Modelling Error
Contents |
linear model Generalized linear model Discrete choice Logistic regression Multinomial logit Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson Multilevel model Fixed effects Random effects Mixed model Nonlinear regression Nonparametric Semiparametric Robust Quantile Isotonic Principal errors in variables model components Least angle Local Segmented Errors-in-variables Estimation Least squares Ordinary least squares Linear
Measurement Error In Dependent Variable
(math) Partial Total Generalized Weighted Non-linear Non-negative Iteratively reweighted Ridge regression Least absolute deviations Bayesian Bayesian multivariate Background Regression model error in variables regression in r validation Mean and predicted response Errors and residuals Goodness of fit Studentized residual Gauss–Markov theorem Statistics portal v t e In statistics, errors-in-variables models or measurement error models[1][2] are regression models that account
Modeling Error Definition
for measurement errors in the independent variables. In contrast, standard regression models assume that those regressors have been measured exactly, or observed without error; as such, those models account only for errors in the dependent variables, or responses.[citation needed] In the case when some regressors have been measured with errors, estimation based on the standard assumption leads to inconsistent estimates, meaning that the parameter estimates do model error statistics not tend to the true values even in very large samples. For simple linear regression the effect is an underestimate of the coefficient, known as the attenuation bias. In non-linear models the direction of the bias is likely to be more complicated.[3][4] Contents 1 Motivational example 2 Specification 2.1 Terminology and assumptions 3 Linear model 3.1 Simple linear model 3.2 Multivariable linear model 4 Non-linear models 4.1 Instrumental variables methods 4.2 Repeated observations 5 References 6 Further reading 7 External links Motivational example[edit] Consider a simple linear regression model of the form y t = α + β x t ∗ + ε t , t = 1 , … , T , {\displaystyle y_ β 0=\alpha +\beta x_ ^ 9^{*}+\varepsilon _ ^ 8\,,\quad t=1,\ldots ,T,} where x t ∗ {\displaystyle x_ ^ 5^{*}} denotes the true but unobserved regressor. Instead we observe this value with an error: x t = x t ∗ + η t {\displaystyle x_ ^ 3=x_ ^ 2^{*}+\eta _ ^ 1\,} where the measurement error η t {\displaystyle \eta _ ^ 7} is assumed to be independent from the true value x t ∗ {\displaystyle x_ ^ 5^{*}} . If th
the modelling error in two operator splitting algorithms for porous media flowAuthorsAuthors and affiliationsK. BrusdalH.K. DahleK. Hvistendahl KarlsenT. MannsethArticleDOI: 10.1023/A:1011585732722Cite this article as: Brusdal,
Modelling Error In Numerical Methods
K., Dahle, H., Karlsen, K.H. et al. Computational Geosciences (1998)
Attenuation Bias Proof
2: 23. doi:10.1023/A:1011585732722 1 Citations 91 Views AbstractOperator splitting methods are often used to solve convection–diffusion measurement error bias definition problems of convection dominated nature. However, it is well known that such methods can produce significant (splitting) errors in regions containing self sharpening fronts. To https://en.wikipedia.org/wiki/Errors-in-variables_models amend this shortcoming, corrected operator splitting methods have been developed. These approaches use the wave structure from the convection step to identify the splitting error. This error is then compensated for in the diffusion step. The main purpose of the present work is to illustrate the importance of the correction step in http://link.springer.com/article/10.1023/A:1011585732722 the context of an inverse problem. The inverse problem will consist of estimating the fractional flow function in a one‐dimensional saturation equation.operator splittingtwo‐phase flowsaturation equationmodelling errorinverse problemReferences[1]Y. Bard, Nonlinear Parameter Estimation (Wiley, New York, 1981).Google Scholar[2]J.T. Beale and A. Majda, Rates of convergence for viscous splitting of the Navier–Stokes equations, Math. Comp. 37(156) (1981) 243–259.Google Scholar[3]G. Chavent and J. Jaffre, Mathematical Models and Finite Elements for Reservoir Simulation, Studies in Mathematics and Its Applications, Vol. 17 (North-Holland, Amsterdam, 1986).Google Scholar[4]H.K. Dahle, Adaptive characteristic operator splitting techniques for convection-dominated diffusion problems in one and two space dimensions, Ph.D. thesis, Department of Mathematics, University of Bergen (1988).[5]H.K. Dahle, ELLAM-based operator splitting for nonlinear advection diffusion equations, Technical Report 98, Department of Mathematics, University of Bergen (1995).[6]H.K. Dahle, M.S. Espedal, R.E. Ewing and O. Sævareid, Characteristic adaptive subdomain methods for reservoir flow problems, Numer. Methods Partial Differential Equations 6 (1990) 279–309.Google Scholar[7]H.K. Dahle, M.S. Es
contact our Journal Customer Services team. http://wiley.force.com/Interface/ContactJournalCustomerServices_V2. If your institution does not currently subscribe to this content, please recommend the title to your librarian.Login error in via other institutional login options http://onlinelibrary.wiley.com/login-options.You can purchase online access to this Article for a 24-hour period (price varies by title) If you already have a Wiley Online Library errors in variables or Wiley InterScience user account: login above and proceed to purchase the article.New Users: Please register, then proceed to purchase the article. Login via OpenAthens or Search for your institution's name below to login via Shibboleth. Institution Name Registered Users please login: Access your saved publications, articles and searchesManage your email alerts, orders and subscriptionsChange your contact information, including your password E-mail: Password: Forgotten Password? Please register to: Save publications, articles and searchesGet email alertsGet all the benefits mentioned below! Register now >
be down. Please try the request again. Your cache administrator is webmaster. Generated Thu, 20 Oct 2016 19:56:35 GMT by s_wx1126 (squid/3.5.20)