Score and Wald tests for the multivariate growth curve model with missing data

We present the score and Wald test analogues to Srivastava's (1985, Comm. Statist. A—Theory Methods, 14, 775–792) likelihood ratio tests for the multivariate growth curve model with missing data, and illustrate their use with data from an immunotherapy experiment (Fukushima et al. (1982, Int. J. Cancer, 29, 107–112, 113–117)).     

On the consistency and finite-sample properties of nonparametric kernel time series regression,autoregression and density estimators

Summary Kernel estimators of conditional expectations and joint probability densities are studied in the context of a vector-valued stationary time series. Weak consistency is established under minimal moment conditions and under a hierarchy of weak dependence and bandwidth conditions. Prompted by these conditions, some finite-sample theory explores the effect of serial dependence on variability of estimators, and its implications for choice of bandwidth. This research was supported by the ESRC.     

Generalized Wald equations in discrete time

Let S = {S_n, n ? 1} be a martingale. Expectations of m^th order quantities associated with S are related by two forms of Wald-type identity, called Generalized Wald equations. The previously known sufficient conditions for the validity of Wald equations are shown to be of a set of three equivalent conditions, each of which is necessary as well as sufficient for the validity of both types of Generalized Wald Equation.     

Asymptotic properties of rank tests under discrete distributions

Summary This paper is devoted to problems of rank tests when samples are drawn from purely discrete distributions. There are considered two ways of treatment of ties, and the distribution of the respective test statistics is derived under the hypothesis of randomness and under the contiguous alternative. Furthermore, their asymptotic power and efficiency are established.     

协整关系中门限效应的Wald检验

在协整的三角表示形式中,利用Wald检验方法检验协整回归关系中存在的门限非线性.在线性协整的原假设下构造了Wald统计量及其泛函形式,给出了不依赖于门限参数的极限分布.利用模拟计算研究了所提检验的有限样本性质.对不同到期时间的债券利率进行检验,结果表明利率之间具有门限协整关系.     

On a theorem of Wald and Wolfowitz on randomization in statistics

In [9] it is proved that to each randomized decision function, there exists an equivalent randomized decision rule (cf. [3]), provided that the space of decisions is Polish. The object of the present paper is to show that the above theorem is a special case of risk-equivalence (cf. [5]) even if the space of decisions is analytic.     

Structure,properties, and tests of carbonreinforced plastics

The effect has been examined of various factors on the realization of mean values of mechanical properties in monofilaments in composites; the necessity has been pointed out of taking account of specific characteristics of the structure and behavior of reinforced polymers based on carbon fibers during determination of strain and tensile properties of these materials.     

Numerical simulations of spalling tests in order to investigate material properties of UHPC

In order to evaluate the material composition of Ultra High Performance Concrete (UHPC), material properties such as dynamic tensile strength or fracture strength and also the fracture energy under impact loading are of significant importance. The use of a modified Hopkinson Bar enables the determination of the required data. On the basis of experimental investigations our contribution deals with the numerical finite element simulation of the Hopkinson Bar test. The propagation of stress waves is reproduced by means of a special time-integration scheme. We simulate the propagation of cracks by using adaptive cohesive elements including a corresponding separation law. The critical energy release rate (Griffith-energy) is calculated and compared to the values determined by experimental results. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Theoretical properties and numerical tests of an efficient nonlinear decomposition algorithm

Kronsjö's nonlinear generalization (Ref. 1) of Benders' algorithm (Ref. 2) is reviewed. At each iteration, this algorithm produces upper and lower bounds to the true optimum, and the sequence of lower bounds is increasing. The algorithm is modified, so that the sequence of upper bounds is -decreasing as well. The two versions are tested numerically using an ALGOL program originally written by Wong (Ref. 3), incorporating the SUMT method (Fiacco and McCormick, Refs. 4 and 5). The two versions are compared against each other, and the problem of the optimal degree of decomposition is considered. Finally, an attempt is made to express the computer time required to solve the test problems as a function of master problem size, number of subproblems, and average subproblem size.The author wishes to express his gratitude to Professor T. O. M. Kronsjö for valuable help and comments.     

Small sample properties of the power function ofF tests in two-way error component regression

In this paper we investigate properties of the power function of the generalized least squaresF test for linear hypotheses under regression models with two-way error component model. The covariance structure of the model depends on the correlation coefficients ρ1 and ρ2 corresponding to the random effects. This model has been frequently applied to the analysis of panel data. In general, we show that the power is a monotonically increasing function of ρ1(ρ2) in a region which is close to the ρ1(ρ2) axis, and a monotonically decreasing function of ρ1(ρ2) in a region close to the ρ2(ρ1) axis. This research is supported by the National Natural Science Foundation of China, the Natural Science Foundation of Beijing, a project of Science and Technology of Beijing Education Committee, the Academy of Finland, and the University of Tampere.     

Compact Matrix Expressions for Generalized Wald Tests of Equality of Moment Vectors

Asymptotic chi-squared test statistics for testing the equality of moment vectors are developed. The test statistics proposed are generalized Wald test statistics that specialize for different settings by inserting an appropriate asymptotic variance matrix of sample moments. Scaled test statistics are also considered for dealing with nonstandard conditions. The specialization will be carried out for testing the equality of multinomial populations, and the equality of variance and correlation matrices for both normal and nonnormal data. When testing the equality of correlation matrices, a scaled version of the normal theory chi-squared statistic is proven to be an asymptotically exact chi-squared statistic in the case of elliptical data.     

Asymptotic properties of some goodness-of-fit tests based on the L 1-norm

Some goodness-of-fit tests based on the L ₁-norm are considered. The asymptotic distribution of each statistic under the null hypothesis is the distribution of the L ₁-norm of the standard Wiener process on [0,1]. The distribution function, the density function and a table of some percentage points of the distribution are given. A result for the asymptotic tail probability of the L ₁-norm of a Gaussian process is also obtained. The result is useful for giving the approximate Bahadur efficiency of the test statistics whose asymptotic distributions are represented as the L ₁-norms of Gaussian processes.     

Robustness of sign tests in autoregression

The robustness of sign tests in autoregression against outliers is studied. The local scheme of observations contamination by additive isolated outliers with the intensity O(n ^?1/2) is considered, n is the number of observations.     

Bootstrap tests in correspondence analysis

A bootstrap test is developed for testing models specified by Goodman in 1985 and 1986 for the correspondence analysis of two-way contingency tables. It enables testing goodness-of-fit in relation with the usual matrix decomposition method. An approximate table of critical values for the proposed test statistic is presented. Bootstrap confidence interval construction is also included. The behaviour of the test statistic and the confidence intervals is studied using Monte Carlo simulation.     

Second-order tests in optimization theories

There are two main kinds of second-order tests in optimization theories. The simplest tests (Refs. 1–13), such as the generalized Legendre-Clebsch condition, require a local study around points of the trajectory of interest (generally, on a singular arc). Tests of the second kind (Refs. 14–22 and 51–53) are more difficult to use but also more efficient: they can be applied under various assumptions of convexity or linearity and generally require some integrations along the trajectory of interest (usually, these integrations can only be done by numerical methods). In favorable cases, the better tests of this second kind lead to either the conclusion of nonoptimality or the conclusion of local optimality. This survey paper begins with a broader question, the question of sufficient conditions for absolute optimality. Some results of this study are used to define anadjoint matrix (extension of the notion ofadjoint vector of Pontryagin). Then, the different second-order tests can be unified and generalized even if the trajectory of interest has switches and singular arcs. On a given trajectory, theconjugate points are easily related to the evolution of the adjoint matrix. Finally, this generalized second-order test is applied to a singular arc of astrodynamics, the reversible arc: this arc is globally optimal from end to end.     

Extension to Markov processes of a result by A. Wald about the consistency of the maximum likelihood estimate

Summary In this note the proof of the consistency of a maximum likelihood estimate (MLE) obtained by Wald in [7] in the case of independent and identically distributed random variables is extended to the case of Markov processes.There is an extensive literature about the existence of a MLE and its consistency, most of which includes the assumption of the existence of derivatives of the densities with respect to the parameter involved. (See, for example, [2] and other references cited there.) Even under the rather strong assumption of pointwise differentiability of densities, and other additional regularity conditions, the problem of existence and consistency of a MLE has not been solved satisfactorily. (See, for example, [1], [2], [4], [6].) On the other hand, there have appeared papers like [3], where the consistency of a MLE is proved for processes with dependent random variables, and without the usual differentiability assumptions. The conditions used in the present paper are, however, of a different nature from those imposed in [3], and also are slightly different from Wald's assumptions in [7]. To our knowledge, a proof of consistency of a MLE under conditions similar to the ones used here has not appeared in the literature.I would like to take this opportunity to thank Professor L. LeCam for a number of remarks in connection with this paper.Prepared with the partial support of the National Science Foundation, Grant GP-10.