模糊最小二乘法模型

本文引入模糊数间的一种距离,把类似的最小二乘法用于对模糊观测数据的分析,提出两类拟合模糊数据的模糊线性回归模型,证明确定模型的条件,给出计算模型参数的简明方法。     

基于相似性叙词表的模糊集合模型

传统的模糊集合模型基于词词关联矩阵来实现模糊检索,词词关联矩阵只考虑语词在文献内部的同时出现.本文提出了一个基于相似性叙词表的模糊集合模型,考虑语词与查询之间的相似性,并将查询扩展包含在此模型中,从而在一定程度上提高了检索性能.     

线性系统理论预报槐果碱在大鼠体内处置动力学

用线性系统理论和生理药代动力学模型理论结合,提出一种预报槐果碱在大鼠各组织中处置动力学的数学方法,并用实验验证该方法的可靠性。结果表明数学模拟值与实验观察值基本吻合。扩展到2.5kg兔,iv 25 mg后和2.5mg/min滴注过程中血药浓度预示值与观察值基本一致。     

基于描述逻辑的模糊ER模型的表示与推理

重点分析了将ER模型分别转化为描述逻辑ALNUI知识库和DLR知识库的不同之处.在深入研究了描述逻辑DLR的基础之上,对DLR进行了模糊化扩展,提出了一种新的模糊描述逻辑FDLR(fuzzyDLR).定义了FDLR的语法结构、语义解释以及知识库的形式,研究了如何将模糊ER模型转化为FDLR的知识库.通过一个转化实例例证了FDLR能够很好地对模糊ER模型进行表示,并利用FDLR的推理机制研究了模糊ER模型的自动推理问题,同时给出了上述转化和推理问题的正确性证明.     

MD-SQL:一种基于MDX的多维数据查询语言

多维数据分析技术在建立企业级数据仓库的过程中起着关键的作用,同时也是面向联机分析处理(OLAP)的核心.本文在分析了传统多维数据查询语言MDX(Multi-Dimensional eXpression)不足的基础上,提出了一种改进的多维数据查询的语言模型MD-SQL,并给予实现,最后对模型提出了优化方法,通过相关实验证明MD-SQL语言性能优于MDX语言.     

基于AHP的教学质量模糊综合评价模型

提出了高校教师的教学质量评价指标体系,利用AHP方法确定各评价指标的权重,建立了一种基于层次分析法的教学质量模糊综合评价模型。算例结果表明,该模型具有一定可操作性和实用性。     

基于模型熵的中药学教学效果评估模型研究

提出一种基于熵权的模糊优选模型,将模型数学与熵权概念有机结合,建立了中药学教学效果评估模型,对教学中的各种因素进行分析,为教学管理等决策提供了科学的依据,具有较高的应用价值。     

模糊深隐马尔可夫模型研究

针对经典马尔可夫模型没有考虑模型应用中状态、观测量间的上下文相关性以及状态转移概率动态性、可变性,提出一种模糊深隐马尔可夫模型.该模型通过增加观测值间的相关性、解决概率转移问题中的不确定性和改进参数优化算法,使之能够较好地应用于强噪声、训练数据缺损等情形的模式识别中.理论证明,显式模糊深隐马尔可夫模型在同等模型复杂度下具有模型优化程度高、区分度好、误识率低、鲁棒性高的特性.     

构件形式化描述与模糊检索研究

在软件复用研究不断深入的情况下,构件的准确描述与高效检索已成为面向构件的软件复用研究的热点和难点.本文参照3C构件模型,提出一种基于形式化方法的、可扩展的构件描述模型,包括构件的功能描述、接口描述、环境依赖描述等,并保留了构件关键字、非功能属性等描述项.在此描述模型基础上提出了构件的分步检索法,并着重论述了包含四级模糊度的构件形式化检索方法,以提高构件的查找效率并兼顾查全率.     

基于模糊熵的中药学教学效果评估模型研究

提出一种基于熵权的模糊优选模型,将模糊数学与熵权概念有机结合,建立了中药学教学效果评估模型,对教学中的各种因素进行分析,为教学管理等决策提供了科学的依据,具有较高的应用价值。     

Fitting nonlinear regression models with correlated errors to individual pharmacodynamic data using SAS software

Nonlinear regression is widely used in pharmacokinetic and pharmacodynamic modeling by applying nonlinear ordinary least squares. Although the assumption of independent errors is frequently not fulfilled, this has received scant attention in the pharmacokinetic literature. As in linear regression, leaving correlation of errors out of account leads to an underestimation of the standard deviations of parameter estimates. On the other hand, the use of models that accommodate correlated errors requires more care and more computation. This paper describes a method to fit log-normal functions to individual response curves containing correlated errors by means of statistical software for time series. A sample computer program is given in which the SAS/ETS procedure MODEL is used. In particular, the problem of finding appropriate starting values for nonlinear iterative algorithms is considered. A linear weighted least squares approach for initial parameter estimation is developed. The adequacy of the method is investigated by means of Monte Carlo simulations. Furthermore, the statistical properties of nonlinear least squares with and without accommodating correlated errors are compared. Time action profiles of a long-acting insulin preparation injected subcutaneously in humans are analyzed to illustrate the usefulness of the method proposed.     

Statistical methodology to determine kinetically derived maximum tolerated dose in repeat dose toxicity studies

Several statistical approaches were evaluated to identify an optimum method for determining a point of nonlinearity (PONL) in toxicokinetic data. (1) A second-order least squares regression model was fit iteratively starting with data from all doses. If the second order term was significant (α < 0.05), the dataset was reevaluated with successive removal of the highest dose until the second-order term became non-significant. This dose, whose removal made the second order term non-significant, is an estimate of the PONL. (2) A least squares linear model was fit iteratively starting with data from all doses except the highest. The mean response for the omitted dose was compared to the 95% prediction interval. If the omitted dose falls outside the confidence interval it is an estimate of the PONL. (3) Slopes of least squares linear regression lines for sections of contiguous doses were compared. Nonlinearity was suggested when slopes of compared sections differed. A total of 33 dose–response datasets were evaluated. For these toxicokinetic data, the best statistical approach was the least squares regression analysis with a second-order term. Changing the α level for the second-order term and weighting the second-order analysis by the inverse of feed consumption were also considered. This technique has been shown to give reproducible identification of nonlinearities in TK datasets.     

Estimation of fixed effects panel data partially linear additive regression models

In this paper, we investigate the estimation problem of fixed effects panel data partially linear additive regression models. Semi‐parametric fixed effects panel data regression models are tools that are well suited to econometric analysis and the analysis of cDNA micro‐arrays. By applying a polynomial spline series approximation and a profile least‐squares procedure, we propose a semi‐parametric least‐squares dummy variables estimator (SLSDVE) for the parametric component and a series estimator for the non‐parametric component. Under very weak conditions, we show that the SLSDVE is asymptotically normal and that the series estimator achieves the optimal convergence rate of the non‐parametric regression. In addition, we propose a two‐stage local polynomial estimation for the non‐parametric component by applying the additive structure and the series estimator. The resultant estimator is asymptotically normal and the asymptotic distribution of each additive component is the same as it would be if the other components were known with certainty. We conduct simulation studies to demonstrate the finite sample performance of the proposed procedures and we also present an illustrative empirical application.     

General approach to handling nonuniform variance in assay calibration

A general method for handling nonuniform variance in data from assay calibrations is discussed. Calibration data from the analysis of ibuprofen and aspirin by high-performance liquid chromatography was analysed by the traditional least squares method; nonuniform error variance was found to be significant. Weighted least squares analysis overcomes the problem of nonuniform variance but relies on good estimates of the error variance. The method of extended least squares, a maximum likelihood method, is described which incorporates handling of the weighting in the regression analysis. The extended least squares method produces accurate and precise estimates of the parameters of the calibration and allows precise estimates of the variance of future predictions, provided that a sufficient number of calibrators are used.     

Pharmacokinetic parameter estimations by minimum relative entropy method

For estimating pharmacokinetic parameters, we introduce the minimum relative entropy (MRE) method and compare its performance with least squares methods. There are several variants of least squares, such as ordinary least squares (OLS), weighted least squares, and iteratively reweighted least squares. In addition to these traditional methods, even extended least squares (ELS), a relatively new approach to nonlinear regression analysis, can be regarded as a variant of least squares. These methods are different from each other in their manner of handling weights. It has been recognized that least squares methods with an inadequate weighting scheme may cause misleading results (the “choice of weights” problem). Although least squares with uniform weights, i.e., OLS, is rarely used in pharmacokinetic analysis, it offers the principle of least squares. The objective function of OLS can be regarded as a distance between observed and theoretical pharmacokinetic values on the Euclidean space ℝ^N, whereN is the number of observations. Thus OLS produces its estimates by minimizing the Euclidean distance. On the other hand, MRE works by minimizing the relative entropy which expresses discrepancy between two probability densities. Because pharmacokinetic functions are not density function in general, we use a particular form of the relative entropy whose domain is extended to the space of all positive functions. MRE never assumes any distribution of errors involved in observations. Thus, it can be a possible solution to the choice of weights problem. Moreover, since the mathematical form of the relative entropy, i.e., an expectation of the log-ratio of two probability density functions, is different from that of a usual Euclidean distance, the behavior of MRE may be different from those of least squares methods. To clarify the behavior of MRE, we have compared the performance of MRE with those of ELS and OLS by carrying out an intensive simulation study, where four pharmacokinetic models (mono- or biexponential, Bateman, Michaelis-Menten) and several variance models for distribution of observation errors are employed. The relative precision of each method was investigated by examining the absolute deviation of each individual parameter estimate from the known value. OLS is the best method and MRE is not a good one when the actual observation error magnitude conforms to the assumption of OLS, that is, error variance is constant, but OLS always behaves poorly with the other variance models. On the other hand, MRE performs better than ELS and OLS when the variance of observation is proportional to its mean. In contrast, ELS is superior to MRE and OLS when the standard deviation of observation is proportional to its mean. In either case the difference between MRE and ELS is relatively small. Generally, the performance of MRE is comparable to that of ELS. Thus MRE provides as reliable a method as ELS for estimating pharmacokinetic parameters.     

Extended least squares nonlinear regression: a possible solution to the "choice of weights" problem in analysis of individual pharmacokinetic data

It is often difficult to specify weights for weighted least squares nonlinear regression analysis of pharmacokinetic data. Improper choice of weights may lead to inaccurate and/or imprecise estimates of pharmacokinetic parameters. Extended least squares nonlinear regression provides a possible solution to this problem by allowing the incorporation of a general parametric variance model. Weighted least squares and extended least squares analyses of data from a simulated pharmacokinetic experiment were compared. Weighted least squares analysis of the simulated data, using commonly used weighting schemes, yielded estimates of pharmacokinetic parameters that were significantly biased, whereas extended least squares estimates were unbiased. Extended least squares estimates were often significantly more precise than were weighted least squares estimates. It is suggested that extended least squares regression should be further investigated for individual pharmacokinetic data analysis.     

Hedonic price index estimation under mean‐independence of time dummies from quality characteristics

Summary. We estimate hedonic price indices (HPI) for rental offices in Tokyo for the period 1985–1991. We take a partially linear regression (PLR) model, linear in x (year dummies) and nonparametric in z (office quality characteristics), as our main model; the usual linear model is used as well. Since x consists of year dummies, the linearity in x is not a restriction in the PLR model; the only restriction is that of no interaction between x and z . For the PLR model, the HPI are estimated ‐consistently with a two‐stage procedure. For our data, x turns out to be (almost) mean‐independent of z . This implies that least squares estimation (LSE) for models with a misspecified function for z is still consistent. The mean‐independence also leads to an efficiency result that, under heteroskedasticity of unknown form, the two‐stage PLR model estimator is at least as efficient as any LSE for models specifying (rightly or wrongly) the part for z . In addition to these, several interesting practical lessons are noted in doing the two‐stage PLR model estimation. First, the cross validation (CV) used in the PLR model literature can fail if the mean‐independence is ignored. Second, high order kernels can make the CV criterion function ill behaved. Third, product kernels work as well as spherically symmetric kernels. Fourth, nonparametric specification tests may work poorly due to a sample splitting problem with outliers in the data or due to choosing more than one bandwidth; in this regard, a test suggested by 18 and 19 is recommended.     

Extended least squares nonlinear regression: A possible solution to the “choice of weights” problem in analysis of individual pharmacokinetic data

It is often difficult to specify weights for weighted least squares nonlinear regression analysis of pharmacokinetic data. Improper choice of weights may lead to inaccurate and/or imprecise estimates of pharmacokinetic parameters. Extended least squares nonlinear regression provides a possible solution to this problem by allowing the incorporation of a general parametric variance model. Weighted least squares and extended least squares analyses of data from a simulated pharmacokinetic experiment were compared. Weighted least squares analysis of the simulated data, using commonly used weighting schemes, yielded estimates of pharmacokinetic parameters that were significantly biased, whereas extended least squares estimates were unbiased. Extended least squares estimates were often significantly more precise than were weighted least squares estimates. It is suggested that extended least squares regression should be further investigated for individual pharmacokinetic data analysis.This work was supported in part by USUHS Grant RO-7516 and NIH Grants GM26676 and GM26691.     

A note on fitting one-compartment models: non-linear least squares versus linear least squares using transformed data

Drug concentrations in one-compartment systems are frequently modeled using a single exponential function. Two methods of estimation are commonly used for determining the parameters of such a model. In the first method, non-linear least-squares regression is used to calculate the parameters. In the second method, the data are first transformed by a logarithmic function, and then the log-concentration data are fit using linear least-squares regression. The assumptions for fitting these models are discussed with special emphasis on which data points are most influential in determining parameter values. The similarities between fitting a linear regression model to the log-concentration data and fitting a weighted regression model to the original data are noted. An example is presented that illustrates the differences in fitting a model to the log-transformed data versus fitting unweighted and weighted models to the original-scale data.