Testing for and against a set of linear inequality constraints in a multinomial setting

There are numerous situations in categorical data analysis where one wishes to test hypotheses involving a set of linear inequality constraints placed upon the cell probabilities. For example, it may be of interest to test for symmetry in k × k contingency tables against one-sided alternatives. In this case, the null hypothesis imposes a set of linear equalities on the cell probabilities (namely p_ij = P_ji ×i > j), whereas the alternative specifies directional inequalities. Another important application (Robertson, Wright, and Dykstra 1988) is testing for or against stochastic ordering between the marginals of a k × k contingency table when the variables are ordinal and independence holds. Here we extend existing likelihood-ratio results to cover more general situations. To be specific, we consider testing H_t,0 against H₁ - H₀ and H₁ against H₂ - H ₁ when H₀:k × i=1 p_ix_ji = 0, j = 1,…, s, H₁:k × i=1 p_ix_ji × 0, j = 1,…, s, and does not impose any restrictions on p. The x_ji's are known constants, and s × k - 1. We show that the asymptotic distributions of the likelihood-ratio tests are of chi-bar-square type, and provide expressions for the weighting values.     

TESTS FOR SEASONAL DIFFERENCING WITH AN UNKNOWN BREAK-POINT

Some Lagrange multiplier tests for seasonal differencing are proposed; their main objective is to avoid over-differencing due to structural change. The null hypothesis is either the presence of both regular and seasonal unit roots or the presence of a seasonal unit root. Alternative hypotheses allow for stationarity around a possible structural change where the break-point is unknown. The location of the structural change is estimated using the proposed procedures, the asymptotic distribution of the test statistics under the null hypothesis is derived and some useful percentiles are tabulated. An illustrative example based on the Canadian Consumer Price Index is presented.     

Influence and residuals in restricte generalized linear models

A particular influence measure for restricted regression models is reviewed in this paper. We give em- phasis on establishing regularity conditions to apply the proposed influence measure in restricted gen- eralized linear models. The development of conditional residuals is also discussed. In particular, a sim- ulation study was conducted in order to compare the distributions of the proposed residuals for various generalized linear models. Finally, an application is given.     

Measuring Measurement Error in Economic Time Series

A spectral decomposition method is described for obtaining an upper bound on the amount of measurement error in a time series. The method is applied to generated data and to M1b, real GNP, and the CPI. The bounds provide insight into both the amount of measurement error in these series and the stochastic specification of the errors.     

Environmental risk assessment model for low dose extrapolation ∗

Use of experimental data from animal studies to estimate human risk due to long-term exposure to very low doses of chemicals in the environment poses a number of biological and statistical problems. One of the statistical problems is to extrapolate the animal dose-response relation from the high dose levels where data are available to low dose, which humans might encounter. Here, a quantal dose-response model is developed based on a multi-hit theory of toxic response. The development of the model utilizes a weighted Lagrange-Poisson distribution for the number of hits. When spontaneous background toxic response is included, the model involves three unknown parameters. The maximum likelihood estimators for these parameters are given as the solution of a nonlinear iterative algorithm. The use of this model for low-dose extrapolation is indicated. The results are applied to nine sets of toxic response data.     

Formative Indicators and Effects of a Causal Model for Household Human Capital with Application

Dagum and Slottje (2000) estimated household human capital (HC) as a latent variable (LV) and proposed its monetary estimation by means of an actuarial approach. This paper introduces an improved method for the estimation of household HC as an LV by means of formative and reflective indicators in agreement with the accepted economic definition of HC. The monetary value of HC is used in a recursive causal model to obtain short- and long-term multipliers that measure the direct and total effects of the variables that determine household HC. The new method is applied to estimate US household HC for year 2004.     

Censored median regression and profile empirical likelihood

We implement profile empirical likelihood-based inference for censored median regression models. Inference for any specified subvector is carried out by profiling out the nuisance parameters from the “plug-in” empirical likelihood ratio function proposed by Qin and Tsao. To obtain the critical value of the profile empirical likelihood ratio statistic, we first investigate its asymptotic distribution. The limiting distribution is a sum of weighted chi square distributions. Unlike for the full empirical likelihood, however, the derived asymptotic distribution has intractable covariance structure. Therefore, we employ the bootstrap to obtain the critical value, and compare the resulting confidence intervals with the ones obtained through Basawa and Koul’s minimum dispersion statistic. Furthermore, we obtain confidence intervals for the age and treatment effects in a lung cancer data set.     

拉格朗日法对溜管输送混凝土流变数学模型探讨

考虑溜管中混凝土重力与管壁的摩擦力，运用拉格朗日法建立了在重力作用下混凝土在软管溜筒中流变的数学模型，运用牛顿迭代求解，并将计算结果与输送情况作了比较。     

响应变量缺失下半参数变系数EV模型的约束统计推断

文章研究了半参数变系数EV模型在线性约束条件下的估计和检验问题,当响应变量缺失、非参数部分协变量带有测量误差时,利用局部纠偏的Profile最小二乘估计、Lagrange乘子方法和借补技术构造了回归模型参数分量两类纠偏约束估计量。此外,为了检验线性约束条件,构造了借补的Profile Lagrange乘子检验统计量,并通过蒙特卡洛数值模拟验证估计量和检验统计量的有效性。