Convergence of non-linear functionals of smoothed empirical processes and kernel density estimates

We consider regularizations by convolution of the empirical process and study the asymptotic behaviour of non-linear functionals of this process. Using a result for the same type of non-linear functionals of the Brownian bridge, shown in a previous paper [4], and a strong approximation theorem, we prove several results for the p-deviation in estimation of the derivatives of the density. We also study the asymptotic behaviour of the number of crossings of the smoothed empirical process defined by Yukich [17] and of a modified version of the Kullback deviation.     

润滑油脂中抗氧化添加剂作用机理

本文针对润滑油及润滑脂中主要添加剂──抗氧化添加剂的作用机理，从化学反应角度进行理论探讨，并进行了实例分析．     

Parameter estimation in semi-linear models using a maximal invariant likelihood function

In this paper, we consider the problem of estimation of semi-linear regression models. Using invariance arguments, Bhowmik and King [2007. Maximal invariant likelihood based testing of semi-linear models. Statist. Papers 48, 357–383] derived the probability density function of the maximal invariant statistic for the non-linear component of these models. Using this density function as a likelihood function allows us to estimate these models in a two-step process. First the non-linear component parameters are estimated by maximising the maximal invariant likelihood function. Then the non-linear component, with the parameter values replaced by estimates, is treated as a regressor and ordinary least squares is used to estimate the remaining parameters. We report the results of a simulation study conducted to compare the accuracy of this approach with full maximum likelihood and maximum profile-marginal likelihood estimation. We find maximising the maximal invariant likelihood function typically results in less biased and lower variance estimates than those from full maximum likelihood.     

Non-linear state space modelling of fisheries biomass dynamics by using Metropolis-Hastings within-Gibbs sampling

State space modelling and Bayesian analysis are both active areas of applied research in fisheries stock assessment. Combining these two methodologies facilitates the fitting of state space models that may be non-linear and have non-normal errors, and hence it is particularly useful for modelling fisheries dynamics. Here, this approach is demonstrated by fitting a non-linear surplus production model to data on South Atlantic albacore tuna ( Thunnus alalunga ). The state space approach allows for random variability in both the data (the measurement of relative biomass) and in annual biomass dynamics of the tuna stock. Sampling from the joint posterior distribution of the unobservables was achieved by using Metropolis-Hastings within-Gibbs sampling.     

Combining non-linear regressions that have unequal error variances and some parameters in common

Methods of estimation and inference are presented for the situation where two non-linear regression models with unequal error variances contain some parameters in common. Such a situation arises in structural chemistry, when bond lengths are available for three nearly collinear atoms in crystals and a model is required to quantify the extent and form of the relationship between the longer and the shorter bond. Some atomic triples are symmetric and require a different model and error variance from those required by the asymmetric triples. The profile likelihood for the regression parameters is a weighted sum of the logarithms of the sums-of-squares functions from each model, and the estimates can be obtained by using a simple modification to a standard non-linear least squares program. A likelihood ratio test for assessing whether the parameters in common are equal is described. When these techniques are applied to two data sets consisting of bond lengths for bromine–tellurium–bromine and sulphur–tellurium–sulphur triples, there is no evidence against the equality hypothesis. An extension to the model to allow for a non-constant variance is required for proper analysis of the sulphur–tellurium–sulphur data.     

Pre-checking for non-monotonicity of the Wald statistic

The non-monotonic behaviour of the Wald test in some finite-sample applications leads to low power when the null hypothesis needs rejection most. This article proposes a simple check for discerning if the Wald statistic for testing significance of regression coefficients is non-monotonic in the neighbourhood of the parameter space from which the sample data are drawn. Monte Carlo simulations show that this method works rather well for detecting situations where the Wald test can be safely applied. An example is provided to illustrate the use of this check.     

Analysis of the human sex ratio by using overdispersion models

For study of the human sex ratio, one of the most important data sets was collected in Saxony in the 19th century by Geissler. The data contain the sizes of families, with the sex of all children, at the time of registration of the birth of a child. These data are reanalysed to determine how the probability for each sex changes with family size. Three models for overdispersion are fitted: the beta–binomial model of Skellam, the 'multiplicative' binomial model of Altham and the double-binomial model of Efron. For each distribution, both the probability and the dispersion parameters are allowed to vary simultaneously with family size according to two separate regression equations. A finite mixture model is also fitted. The models are fitted using non-linear Poisson regression. They are compared using direct likelihood methods based on the Akaike information criterion. The multiplicative and beta–binomial models provide similar fits, substantially better than that of the double-binomial model. All models show that both the probability that the child is a boy and the dispersion are greater in larger families. There is also some indication that a point probability mass is needed for families containing children uniquely of one sex.     

我国通货膨胀率非线性特征研究

 本文应用带单位根的门限自回归模型,对我国1990年来以来通货膨胀率的动态路径进行了模拟分析。估计和检验发现了我国通货膨胀具有明显的非线性特征,模型较好地拟合了通货膨胀的动态调整过程。我国通货膨胀调整存在减速通货膨胀状态、适中通货膨胀状态和加速通货膨胀状态三个区制。适中通货膨胀状态是一个平稳的自回归过程,减速通货膨胀状态、加速通货膨胀状态则是具有单位根的自回归过程,具有自我加速的作用。在不同的区制下,通货膨胀率均有较高的持久性,但中间状态的持久性明显低于其他两种状态。     

A constrained optimum experimental design problem for model discrimination with a continuously varying factor

We present the theoretical background and the numerical procedure for calculating optimum experimental designs for non-linear model discrimination in the presence of constraints. The design support points consist of two kinds of factors: a continuous function of time and discrete levels of other quantitative factors. That is, some of the experimental conditions are allowed to continually vary during the experimental run. We implement the theory in a chemical kinetic model discrimination problem.     

A review of the effectiveness of empowering leadership

Based on a review of empirical literature on empowering leadership, given incongruent and mixed results, the current work suggests reconsidering the effectiveness of empowering leadership. We propose a framework for examining the effectiveness of empowering leadership that considers: 1) feasibility of non-linear main effects of empowering leadership on work-related outcomes, 2) possibility of reverse causation between empowering leadership and work-related outcomes, 3) potential contradictory mediating mechanisms through which empowering leadership influences work-related outcomes, 4) consideration of boundary conditions which could alter the relationships between empowering leadership and work-related outcomes, and 5) consideration of levels-of-analysis and multilevel issues in empowering leadership. Our framework considers the multifaceted nature of empowering leadership and offers a guiding tool for advancing future research in this area.