons, Ltd.     

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??In this paper, we focus on the tests for covariance matrices in panel data model with interactive fixed effects. For the problem of testing identity and sphericity of covariance matrices, we first propose test statistics based on the estimators of the trace of covariance matrices. Under both the null hypothesis and the alternatives, we establish the asymptotic distributions of the proposed test statistics under some regularity conditions, and we further show that the proposed tests are distribution free. Subsequently simulation studies suggest that the proposed tests perform well under the high dimensional panel data.     

Testing for Covariance Matrices in Panel Data Models with Interactive Fixed Effect

In this paper, we focus on the tests for covariance matrices in panel data model with interactive fixed effects. For the problem of testing identity and sphericity of covariance matrices, we first propose test statistics based on the estimators of the trace of covariance matrices. Under both the null hypothesis and the alternatives, we establish the asymptotic distributions of the proposed test statistics under some regularity conditions, and we further show that the proposed tests are distribution free. Subsequently simulation studies suggest that the proposed tests perform well under the high dimensional panel data.     

Locally optimal rank tests for independence

The problem of testing the hypothesis of independence against multiparametrical set of alternatives is considered. Rank tests, having some locally maximin property are studied and a certain characterization of these tests is given. Finite sample and asymptotic test statistics in a restricted class of tests are derived.     

Some Simple Test Procedures for Normal Mean Vector with Incomplete Data

The problem of testing normal mean vector when the observations are missing from subsets of components is considered. For a data matrix with a monotone pattern, three simple exact tests are proposed as alternatives to the traditional likelihood ratio test. Numerical power comparisons between the proposed tests and the likelihood ratio test suggest that one of the proposed tests is indeed comparable to the likelihood ratio test and the other two tests perform better than the likelihood ratio test over a part of the parameter space. The results are extended to a nonmonotone pattern and illustrated using an example.     

On goodness-of-fit testing for ergodic diffusion process with shift parameter

A problem of goodness-of-fit test for ergodic diffusion processes is presented. In the null hypothesis the drift of the diffusion is supposed to be in a parametric form with unknown shift parameter. Two Cramer–von Mises type test statistics are studied. The first test uses the local time estimator of the invariant density, the second one uses the empirical distribution function. The unknown parameter is estimated via the maximum likelihood estimator. It is shown that the limit distribution of the two test statistics does not depend on the unknown parameter, thus both the tests are asymptotically parameter free. Some considerations on the consistency of the proposed tests and some simulation studies are also given.