Semiparametric Regression with Kernel Error Model

Abstract.  We propose and study a class of regression models, in which the mean function is specified parametrically as in the existing regression methods, but the residual distribution is modelled non-parametrically by a kernel estimator, without imposing any assumption on its distribution. This specification is different from the existing semiparametric regression models. The asymptotic properties of such likelihood and the maximum likelihood estimate (MLE) under this semiparametric model are studied. We show that under some regularity conditions, the MLE under this model is consistent (when compared with the possibly pseudo-consistency of the parameter estimation under the existing parametric regression model), is asymptotically normal with rate and efficient. The non-parametric pseudo-likelihood ratio has the Wilks property as the true likelihood ratio does. Simulated examples are presented to evaluate the accuracy of the proposed semiparametric MLE method.     

网格和密度的聚类算法在CRM中的应用

聚类分析是数据挖掘领域中一种非常有用的技术,它用于从大量数据中寻找隐含的数据分布模式,主要有分割法、层次法、密度法、网格法和模型法等。该文主要讨论数据挖掘中一种基于密度和网格的聚类分析算法及其在客户关系管理中的应用。该算法具有较高的聚类效率而且容易实现,可以发现任意形状的聚类,时间复杂度低,聚类精度高,适用于数据的批量更新。该文还提出增量式聚类技术,它不仅能够利用前期聚类的结果,充分提高聚类分析的效率,而且可以降低维护知识库所带来的巨大开销。实验证明了算法的有效性。     

Likelihood-based estimation for Gaussian MRFs

Markov random fields (MRFs) express spatial dependence through conditional distributions, although their stochastic behavior is defined by their joint distribution. These joint distributions are typically difficult to obtain in closed form, the problem being a normalizing constant that is a function of unknown parameters. The Gaussian MRF (or conditional autoregressive model) is one case where the normalizing constant is available in closed form; however, when sample sizes are moderate to large (thousands to tens of thousands), and beyond, its computation can be problematic. Because the conditional autoregressive (CAR) model is often used for spatial-data modeling, we develop likelihood-inference methodology for this model in situations where the sample size is too large for its normalizing constant to be computed directly. In particular, we use simulation methodology to obtain maximum likelihood estimators of mean, variance, and spatial-depencence parameters (including their asymptotic variances and covariances) of CAR models.     

Nonparametric Estimation of Duration Dependence in Militarized Interstate Disputes

A militarized interstate dispute (MID) involves military conflict between states with diplomatic ties and exists because two or more states have failed to resolve their differences through diplomatic channels. Jones et al. (1996) characterize an MID as the threat, display or use of military force short of war. They analyze over 2000 disputes spanning two centuries across the globe and conclude that disputes tend to be persistent once established. In this paper, I find that the passage of time can be a favorable factor in dispute resolution, and thus historical mechanisms for dispute resolution favor ending, not extending, militarized disputes. I emphasize the use of non-parametric procedures first to estimate the hazard function and then to estimate the benefits of negotiated settlements.     

与菲涅耳数有关的高斯光束的轴上相对光强分布

在考虑像差的情况下,得到了与菲涅耳数聚焦激光光学系统的衍射积分公式,并推出了轴上相对光强分布的普遍近似公式,在此基础上得到了初级球差系统的轴上相对光强分布公式,并在不考虑像差因素和截取效应时,对得到的公式进行了简化,所得结果与以前的结论吻合得较好。     

Conditional logspline density estimation

In conditional logspline modelling, the logarithm of the conditional density function, log f(y|x), is modelled by using polynomial splines and their tensor products. The parameters of the model (coefficients of the spline functions) are estimated by maximizing the conditional log-likelihood function. The resulting estimate is a density function (positive and integrating to one) and is twice continuously differentiable. The estimate is used further to obtain estimates of regression and quantile functions in a natural way. An automatic procedure for selecting the number of knots and knot locations based on minimizing a variant of the AIC is developed. An example with real data is given. Finally, extensions and further applications of conditional logspline models are discussed.     

Intentionally biased bootstrap methods

A class of weighted bootstrap techniques, called biased bootstrap or b-bootstrap methods, is introduced. It is motivated by the need to adjust empirical methods, such as the 'uniform' bootstrap, in a surgical way to alter some of their features while leaving others unchanged. Depending on the nature of the adjustment, the b-bootstrap can be used to reduce bias, or to reduce variance or to render some characteristic equal to a predetermined quantity. Examples of the last application include a b-bootstrap approach to hypothesis testing in nonparametric contexts, where the b-bootstrap enables simulation 'under the null hypothesis', even when the hypothesis is false, and a b-bootstrap competitor to Tibshirani's variance stabilization method. An example of the bias reduction application is adjustment of Nadaraya–Watson kernel estimators to make them competitive with local linear smoothing. Other applications include density estimation under constraints, outlier trimming, sensitivity analysis, skewness or kurtosis reduction and shrinkage.     

Calibration of the estimators of variance

This investigation suggests new techniques to calibrate estimators of variance. Estimators of the variance of simple mean, ratio and regression estimators under different sampling schemes are shown to be special cases of the proposed calibration techniques. The approach has more practical use due to recent advances in programming techniques and computational speed. An empirical study has been carried out to address the properties of these proposed strategies.     

A dynamic EM algorithm for estimating mixture proportions

We investigate the use of a dynamic form of the EM algorithm to estimate proportions in finite mixtures of known distributions. We prove a consistency result for this algorithm, which employs only a single EM update for each new observation. Our aim is to demonstrate that the slow convergence rate of the EM algorithm in many applications is of little practical consequence in a situation when data is frequently being updated.     

Individual Prior Information in a Physiological Model of 2H8-Toluene Kinetics: An Empirical Bayes Estimation Strategy

Physiologically-based toxicokinetic (PBTK) models are widely used to quantify whole-body kinetics of various substances. However, since they attempt to reproduce anatomical structures and physiological events, they have a high number of parameters. Their identification from kinetic data alone is often impossible, and other information about the parameters is needed to render the model identifiable. The most commonly used approach consists of independently measuring, or taking from literature sources, some of the parameters, fixing them in the kinetic model, and then performing model identification on a reduced number of less certain parameters. This results in a substantial reduction of the degrees of freedom of the model. In this study, we show that this method results in final estimates of the free parameters whose precision is overestimated. We then compared this approach with an empirical Bayes approach, which takes into account not only the mean value, but also the error associated with the independently determined parameters. Blood and breath ²H₈-toluene washout curves, obtained in 17 subjects, were analyzed with a previously presented PBTK model suitable for person-specific dosimetry. Model parameters with the greatest effect on predicted levels were alveolar ventilation rate Q_PC, fat tissue fraction V_FC, blood-air partition coefficient K_b, fraction of cardiac output to fat Q_a/co and rate of extrahepatic metabolism V_max-p. Differences in the measured and Bayesian-fitted values of Q_PC, V_FC and K_b were significant (p < 0.05), and the precision of the fitted values V_max-p and Q_a/co went from 11 ± 5% to 75 ± 170% (NS) and from 8 ± 2% to 9 ± 2% (p < 0.05) respectively. The empirical Bayes approach did not result in less reliable parameter estimates: rather, it pointed out that the precision of parameter estimates can be overly optimistic when other parameters in the model, either directly measured or taken from literature sources, are treated as known without error. In conclusion, an empirical Bayes approach to parameter estimation resulted in a better model fit, different final parameter estimates, and more realistic parameter precisions.