Defining the linear portion of a sigmoid‐shaped curve: bend points

Formulae are provided that define the ‘bend points’, the beginning and end of the essentially linear dose–response region, for the four‐parameter logistic model. The formulae are expressed in both response and dose units. The derivation of the formulae is shown in order to illustrate the general nature of the methodology. Examples are given that describe how the formulae may be used while planning and conducting bioassays. Copyright © 2003 John Wiley & Sons, Ltd.     

Approximation of density functions by orthogonal series with grouped data

Summary Letg(x) andf(x) be continuous density function on (a, b) and let {ϕ_j} be a complete orthonormal sequence of functions onL ₂(g), which is the set of squared integrable functions weighted byg on (a, b). Suppose that over (a, b). Given a grouped sample of sizen fromf(x), the paper investigates the asymptotic properties of the restricted maximum likelihood estimator of density, obtained by setting all but the firstm of the ϑ_j’s equal to0. Practical suggestions are given for performing estimation via the use of Fourier and Legendre polynomial series. Research partially supported by: CNR grant, n. 93. 00837. CT10.     

Implementing partial least squares

Partial least squares (PLS) regression has been proposed as an alternative regression technique to more traditional approaches such as principal components regression and ridge regression. A number of algorithms have appeared in the literature which have been shown to be equivalent. Someone wishing to implement PLS regression in a programming language or within a statistical package must choose which algorithm to use. We investigate the implementation of univariate PLS algorithms within FORTRAN and the Matlab (1993) and Splus (1992) environments, comparing theoretical measures of execution speed based on flop counts with their observed execution times. We also comment on the ease with which the algorithms may be implemented in the different environments. Finally, we investigate the merits of using the orthogonal invariance of PLS regression to improve the algorithms.     

A simple,automatic and adaptive bivariate density estimator based on conditional densities

The standard approach to non-parametric bivariate density estimation is to use a kernel density estimator. Practical performance of this estimator is hindered by the fact that the estimator is not adaptive (in the sense that the level of smoothing is not sensitive to local properties of the density). In this paper a simple, automatic and adaptive bivariate density estimator is proposed based on the estimation of marginal and conditional densities. Asymptotic properties of the estimator are examined, and guidance to practical application of the method is given. Application to two examples illustrates the usefulness of the estimator as an exploratory tool, particularly in situations where the local behaviour of the density varies widely. The proposed estimator is also appropriate for use as a pilot estimate for an adaptive kernel estimate, since it is relatively inexpensive to calculate.     

On the shrinkage of local linear curve estimators

Local linear curve estimators are typically constructed using a compactly supported kernel, which minimizes edge effects and (in the case of the Epanechnikov kernel) optimizes asymptotic performance in a mean square sense. The use of compactly supported kernels can produce numerical problems, however. A common remedy is ridging, which may be viewed as shrinkage of the local linear estimator towards the origin. In this paper we propose a general form of shrinkage, and suggest that, in practice, shrinkage be towards a proper curve estimator. For the latter we propose a local linear estimator based on an infinitely supported kernel. This approach is resistant against selection of too large a shrinkage parameter, which can impair performance when shrinkage is towards the origin. It also removes problems of numerical instability resulting from using a compactly supported kernel, and enjoys very good mean squared error properties.     

Estimation of the parameters of symmetric stable ARMA and ARMA–GARCH models

In this article, we first propose the modified Hannan–Rissanen Method for estimating the parameters of autoregressive moving average (ARMA) process with symmetric stable noise and symmetric stable generalized autoregressive conditional heteroskedastic (GARCH) noise. Next, we propose the modified empirical characteristic function method for the estimation of GARCH parameters with symmetric stable noise. Further, we show the efficiency, accuracy and simplicity of our methods with Monte-Carlo simulation. Finally, we apply our proposed methods to model the financial data.     

应用AutoLISP对AutoCAD进行二次开发时的研究

AutoLISP语言是AutoCAD用户广泛使用的二次开发工具,本文结合笔者的开发体会,提出了在AutoLISP编程中需要注意的几个问题。     

企业IT能力系统动态演变的分析模型研究

揭示企业IT能力的演变规律,有助于把握影响IT能力系统的关键因素,从而提高企业信息系统的应用效果。本文以系统观为基础,依据协同学理论,讨论了企业IT能力系统的概念及其构成,探讨了企业IT能力系统的协同特征,提出了企业IT能力成熟度作为企业IT能力系统序参量的五种状态特征,并建立了企业IT能力系统的序参量方程,最后构造了该系统动态演化机制理论模型。     

股票市场的极值风险测度及后验分析研究

通过对上证综指和世界股市若干重要指数的实证研究发现,无论是在成熟资本市场还是新兴资本市场当中,极值理论(EVT)及其工具都能更加准确地刻画实际市场的极端波动和风险状况.详细说明了不同收益分布假定下风险价值(VaR)的计算方法及其后验分析(Back-testing)过程,证明了与非条件和条件正态分布以及条件t分布等主流金融理论的收益分布假定相比,条件EVT分布在测度极端市场风险时所表现出的优越性,同时说明了在不同概率水平下各种收益分布假定的精确度和适用范围.