消费者行为的一般均衡和角点均衡

消费者行为的角点均衡不应只看作是一般均衡的特例。取得一般均衡还是角点均衡首先取决于不同商品价格之间的关系 ,其次取决于收入与价格的关系 ,角点均衡与一般均衡 ,相互依存 ,密不可分。强可加效用函数的一般均衡和角点均衡的求解 ,均可采用边际分析方法。     

汉语增量语词的强调标记化

基于语用和语言的互动关联,语用上的强调可能会渗入语言而成为语言自身的构成部分,语言会用某些显性语法形式标志被强调成分并使其范畴化。意义制约着汉语语词的历时流向,其主要表现之一是有相同或相似语义特征的语词往往会呈现为相同或相似的演变趋势。汉语的增量语词有通过语法隐喻、从其他认知域投射到言域中演变为强调标记的可能。这可通过增量语词的基本类型,如持续量语词、延及类语词、复加类语词的某些演变范例给以说明及解释。汉语的虚化成分并不单纯,从增量语词演变来的诸强调标记既有作用上的相似性,也有价值上的对立性,造成对立的主要原因是诸强调标记从它们的源词那里继承了某些特征,并且可能演变出了新特征。     

Fourier smoother and additive models

Suppose the observations (t_i,y_i), i = 1,… n, follow the model where g_j are unknown functions. The estimation of the additive components can be done by approximating g_j, with a function made up of the sum of a linear fit and a truncated Fourier series of cosines and minimizing a penalized least-squares loss function over the coefficients. This finite-dimensional basis approximation, when fitting an additive model with r predictors, has the advantage of reducing the computations drastically, since it does not require the use of the backfitting algorithm. The cross-validation (CV) [or generalized cross-validation (GCV)] for the additive fit is calculated in a further 0(n) operations. A search path in the r-dimensional space of degrees of freedom is proposed along which the CV (GCV) continuously decreases. The path ends when an increase in the degrees of freedom of any of the predictors yields an increase in CV (GCV). This procedure is illustrated on a meteorological data set.     

几种添加剂组合饲喂鲤鱼效果研究

将270尾一冬龄健康建鲤随机分成9组,选用均匀设计U_8(8~5),通过30天的试验,研究基础日粮的2％添加剂成分甲基睾丸酮X_1、甲状腺素X_2、甜菜碱X_3、柠檬酸X_4的最佳组合。结果表明:添加成分与增重率呈显著回归关系:Y=7.7917+0.9062X_1~2-0.32X_2X_3+4.3979×10~(-6)X_3X_4,其拟合度R~2=0.9062。经格点网络筛选,最优组合为X_1=6,X_2=0.004,X_3=4000,Y_4=3700。其增重率为100.39％,该结果比试验最优方案Ⅱ的增重率高33.15％。方案Ⅱ与对照组比较;增重率提高41.98％,饵料系数降低0.74,鱼体单位增重成本降低0.96元/kg。     

Some critical aspects of the use of exchangeability in statistics

Summary This expository paper provides a framework for analysing de Finetti's representation theorem for exchangeable finitely additive probabilities. Such an analysis is justified by reasoning of statistical nature, since it is shown that the abandonment of the axiom of σ-additivity has some noteworthy consequences on the common interpretation of the Bayesian paradigm. The usual (strong) fromulation of de Finetti's theorem is deduced from the finitely additive (weak) formulation, and it is used to solve the problem of stating the existence of a stochastic process, with given finite-dimensional probability distributions, whose sample paths are probability distributions. It is of importance, in particular, to specify prior distributions for nonparametric inferential problems in a Bayesian setting. Research partially supported by MPI (40% 1990, Gruppo Nazionale ?Modelli Probabilistici e Statistica Matematica?).     

Exponential-Bound Property of Estimators and Variable Selection in Generalized Additive Models

In this article, utilizing a scale mixture of skew-normal distribution in which mixing random variable is assumed to follow a mixture model with varying weights for each observation, we introduce a generalization of skew-normal linear regression model with the aim to provide resistant results. This model, which also includes the skew-slash distribution in a particular case, allows us to accommodate and detect outlying observations under the skew-normal linear regression model. Inferences about the model are carried out through the empirical Bayes approach. The conditions for propriety of the posterior and for existence of posterior moments are given under the standard noninformative priors for regression and scale parameters as well as proper prior for skewness parameter. Then, for Bayesian inference, a Markov chain Monte Carlo method is described. Since posterior results depend on the prior hyperparameters, we estimate them adopting the empirical Bayes method as well as using a Monte Carlo EM algorithm. Furthermore, to identify possible outliers, we also apply the Bayes factor obtained through the generalized Savage-Dickey density ratio. Examining the proposed approach on simulated instance and real data, it is found to provide not only satisfactory parameter estimates rather allow identifying outliers favorably.     

An Adaptive Two-stage Estimation Method for Additive Models

Abstract.  In this paper, a two-stage estimation method for non-parametric additive models is investigated. Differing from Horowitz and Mammen's two-stage estimation, our first-stage estimators are designed not only for dimension reduction but also as initial approximations to all of the additive components. The second-stage estimators are obtained by using one-dimensional non-parametric techniques to refine the first-stage ones. From this procedure, we can reveal a relationship between the regression function spaces and convergence rate, and then provide estimators that are optimal in the sense that, better than the usual one-dimensional mean-squared error (MSE) of the order n ^−4/5 , the MSE of the order n ^{− 1} can be achieved when the underlying models are actually parametric. This shows that our estimation procedure is adaptive in a certain sense. Also it is proved that the bandwidth that is selected by cross-validation depends only on one-dimensional kernel estimation and maintains the asymptotic optimality. Simulation studies show that the new estimators of the regression function and all components outperform the existing estimators, and their behaviours are often similar to that of the oracle estimator.     

Spatially-adaptive Penalties for Spline Fitting

The paper studies spline fitting with a roughness penalty that adapts to spatial heterogeneity in the regression function. The estimates are p th degree piecewise polynomials with p − 1 continuous derivatives. A large and fixed number of knots is used and smoothing is achieved by putting a quadratic penalty on the jumps of the p th derivative at the knots. To be spatially adaptive, the logarithm of the penalty is itself a linear spline but with relatively few knots and with values at the knots chosen to minimize the generalized cross validation (GCV) criterion. This locally-adaptive spline estimator is compared with other spline estimators in the literature such as cubic smoothing splines and knot-selection techniques for least squares regression. Our estimator can be interpreted as an empirical Bayes estimate for a prior allowing spatial heterogeneity. In cases of spatially heterogeneous regression functions, empirical Bayes confidence intervals using this prior achieve better pointwise coverage probabilities than confidence intervals based on a global-penalty parameter. The method is developed first for univariate models and then extended to additive models.     

Estimation of partially linear single-index additive hazards model with current status data

In this paper, we introduce a partially linear single-index additive hazards model with current status data. Both the unknown link function of the single-index term and the cumulative baseline hazard function are approximated by B-splines under a monotonicity constraint on the latter. The sieve method is applied to estimate the nonparametric and parametric components simultaneously. We show that, when the nonparametric link function is an exact B-spline, the resultant estimator of regression parameter vector is asymptotically normal and achieves the semiparametric information bound and the rate of convergence of the estimator for the cumulative baseline hazard function is optimal. Simulation studies are presented to examine the finite sample performance of the proposed estimation method. For illustration, we apply the method to a clinical dataset with current status outcome.