Errors-in-variables模型的参数估计

介绍了Errors_in_variables模型 ,利用Fisher得分算法 ,给出了在自变量的随机影响因素和因变量的随机影响因素相互独立和无重复测量数据情况下Errors_in_variables模型参数估计的迭代公式 .

基于errors-in-variables的预测模型及其应用

预测是统计学实际应用的一个主要方面,多元线性回归预测是一种很好的方法,广泛地应用在各种实际领域,但其局限性及不足也是明显的。本文以一种新的观点认识数据,即认为变量的观测里均含有误差,同时认为不应删除经慎重选择进来的解释变量。为此,本文提出了一种新的多元预测方法———多元线性EIV预测。本文还考虑了新预测模型的一个实例应用,并从相对偏差上与多元回归预测进行了比较,从而揭示了多元线性EIV预测的先进性及较好的预测精度。

Error model identification of inertial navigation platform based on errors-in-variables model

Because the real input acceleration cannot be obtained during the error model identification of inertial navigation platform, both the input and output data contain noises. In this case, the conventional regression model and the least squares （LS） method will result in bias. Based on the models of inertial navigation platform error and observation error, the errors-in-variables （EV） model and the total least squares （TLS） method axe proposed to identify the error model of the inertial navigation platform. The estimation precision is improved and the result is better than the conventional regression model based LS method. The simulation results illustrate the effectiveness of the proposed method.

APPLICATION OF FRF ESTIMATOR BASED ON ERRORS-IN-VARIABLES MODEL IN MULTI-INPUT MULTI-OUTPUT VIBRATION CONTROL SYSTEM

The FRF estimator based on the errors-in-variables （EV） model of multi-input multi-output （MIMO） system is presented to reduce the bias error of FRF HI estimator. The FRF HI estimator is influenced by the noises in the inputs of the system and generates an under-estimation of the true FRF. The FRF estimator based on the EV model takes into account the errors in both the inputs and outputs of the system and would lead to more accurate FRF estimation. The FRF estimator based on the EV model is applied to the waveform replication on the 6-DOF （degree-of-freedom） hydraulic vibration table. The result shows that it is favorable to improve the control precision of the MIMO vibration control system.

Effects of errors-in-variables on the internal and external reliability measures

The reliability theory has been an important element of the classical geodetic adjustment theory and methods in the linear Gauss-Markov model. Although errors-in-variables(EIV) models have been intensively investigated, little has been done about reliability theory for EIV models. This paper first investigates the effect of a random coefficient matrix A on the conventional geodetic reliability measures as if the coefficient matrix were deterministic. The effects of such geodetic internal and external reliability measures due to the randomness of the coefficient matrix are worked out, which are shown to depend not only on the noise level of the random elements of A but also on the values of parameters. An alternative, linear approximate reliability theory is accordingly developed for use in EIV models. Both the EIV-affected reliability measures and the corresponding linear approximate measures fully account for the random errors of both the coefficient matrix and the observations, though formulated in a slightly different way. Numerical experiments have been carried to demonstrate the effects of errors-in-variables on reliability measures and compared with the conventional Baarda's reliability measures. The simulations have confirmed our theoretical results that the EIV-reliability measures depend on both the noise level of A and the parameter values. The larger the noise level of A, the larger the EIV-affected internal and external reliability measures;the larger the parameters,the larger the EIV-affected internal and external reliability measures.

线性Errors-in-Variables模型在确定汶川地震主震断层面中的应用

首先介绍线性Errors-in-Variables模型,给出求解回归系数的奇异值分解(SVD)算法和MATLAB源代码,其次指出在模型中所有变量均具有不可忽略的误差时,全最小二乘法得到回归系数估计更接近于模型中的真实系数,并通过理论分析和计算机仿真说明了这一结果,最后将线性模型和算法用于确定汶川大地震主震断层面,取得了与震源机制解一致的结果,说明了模型和算法的有效性。

Estimation in the polynomial errors-in-variables model

Estimators are presented for the coefficients of the polynomial errors-in-variables (EV) model when replicated observations are taken at some experimental points. These estimators are shown to be strongly consistent under mild conditions.

Error quantification of the normalized right graph symbol for an errors-in-variables system

This paper proposes a novel method to quantify the error of a nominal normalized right graph symbol （NRGS） for an errors- in-variables （EIV） system corrupted with bounded noise. Following an identification framework for estimation of a perturbation model set, a worst-case v-gap error bound for the estimated nominal NRGS can be first determined from a priori and a posteriori information on the underlying EIV system. Then, an NRGS perturbation model set can be derived from a close relation between the v-gap metric of two models and H∞-norm of their NRGSs＇ difference. The obtained NRGS perturbation model set paves the way for robust controller design using an H∞ loop-shaping method because it is a standard form of the well-known NCF （normalized coprime factor） perturbation model set. Finally, a numerical simulation is used to demonstrate the effectiveness of the proposed identification method.

Identification of Errors-in-Variables Systems with General Nonlinear Output Observations and with ARMA Observation Noises

This paper concerns the identification problem of scalar errors-in-variables(EIV)systems with general nonlinear output observations and ARMA observation noises.Under independent and identically distributed(i.i.d.)Gaussian inputs with unknown variance,recursive algorithms for estimating the parameters of the EIV systems are presented.For general nonlinear observations,conditions on the system are imposed to guarantee the almost sure convergence of the estimates.A simulation example is included to justify the theoretical results.

Robust Nonparametric Function Estimation for Errors-in-variables Models

This paper discusses robust nonparametric estimators of location regression function for errorsin-variables model with de-convolution kernel.The local constant smoother is used for the estimation of the nonparametric function,and the local linear smoother is proposed to deal with the boundary problem,as well as to improve the local constant smoother.We establish the asymptotic properties of the estimator,the influence function of the statistical functional and the breakdown point.A simulation study is carried out to demonstrate robust performance of the proposed estimator.The motorcycle data is presented to illustrate the application of the robust estimator further.

Asymptotic Properties of Wavelet Estimators in Partially Linear Errors-in-variables Models with Long-memory Errors

While the random errors are a function of Gaussian random variables that are stationary and long dependent, we investigate a partially linear errors-in-variables（EV） model by the wavelet method. Under general conditions, we obtain asymptotic representation of the parametric estimator, and asymptotic distributions and weak convergence rates of the parametric and nonparametric estimators. At last, the validity of the wavelet method is illuminated by a simulation example and a real example.

Efficient Statistical Inference for Partially Nonlinear Errors-in-Variables Models

In this paper, we consider the partially nonlinear errors-in-variables models when the non- parametric component is measured with additive error. The profile nonlinear least squares estimator of unknown parameter and the estimator of nonparametric component are constructed, and their asymptotic properties are derived under general assumptions. Finite sample performances of the proposed statistical inference procedures are illustrated by Monte Carlo simulation studies.

L-two-optimal identification of errors-in-variables models:a frequency-domain approach

This paper proposes an L-two-optimal identification approach to cope with errors-in-variables model （EIVM） identification. With normalized coprime factor model （NCFM） representations, L-two-optimal approximate models are derived from the framework of an EIVM according to the kernel and image representations of related signals. Based on the optimal approximate models, the v-gap metric is employed as a minimization criterion to optimize the parameters of a system model, and thus the resulting optimization problem can be solved by linear matrix inequalities （LMIs）. In terms of the optimized system model, the noise model （NM） can be readily obtained by right multiplication of an inner. Compared with other EIVM identification methods, the proposed one has a wider scope of applications because the statistical properties of disturbing noises are not demanded. It is also capable of giving identifiabiUty. Finally, a numerical simulation is used to verify the effectiveness of the proposed method.

Variable Selection in the Partially Linear Errors-in-Variables Models for Longitudinal Data

This paper proposes a new approach for variable selection in partially linear errors-in-variables （EV） models for longitudinal data by penalizing appropriate estimating functions. We apply the SCAD penalty to simultaneously select significant variables and estimate unknown parameters. The rate of convergence and the asymptotic normality of the resulting estimators are established. Furthermore, with proper choice of regularization parameters, we show that the proposed estimators perform as well as the oracle procedure. A new algorithm is proposed for solving penalized estimating equation. The asymptotic results are augmented by a simulation study.

Subspace identification for continuous-time errors-in-variables model from sampled data

We study the subspace identification for the continuous-time errors-in-variables model from sampled data.First,the filtering approach is applied to handle the time-derivative problem inherent in continuous-time identification.The generalized Poisson moment functional is focused.A total least squares equation based on this filtering approach is derived.Inspired by the idea of discrete-time subspace identification based on principal component analysis,we develop two algorithms to deliver consistent estimates for the continuous-time errors-in-variables model by introducing two different instrumental variables.Order determination and other instrumental variables are discussed.The usefulness of the proposed algorithms is illustrated through numerical simulation.

Estimation of Parameters of Partially Linear Errors-in-variables Models with Replicated Net Points of Observation

A kind of partially linear errors-in-variables models with replicated net points of observation are studied in this paper. Estimators of unknown parameters are given. Under certain regular conditions, it is shown that the estimators of the unknown parameters are strongly consistent and their a.s. convergence rates are achieved.

Randomly Weighted LAD-Estimation for Partially Linear Errors-in-Variables Models

The authors consider the partially linear model relating a response Y to predictors （x, T） with a mean function x^Tβ0 ＋ g（T） when the x＇s are measured with an additive error. The estimators of parameter β0 are derived by using the nearest neighbor-generalized randomly weighted least absolute deviation （LAD for short） method. The resulting estimator of the unknown vector 30 is shown to be consistent and asymptotically normal. In addition, the results facilitate the construction of confidence regions and the hypothesis testing for the unknown parameters. Extensive simulations are reported, showing that the proposed method works well in practical settings. The proposed methods are also applied to a data set from the study of an AIDS clinical trial group.

ON ASYMPTOTIC NORMALITY OF PARAMETERS IN MULTIPLE LINEAR ERRORS-IN-VARIABLES MODEL

This paper studies the parameter estimation of multiple dimensional linear errors-in-variables (EV) models in the case where replicated observations are available in some experimental points. Asymptotic normality is established under mild conditions, and the parameters entering the asymptotic variance are consistently estimated to render the result useable in the construction of large-sample confidence regions.

Testing Lack-of-fit for a Polynomial Errors-in-variables Model

When a regression model is applied as an approximation of underlying model of data, the model checking is important and relevant. In this paper, we investigate the lack-of-fit test for a polynomial errorin-variables model. As the ordinary residuals are biased when there exist measurement errors in covariables, we correct them and then construct a residual-based test of score type. The constructed test is asymptotically chi-squared under null hypotheses. Simulation study shows that the test can maintain the signi.cance level well. The choice of weight functions involved in the test statistic and the related power study are also investigated. The application to two examples is illustrated. The approach can be readily extended to handle more general models.

Algorithms and statistical analysis for linear structured weighted total least squares problem

Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.