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1.
戴和谱  刘刚  何妍妍 《计算机应用》2017,37(6):1793-1797
针对功能磁共振成像(fMRI)模型回归量之间存在共线性的问题,提出了一种正交化的方法。首先,确定感兴趣以及待正交的回归量;其次,从待正交回归量中减去与感兴趣回归量相关的部分,使模型中共线的回归量正交分解为相互独立的部分,以此来消除共线性的影响。此外,还讨论和分析了正交化对一般线性模型的影响。最后,分别使用一些合成数据和当前一个流行的fMRI数据分析软件包——脑功能磁共振图像软件包(FSL)进行实验。实验结果表明,正交化方法可以消除模型中的共线性,并且提高感兴趣回归量的显著性,从而实现准确的脑功能定位,可以应用于对脑的基础研究和临床治疗。  相似文献   

2.
The Poisson regression model is the most common framework for modeling count data, but it is constrained by its equidispersion assumption. The hyper-Poisson regression model described in this paper generalizes it and allows for over- and under-dispersion, although, unlike other models with the same property, it introduces the regressors in the equation of the mean. Additionally, regressors may also be introduced in the equation of the dispersion parameter, in such a way that it is possible to fit data that present overdispersion and underdispersion in different levels of the observations. Two applications illustrate that the model can provide more accurate fits than those provided by alternative usual models.  相似文献   

3.
In this paper, the estimation of a scalar parameter is considered with given lower and upper bounds of the scalar regressor. We derive non-asymptotic, lower and upper bounds on the convergence rates of the parameter estimate variances of the central and the minimax algorithms for noise probability density functions characterized by a thin tail distribution. This presents an extension of the previous work for constant scalar regressors to arbitrary scalar regressors with magnitude constraints. We expect our results to stimulate further research interests in the statistical analysis of these set-based estimators when the unknown parameter is multi-dimensional and the probability distribution function of the noise is more general than the present setup.  相似文献   

4.
Remote sensing often involves the estimation of in situ quantities from remote measurements. Linear regression, where there are no non-linear combinations of regressors, is a common approach to this prediction problem in the remote sensing community. A review of recent remote sensing articles using univariate linear regression indicates that in the majority of cases, ordinary least squares (OLS) linear regression has been applied, with approximately half the articles using the in situ observations as regressors and the other half using the inverse regression with remote measurements as regressors. OLS implicitly assume an underlying normal structural data model to arrive at unbiased estimates of the response. OLS regression can be a biased predictor in the presence of measurement errors when the regression problem is based on a functional rather than structural data model. Parametric (Modified Least Squares) and non-parametric (Theil-Sen) consistent predictors are given for linear regression in the presence of measurement errors together with analytical approximations of their prediction confidence intervals. Three case studies involving estimation of leaf area index from nadir reflectance estimates are used to compare these unbiased estimators with OLS linear regression. A comparison to Geometric Mean regression, a standardized version of Reduced Major Axis regression, is also performed. The Theil-Sen approach is suggested as a potential replacement of OLS for linear regression in remote sensing applications. It offers simplicity in computation, analytical estimates of confidence intervals, robustness to outliers, testable assumptions regarding residuals and requires limited a priori information regarding measurement errors.  相似文献   

5.
Adaptive filtering algorithms are investigated when system models are subject to model structure errors and regressor signal perturbations.System models for practical applications are often approximati...  相似文献   

6.
We consider a class of systems influenced by perturbations that are nonlinearly parameterized by unknown constant parameters, and develop a method for estimating the unknown parameters. The method applies to systems where the states are available for measurement, and perturbations with the property that an exponentially stable estimate of the unknown parameters can be obtained if the whole perturbation is known. The main contribution is to introduce a conceptually simple, modular design that gives freedom to the designer in accomplishing the main task, which is to construct an update law to asymptotically invert a nonlinear equation. Compensation for the perturbations in the system equations is considered for a class of systems with uniformly globally bounded solutions, for which the origin is uniformly globally asymptotically stable when no perturbations are present. We also consider the case when the parameters can only be estimated when the controlled state is bounded away from the origin, and show that we may still be able to achieve convergence of the controlled state. We illustrate the method through examples, and apply it to the problem of downhole pressure estimation during oil well drilling.  相似文献   

7.
A functional observer and state feedback are proposed for singular systems in the polynomial fraction form that requires no impulsive mode elimination. The order of the compensator is determined by the newly defined generalized observability index that is associated with the McMillan degree of the system. A new generalized Lyapunov equation is also proposed through a realization scheme that can be applied to both ordinary and singular systems. The solution to the equation provides an algebraic approach to the observer of singular systems in the generalized state-space form  相似文献   

8.
It is often the case that an outcome of interest is observed for a restricted non-randomly selected sample of the population. In such a situation, standard statistical analysis yields biased results. This issue can be addressed using sample selection models which are based on the estimation of two regressions: a binary selection equation determining whether a particular statistical unit will be available in the outcome equation. Classic sample selection models assume a priori that continuous regressors have a pre-specified linear or non-linear relationship to the outcome, which can lead to erroneous conclusions. In the case of continuous response, methods in which covariate effects are modeled flexibly have been previously proposed, the most recent being based on a Bayesian Markov chain Monte Carlo approach. A frequentist counterpart which has the advantage of being computationally fast is introduced. The proposed algorithm is based on the penalized likelihood estimation framework. The construction of confidence intervals is also discussed. The empirical properties of the existing and proposed methods are studied through a simulation study. The approaches are finally illustrated by analyzing data from the RAND Health Insurance Experiment on annual health expenditures.  相似文献   

9.
Feedforward multi-layer perceptrons (MLPs) are valuable modeling tools when considered as non-linear regression technique. MLPs are employed to estimate a priori unknown relationships between a response variable and regressors. Their estimates can serve as a basis for statistical inference. Hypotheses are more substantial and appropriate than those within reach of more traditional methods. This is due to the ability to extract complex non-linear interactive effects. The methodology of drawing valid statistical inference by MLPs in the context of spatially dependent heteroscedastic data is provided. The approach is data-driven and computationally feasible. The appropriateness and suitability of the procedure is demonstrated with an artificial data set and a practical application. Three-layer feedforward networks are applied to approximate the data-generating process. In context of spatially correlated residuals, a suitable statistic is given to test if a specific input variable is predictive of the response variable. Finally, sub-sampling techniques are adopted to arrive at valid statistical conclusions.  相似文献   

10.
A new unified modelling framework based on the superposition of additive submodels, functional components, and wavelet decompositions is proposed for non-linear system identification. A non-linear model, which is often represented using a multivariate non-linear function, is initially decomposed into a number of functional components via the well-known analysis of variance (ANOVA) expression, which can be viewed as a special form of the NARX (non-linear autoregressive with exogenous inputs) model for representing dynamic input–output systems. By expanding each functional component using wavelet decompositions including the regular lattice frame decomposition, wavelet series and multiresolution wavelet decompositions, the multivariate non-linear model can then be converted into a linear-in-the-parameters problem, which can be solved using least-squares type methods. An efficient model structure determination approach based upon a forward orthogonal least squares (OLS) algorithm, which involves a stepwise orthogonalization of the regressors and a forward selection of the relevant model terms based on the error reduction ratio (ERR), is employed to solve the linear-in-the-parameters problem in the present study. The new modelling structure is referred to as a wavelet-based ANOVA decomposition of the NARX model or simply WANARX model, and can be applied to represent high-order and high dimensional non-linear systems.  相似文献   

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