基于固定效应的纵向数据分位点回归模型的参数估计及CDM和MSOM的等价性

研究了基于固定效应的纵向数据模分位点回归模型的参数估计及统计诊断问题.首先给出了参数估计的MM迭代算法,然后讨论了统计诊断中数据删除模型(CDM)和均值移模型(MSOM)的等价性问题,最后利用消炎镇痛药数据说明了方法的应用.     

Local influence analysis for semiparametric reproductive dispersion nonlinear models

The present paper proposes a semiparametric reproductive dispersion nonlinear model (SRDNM) which is an extension of the nonlinear reproductive dispersion models and the semiparameter regression models. Maximum penalized likelihood estimates (MPLEs) of unknown parameters and nonparametric functions in SRDNM are presented. Assessment of local influence for various perturbation schemes are investigated. Some local influence diagnostics are given. A simulation study and a real example are used to illustrate the proposed methodologies.     

自动选取多非线性参数初始值的循环搜索法

1几何中心化加权最小二乘法给定观测数据集(x_i,y_i),i=1,2,…,n．(1．1)欲拟合加权非线性模型y_i=f(x_i,θ) ε_i,(1．2)其中模型函数f的参数为θ=(θ_1,…,θ_p)~T,随机观测误差项满足ε_i～N[0,(?)~2m(z_i,λ)],(1．3) m(z_i,λ)为已知正值函数,z_i可以是x_i,也可以是μ_i=f(x_i,θ)或二者的组合,λ为权参数,而(?)~2为未知的方差参数,λ和θ可统称为模型参数．模型的似然函数为     

Linearization conditions for regression models with unknown variance parameter

In the case of the nonlinear regression model, methods and procedures have been developed to obtain estimates of the parameters. These methods are much more complicated than the procedures used if the model considered is linear. Moreover, unlike the linear case, the properties of the resulting estimators are unknown and usually depend on the true values of the estimated parameters. It is sometimes possible to approximate the nonlinear model by a linear one and use the much more developed linear methods, but some procedure is needed to recognize such situations. One attempt to find such a procedure, taking into account the requirements of the user, is given in [4], [5], [3], where the existence of an a priori information on the parameters is assumed. Here some linearization criteria are proposed and the linearization domains, i.e. domains in the parameter space where these criteria are fulfilled, are defined. The aim of the present paper is to use a similar approach to find simple conditions for linearization of the model in the case of a locally quadratic model with unknown variance parameter ². Also a test of intrinsic nonlinearity of the model and an unbiased estimator of this parameter are derived.     

Linear Versus Quadratic Estimators in Linearized Models

In nonlinear regression models an approximate value of an unknown parameter is frequently at our disposal. Then the linearization of the model is used and a linear estimate of the parameter can be calculated. Some criteria how to recognize whether a linearization is possible are developed. In the case that they are not satisfied, it is necessary to take into account either some quadratic corrections or to use the nonlinear least squares method. The aim of the paper is to find some criteria for an ordering linear and quadratic estimators.     

Asymptotic properties of maximum likelihood estimator for two-step logit models

Two-step logit models are extensions of the ordinary logistic regression model, which are designed for complex ordinal outcomes commonly seen in practice. In this paper, we establish some asymptotic properties of the maximum likelihood estimator (MLE) of the regression parameter vector under some mild conditions, which include existence of the MLE, convergence rate and asymptotic normality of the MLE. We relax the boundedness condition of the regressors required in most existing theoretical results, and all conditions are easy to verify.     

TESTING OF CORRELATION AND HETEROSCEDASTICITY IN NONLINEAR REGRESSION MODELS WITH DBL(p,q,1) RANDOM ERRORS

Chaos theory has taught us that a system which has both nonlinearity and random input will most likely produce irregular data. If random errors are irregular data, then random error process will raise nonlinearity (Kantz and Schreiber (1997)). Tsai (1986) introduced a composite test for autocorrelation and heteroscedasticity in linear models with AR(1) errors. Liu (2003) introduced a composite test for correlation and heteroscedasticity in nonlinear models with DBL(p, 0, 1) errors. Therefore, the important problems in regres- sion model are detections of bilinearity, correlation and heteroscedasticity. In this article, the authors discuss more general case of nonlinear models with DBL(p, q, 1) random errors by score test. Several statistics for the test of bilinearity, correlation, and heteroscedas-ticity are obtained, and expressed in simple matrix formulas. The results of regression models with linear errors are extended to those with bilinear errors. The simulation study is carried out to investigate the powers of the test statistics. All results of this article extend and develop results of Tsai (1986), Wei, et al (1995), and Liu, et al (2003).     

似然距离之间的近似等量关系

本文研究了线性回归模型的影响分析中常用的三种重要的诊断统计量,即似然距离LD_i(β,σ~2),LD_i(β|σ~2)和LD_i(σ~2|β)之间的关系.利用对数函数ln(1+χ)的马克劳林展开,在非线件最小二乘回归模型中得到了LD_i(β,σ~2)≈LD_i(β|σ~2)+LD_i(σ~2|β),类似的近似关系式对包括非线性分位点回归在内的一类较为广泛的统计模型都成立一个线性和一个非线性数据实例的分析结果很好地说明了我们的结论.     

Properties of empirical estimates in stochastic optimization and identification problems

This paper deals with a stochastic optimization problem when its decision parameter belongs to a separable Banach space. Conditions under which strong consistency of the parameter empirical estimates holds, are established. Leastl ₁-norm estimates for two models (nonlinear and nonparametric regression) are investigated as special cases of such empirical estimates.     

应用SAS解非线性回归问题

.应用SAS/STAT估计非线性回归模型中的参数.首先,通过变量代换,把可以线性化的非线性回归模型化为线性回归模型,并用普通最小二乘法、主成分分析法和偏最小二乘法求模型中的参数和回归模型.其次,通过改良的高斯—牛顿迭代法来估计Logistic模型和Compertz模型中的参数.     

Asymptotics of estimates in constrained nonlinear regression with long-range dependent innovations

The purpose of this paper is to investigate the asymptotic properties of the least squares estimates (L ₂-estimates) and the least absolute deviation estimates (L ₁-estimates) of the parameters of a nonlinear regression model subject to a set of equality and inequality restrictions, which has a long-range dependent stationary process as its stochastic errors. Then we will compare the asymptotic relative efficiencies of the above estimators.     

非零截距线性和非线性回归模型的T-型稳健估计算法

首先给出非零截距线性模型T-型估计的模型与EM算法,其次给出非线性回归模型参数的T-型估计,利用泰勒级数对模型线性化,得到参数估计的迭代算法,最后用数值模拟实验验证了该算法的正确性和证实了T-型估计的稳健性.     

具有双线性BL(1,1,1,1)误差的非线性回归模型相关性和方差齐性的检验

在时间序列回归模型分析中,相关性和方差齐性的检验是一个很基本的问题.本文讨论了具有双线性BL(1,1,1,1)误差的非线性回归模型的相关性和方差齐性的检验问题, 用Score检验方法给出了双线性项检验、相关性检验、方差齐性检验、以及相关性和方差齐性同时检验的检验统计量.推广和发展了具有线性序列误差项回归模型的结果.本文还用数值实例说明了检验方法的实用价值.     

Linearized Regression Model with Constraints of Type II

A linearization of the nonlinear regression model causes a bias in estimators of model parameters. It can be eliminated, e.g., either by a proper choice of the point where the model is developed into the Taylor series or by quadratic corrections of linear estimators. The aim of the paper is to obtain formulae for biases and variances of estimators in linearized models and also for corrected estimators.     

非线性回归模型中的约束拟似然

在非线性回归模型中,拟得分函数是一类线性无偏估计函数中的最优者(GodambeandHeyde(1987),朱仲义(1996)),而由拟得分函数得到的拟似然估计在由线性无偏估计函数得到的估计类中具有渐近最优性(林路(1999)).本文则研究非线性回归模型中的有偏估计函数理论,构造了参数的约束拟似然估计,得到了约束拟似然的局部最优性,局部改进了拟似然估计,从而扩充了线性模型中的有偏估计理论.     

ON CONFIDENCE REGIONS OF SEMIPARAMETRIC NONLINEAR REGRESSION MODELS(A GEOMETRIC APPROACH)

1IntroductionSelltipaxanetricmodelsaxemodelscolltaillingbothparametricalldnonparametriccom-pOnents,wl1erethenol1parametriccomponentplaystheroleofanusianceparameter.Moreprecisely,asellliparametriclllodelisparameterizedbyaparameterofillteresttakingvaI1lesinfinite-din1el1sionajEuclidenspaceal1danusianceparantetertakingvaluesininfinite-dimellsionalspace.Tl1ismodelembodiesacolllpro11tisebetweenemployingagelleralnonparametricspeci-ficatioll.wl1ich,iftheconditiol1il1gvariablesarehighdimensional,woul…     

大数据背景下水厂自动投矾模型研究

根据某市自来水有限责任公司第二水厂的历史矾耗数据，建立矾耗流量关于原水浊度、温度等的动态矾耗模型. 通过对数据进行处理得到10900个合格且净水效果高效的数据，将筛选出的数据分为训练样本集和测试样本集. 在回归拟合中，通过拟合R2的大小将原水浊度划分为“低浊”“中浊”“高浊”3个区间，利用泰勒展开公式的非线性变量代换分别对3个区间建立不同的多项式回归模型，得到预测正确率约为72%，总的矾耗流量值约减少了9.6%的结果；在随机森林模型中，使用10900个合格数据，利用训练样本集，以“原水浊度”“pH值”“原水流量”和“水温”为输入变量，建立包含2000棵决策树的随机森林模型，得到预测正确率约为44. 21%，总的矾耗流量值增加了0.04%的结果. 从模型对合格数据的拟合优度看，随机森林模型比非线性回归模型效果更好；在平均绝对误差、平均绝对偏差百分比等评价指标上，前者均优于后者；但从历史数据检验的结果，模型的可解读性，模型的操作难度和推广角度看，分段二元非线性回归模型的优势更为突出.     

A semiparametric panel approach to mortality modeling

During the past twenty years, there has been a rapid growth in life expectancy and an increased attention on funding for old age. Attempts to forecast improving life expectancy have been boosted by the development of stochastic mortality modeling, for example the Cairns–Blake–Dowd (CBD) 2006 model. The most common optimization method for these models is maximum likelihood estimation (MLE) which relies on the assumption that the number of deaths follows a Poisson distribution. However, several recent studies have found that the true underlying distribution of death data is overdispersed in nature (see Cairns et al. 2009 and Dowd et al. 2010). Semiparametric models have been applied to many areas in economics but there are very few applications of such models in mortality modeling. In this paper we propose a local linear panel fitting methodology to the CBD model which would free the Poisson assumption on number of deaths. The parameters in the CBD model will be considered as smooth functions of time instead of being treated as a bivariate random walk with drift process in the current literature. Using the mortality data of several developed countries, we find that the proposed estimation methods provide comparable fitting results with the MLE method but without the need of additional assumptions on number of deaths. Further, the 5-year-ahead forecasting results show that our method significantly improves the accuracy of the forecast.     

Derivative-free optimization and neural networks for robust regression

Large outliers break down linear and nonlinear regression models. Robust regression methods allow one to filter out the outliers when building a model. By replacing the traditional least squares criterion with the least trimmed squares (LTS) criterion, in which half of data is treated as potential outliers, one can fit accurate regression models to strongly contaminated data. High-breakdown methods have become very well established in linear regression, but have started being applied for non-linear regression only recently. In this work, we examine the problem of fitting artificial neural networks (ANNs) to contaminated data using LTS criterion. We introduce a penalized LTS criterion which prevents unnecessary removal of valid data. Training of ANNs leads to a challenging non-smooth global optimization problem. We compare the efficiency of several derivative-free optimization methods in solving it, and show that our approach identifies the outliers correctly when ANNs are used for nonlinear regression.     

Semiparametric quantile modelling of hierarchical data

The classic hierarchical linear model formulation provides a considerable flexibility for modelling the random effects structure and a powerful tool for analyzing nested data that arise in various areas such as biology, economics and education. However, it assumes the within-group errors to be independently and identically distributed （i.i.d.） and models at all levels to be linear. Most importantly, traditional hierarchical models （just like other ordinary mean regression methods） cannot characterize the entire conditional distribution of a dependent variable given a set of covariates and fail to yield robust estimators. In this article, we relax the aforementioned and normality assumptions, and develop a so-called Hierarchical Semiparametric Quantile Regression Models in which the within-group errors could be heteroscedastic and models at some levels are allowed to be nonparametric. We present the ideas with a 2-level model. The level-1 model is specified as a nonparametric model whereas level-2 model is set as a parametric model. Under the proposed semiparametric setting the vector of partial derivatives of the nonparametric function in level-1 becomes the response variable vector in level 2. The proposed method allows us to model the fixed effects in the innermost level （i.e., level 2） as a function of the covariates instead of a constant effect. We outline some mild regularity conditions required for convergence and asymptotic normality for our estimators. We illustrate our methodology with a real hierarchical data set from a laboratory study and some simulation studies.