Skip to main content

2013 | OriginalPaper | Buchkapitel

Measurement Error in Dynamic Models

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Many time series contain measurement (often sampling) error and the problem of assessing the impacts of such errors and accounting for them has been receiving increasing attention of late. This paper provides a survey of this problem with an emphasis on estimating the coefficients of the underlying dynamic model, primarily in the context of fitting linear and nonlinear autoregressive models. An overview is provided of the biases induced by ignoring the measurement error and of methods that have been proposed to correct for it, and remaining inferential challenges are outlined.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Anhänge
Nur mit Berechtigung zugänglich
Literatur
Zurück zum Zitat Aigner, D., Hsiao, C., Kapteyn, A., Wansbeek, T.: Latent variable models in econometrics. In: Griliches, Z., Intriligator, M.D. (eds.) Handbook of Econometrics, pp. 1321–1393. Elsevier, Amsterdam (1984) Aigner, D., Hsiao, C., Kapteyn, A., Wansbeek, T.: Latent variable models in econometrics. In: Griliches, Z., Intriligator, M.D. (eds.) Handbook of Econometrics, pp. 1321–1393. Elsevier, Amsterdam (1984)
Zurück zum Zitat Barker, D., Sibly, R.M.: The effects of environmental perturbation and measurement error on estimates of the shape parameter in the theta-logistic model of population regulation. Ecol. Model. 219, 170–177 (2008)CrossRef Barker, D., Sibly, R.M.: The effects of environmental perturbation and measurement error on estimates of the shape parameter in the theta-logistic model of population regulation. Ecol. Model. 219, 170–177 (2008)CrossRef
Zurück zum Zitat Bell, W.R., Wilcox, D.W.: The effect of sampling error on the time series behavior of consumption data. J. Econometrics. 55, 235–265 (1993)CrossRef Bell, W.R., Wilcox, D.W.: The effect of sampling error on the time series behavior of consumption data. J. Econometrics. 55, 235–265 (1993)CrossRef
Zurück zum Zitat Bolker, B.: Ecological Models and Data in R. Princeton University Press, Princeton, NJ (2008)MATH Bolker, B.: Ecological Models and Data in R. Princeton University Press, Princeton, NJ (2008)MATH
Zurück zum Zitat Box, G., Jenkins, G., Reinsel, G.: Time Series Analysis, Forecasting and Control, 3rd edn. Prentice Hall, Englewood Cliffs, NJ (1994)MATH Box, G., Jenkins, G., Reinsel, G.: Time Series Analysis, Forecasting and Control, 3rd edn. Prentice Hall, Englewood Cliffs, NJ (1994)MATH
Zurück zum Zitat Brockwell, P., Davis, R.: Introduction to Time Series and Forecasting. Springer, New York (2002)MATHCrossRef Brockwell, P., Davis, R.: Introduction to Time Series and Forecasting. Springer, New York (2002)MATHCrossRef
Zurück zum Zitat Buonaccorsi, J.P.: Measurement Error, Models, Methods, and Applications. Chapman and Hall, London (2010)MATHCrossRef Buonaccorsi, J.P.: Measurement Error, Models, Methods, and Applications. Chapman and Hall, London (2010)MATHCrossRef
Zurück zum Zitat Buonaccorsi, J.P., Staudenmayer, J., Carreras, M.: Modeling observation error and its effects in a random walk/extinction model. Theor. Popul. Biol. 70, 322–335 (2006)MATHCrossRef Buonaccorsi, J.P., Staudenmayer, J., Carreras, M.: Modeling observation error and its effects in a random walk/extinction model. Theor. Popul. Biol. 70, 322–335 (2006)MATHCrossRef
Zurück zum Zitat Buonaccorsi J,P., Staudenmayer, J.: Statistical methods to correct for observation error in a density-independent population model. Ecol. Monogr. 79, 299–324 (2009) Buonaccorsi J,P., Staudenmayer, J.: Statistical methods to correct for observation error in a density-independent population model. Ecol. Monogr. 79, 299–324 (2009)
Zurück zum Zitat Buonaccorsi, J.P., Staudenmayer, J.: Measurement error in linear autoregressive models II: further results and inferences. Working Paper, University of Massachusetts (2012) Buonaccorsi, J.P., Staudenmayer, J.: Measurement error in linear autoregressive models II: further results and inferences. Working Paper, University of Massachusetts (2012)
Zurück zum Zitat Burr, T., Chowell, G.: Observation and model error effects on parameter estimates in susceptible-infected-recovered epidemic model. Far East J. Theor. Stat. 19, 163–183 (2006)MathSciNetMATH Burr, T., Chowell, G.: Observation and model error effects on parameter estimates in susceptible-infected-recovered epidemic model. Far East J. Theor. Stat. 19, 163–183 (2006)MathSciNetMATH
Zurück zum Zitat Calder, C., Lavine, M., Muller, P., Clark, J.: Incorporating multiple sources of stochasticity into dynamic population models. Ecology 84, 1395–1402 (2003)CrossRef Calder, C., Lavine, M., Muller, P., Clark, J.: Incorporating multiple sources of stochasticity into dynamic population models. Ecology 84, 1395–1402 (2003)CrossRef
Zurück zum Zitat Carroll, R.J., Stefanski, L.A., Ruppert, D., Crainiceanu C.M.: Measurement Error in Nonlinear Models, 2nd edn. Chapman and Hall, London (2006)MATHCrossRef Carroll, R.J., Stefanski, L.A., Ruppert, D., Crainiceanu C.M.: Measurement Error in Nonlinear Models, 2nd edn. Chapman and Hall, London (2006)MATHCrossRef
Zurück zum Zitat Chanda, K.C.: Asymptotic properties of estimators for autoregressive models with errors in variables. Ann. Stat. 24, 423–430 (1996)MathSciNetMATHCrossRef Chanda, K.C.: Asymptotic properties of estimators for autoregressive models with errors in variables. Ann. Stat. 24, 423–430 (1996)MathSciNetMATHCrossRef
Zurück zum Zitat Cheang, W., Reinsel, G.C.: Bias reduction of autoregressive estimates in time series regression model through restricted maximum likelihood. J. Am. Stat. Assoc. 95, 1173–1184 (2000)MathSciNetMATHCrossRef Cheang, W., Reinsel, G.C.: Bias reduction of autoregressive estimates in time series regression model through restricted maximum likelihood. J. Am. Stat. Assoc. 95, 1173–1184 (2000)MathSciNetMATHCrossRef
Zurück zum Zitat Clark, J.S., Bjornstad, O.N.: Population time series, process variability, observation errors, missing values, lags, and hidden states. Ecology. 85, 3140–3150 (2004)CrossRef Clark, J.S., Bjornstad, O.N.: Population time series, process variability, observation errors, missing values, lags, and hidden states. Ecology. 85, 3140–3150 (2004)CrossRef
Zurück zum Zitat Dennis, B., Ponciano, J., Lele, S., Taper, M., Staples, D.: Estimating density dependence, process noise, and observation error. Ecol. Monogr. 76, 323–341 (2006)CrossRef Dennis, B., Ponciano, J., Lele, S., Taper, M., Staples, D.: Estimating density dependence, process noise, and observation error. Ecol. Monogr. 76, 323–341 (2006)CrossRef
Zurück zum Zitat Dennis, B., Ponciano, J.M., Taper, M.L.: Replicated sampling increases efficiency in monitoring biological populations. Ecology 91, 610–620 (2010)CrossRef Dennis, B., Ponciano, J.M., Taper, M.L.: Replicated sampling increases efficiency in monitoring biological populations. Ecology 91, 610–620 (2010)CrossRef
Zurück zum Zitat De Valpine, P.: Review of methods for fitting time-series models with process and observation error and likelihood calculations for nonlinear non-Gaussian state-space models. Bull. Mar. Sci. 70, 455–471 (2002) De Valpine, P.: Review of methods for fitting time-series models with process and observation error and likelihood calculations for nonlinear non-Gaussian state-space models. Bull. Mar. Sci. 70, 455–471 (2002)
Zurück zum Zitat De Valpine, P.: Monte-Carlo state-space likelihoods by weighted posterior kernel density estimation. J. Am. Stat. Assoc. 99, 523–536 (2004)MATHCrossRef De Valpine, P.: Monte-Carlo state-space likelihoods by weighted posterior kernel density estimation. J. Am. Stat. Assoc. 99, 523–536 (2004)MATHCrossRef
Zurück zum Zitat De Valpine, P., Hastings, A.: Fitting population models incorporating process noise and observation error. Ecol. Monogr. 72, 57–76 (2002)CrossRef De Valpine, P., Hastings, A.: Fitting population models incorporating process noise and observation error. Ecol. Monogr. 72, 57–76 (2002)CrossRef
Zurück zum Zitat De Valpine, P., Hilborn, R.: State-space likelihoods for nonlinear fisheries time series. Can. J. Fish. Aquat. Sci. 62, 1937–1952 (2005)CrossRef De Valpine, P., Hilborn, R.: State-space likelihoods for nonlinear fisheries time series. Can. J. Fish. Aquat. Sci. 62, 1937–1952 (2005)CrossRef
Zurück zum Zitat Ellner, S., Yodit, S., Smith, R.: Fitting population dynamic models to time-series by gradient matching. Ecology 83, 2256–2270 (2002)CrossRef Ellner, S., Yodit, S., Smith, R.: Fitting population dynamic models to time-series by gradient matching. Ecology 83, 2256–2270 (2002)CrossRef
Zurück zum Zitat Harvey, A.C.: Forecasting, Structural Time Series Models, and the Kalman Filter. Cambridge University Press, Cambridge (1990)MATH Harvey, A.C.: Forecasting, Structural Time Series Models, and the Kalman Filter. Cambridge University Press, Cambridge (1990)MATH
Zurück zum Zitat Fuller, W.: Time Series Analysis. Wiley, New York (1996) Fuller, W.: Time Series Analysis. Wiley, New York (1996)
Zurück zum Zitat Hovestadt, T., Nowicki, P.: Process and measurement errors of population size, their mutual effects on precision and bias of estimates for demographic parameters. Biodivers. Conserv. 17, 3417–3429 (2008)CrossRef Hovestadt, T., Nowicki, P.: Process and measurement errors of population size, their mutual effects on precision and bias of estimates for demographic parameters. Biodivers. Conserv. 17, 3417–3429 (2008)CrossRef
Zurück zum Zitat Ives, A.R., Dennis, B., Cottingham, K.L., Carpenter, S.R.: Estimating community stability and ecological interactions from time-series data. Ecol. Monogr. 73, 301–330 (2003)CrossRef Ives, A.R., Dennis, B., Cottingham, K.L., Carpenter, S.R.: Estimating community stability and ecological interactions from time-series data. Ecol. Monogr. 73, 301–330 (2003)CrossRef
Zurück zum Zitat Ives, A.R, Abbott, K., Ziebarth, N.: Analysis of ecological time series with ARMA(p,q) models. Ecololgy 91, 858–871 (2010)CrossRef Ives, A.R, Abbott, K., Ziebarth, N.: Analysis of ecological time series with ARMA(p,q) models. Ecololgy 91, 858–871 (2010)CrossRef
Zurück zum Zitat Jungbacker, B., Koopman, S.J.: Monte Carlo estimation for nonlinear non-Gaussian state space models. Biometrika 94, 827–839 (2007)MathSciNetMATHCrossRef Jungbacker, B., Koopman, S.J.: Monte Carlo estimation for nonlinear non-Gaussian state space models. Biometrika 94, 827–839 (2007)MathSciNetMATHCrossRef
Zurück zum Zitat Knape, J.: Estimability of density dependence in models of time series data. Ecology 89, 2994–3000 (2008)CrossRef Knape, J.: Estimability of density dependence in models of time series data. Ecology 89, 2994–3000 (2008)CrossRef
Zurück zum Zitat Knape, J., Jonzén, N., Skold, M.: Observation distributions for state space models of population survey data. J. Anim. Ecol. 80, 1269–1277 (2011)CrossRef Knape, J., Jonzén, N., Skold, M.: Observation distributions for state space models of population survey data. J. Anim. Ecol. 80, 1269–1277 (2011)CrossRef
Zurück zum Zitat Koons, B.K., Foutz, R.V.: Estimating moving average parameters in the presence of measurement error. Comm. Stat. 19, 3179–3187 (1990)MathSciNetCrossRef Koons, B.K., Foutz, R.V.: Estimating moving average parameters in the presence of measurement error. Comm. Stat. 19, 3179–3187 (1990)MathSciNetCrossRef
Zurück zum Zitat Lee, J.H., Shin, D.W.: Maximum likelihood estimation for ARMA models in the presence of ARMA errors. Comm. Stat. Theor. Meth. 26, 1057–1072 (1997)MathSciNetMATHCrossRef Lee, J.H., Shin, D.W.: Maximum likelihood estimation for ARMA models in the presence of ARMA errors. Comm. Stat. Theor. Meth. 26, 1057–1072 (1997)MathSciNetMATHCrossRef
Zurück zum Zitat Lele, S.R.: Sampling variability and estimates of density dependence, a composite-likelihood approach. Ecology 87, 189–202 (2006)CrossRef Lele, S.R.: Sampling variability and estimates of density dependence, a composite-likelihood approach. Ecology 87, 189–202 (2006)CrossRef
Zurück zum Zitat Lele, S.R., Dennis, B., Lutscher, F.: Data cloning, easy maximum likelihood estimation for complex ecological models using Bayesian Markov chain Monte Carlo methods. Ecol. Lett. 10, 551–563 (2007)CrossRef Lele, S.R., Dennis, B., Lutscher, F.: Data cloning, easy maximum likelihood estimation for complex ecological models using Bayesian Markov chain Monte Carlo methods. Ecol. Lett. 10, 551–563 (2007)CrossRef
Zurück zum Zitat Lillegard, M., Engen, S., Saether, B.E., Grotan, V., Drever, M.: Estimation of population parameters from aerial counts of North American mallards: a cautionary tale. Ecol. Appl. 18, 197–207 (2008)CrossRef Lillegard, M., Engen, S., Saether, B.E., Grotan, V., Drever, M.: Estimation of population parameters from aerial counts of North American mallards: a cautionary tale. Ecol. Appl. 18, 197–207 (2008)CrossRef
Zurück zum Zitat Mallick, T., Sutradhar, B.: GQL versus conditional GQL inferences for non-stationary time series of counts with overdispersion. J. Time Anal. 29, 402–420 (2008)MathSciNetMATHCrossRef Mallick, T., Sutradhar, B.: GQL versus conditional GQL inferences for non-stationary time series of counts with overdispersion. J. Time Anal. 29, 402–420 (2008)MathSciNetMATHCrossRef
Zurück zum Zitat Miazaki, E.S., Dorea, C.C.Y.: Estimation of the parameters of a time series subject to the error of rotation sampling. Commun. Stat. A - Theor. Meth. 22, 805–825 (1993)MathSciNetMATHCrossRef Miazaki, E.S., Dorea, C.C.Y.: Estimation of the parameters of a time series subject to the error of rotation sampling. Commun. Stat. A - Theor. Meth. 22, 805–825 (1993)MathSciNetMATHCrossRef
Zurück zum Zitat McCulloch, C., Searle, S., Neuhaus, J.: Generalized, Linear, and Mixed Models, 2nd edn. Wiley, New York (2008)MATH McCulloch, C., Searle, S., Neuhaus, J.: Generalized, Linear, and Mixed Models, 2nd edn. Wiley, New York (2008)MATH
Zurück zum Zitat Morris, W.F., Doak, D.F.: Quantitative Conservation Biology: Theory and Practice of Population Variability Analysis. Sinauer Associates, Sunderland, MA (2002) Morris, W.F., Doak, D.F.: Quantitative Conservation Biology: Theory and Practice of Population Variability Analysis. Sinauer Associates, Sunderland, MA (2002)
Zurück zum Zitat Pfeffermann, D., Feder, M., Signorelli, D.: Estimation of autocorrelations of survey errors with application to trend estimation in small areas. J. Bus. Econ. Stat. 16, 339–348 (1998)MathSciNet Pfeffermann, D., Feder, M., Signorelli, D.: Estimation of autocorrelations of survey errors with application to trend estimation in small areas. J. Bus. Econ. Stat. 16, 339–348 (1998)MathSciNet
Zurück zum Zitat Ponciano, J., Taper, M., Dennis, B., Lele, S.: Hierarchical models in ecology, confidence intervals hypothesis testing, and model selection using data cloning. Ecology 90, 356–362 (2009)CrossRef Ponciano, J., Taper, M., Dennis, B., Lele, S.: Hierarchical models in ecology, confidence intervals hypothesis testing, and model selection using data cloning. Ecology 90, 356–362 (2009)CrossRef
Zurück zum Zitat Resendes, D.: Statistical methods for nonlinear dynamic models with measurement error using the Ricker model. Ph.D. thesis, University of Massachusetts, Amherst (2011) Resendes, D.: Statistical methods for nonlinear dynamic models with measurement error using the Ricker model. Ph.D. thesis, University of Massachusetts, Amherst (2011)
Zurück zum Zitat Sakai, H., Soeda, T., Hidekatsu, T.: On the relation between fitting autoregression and periodogram with applications. Ann. Stat. 7, 96–107 (1979)MATHCrossRef Sakai, H., Soeda, T., Hidekatsu, T.: On the relation between fitting autoregression and periodogram with applications. Ann. Stat. 7, 96–107 (1979)MATHCrossRef
Zurück zum Zitat Saether, B., Lilligard, M., Grotan, V., Drever, M., Engen, S., Nudds, T., Podruzny, K.: Geographical gradients in the population dynamics of North American prairie ducks. J. Anim. Ecol. 77, 869–882 (2008)CrossRef Saether, B., Lilligard, M., Grotan, V., Drever, M., Engen, S., Nudds, T., Podruzny, K.: Geographical gradients in the population dynamics of North American prairie ducks. J. Anim. Ecol. 77, 869–882 (2008)CrossRef
Zurück zum Zitat Schmid, C.H., Segal, M.R., Rosner, B.: Incorporating measurement error in the estimation of autoregressive models for longitudinal data. J. Stat. Plann. Infer. 42, 1–18 (1994)MathSciNetMATHCrossRef Schmid, C.H., Segal, M.R., Rosner, B.: Incorporating measurement error in the estimation of autoregressive models for longitudinal data. J. Stat. Plann. Infer. 42, 1–18 (1994)MathSciNetMATHCrossRef
Zurück zum Zitat Solow, A.R.: On fitting a population model in the presence of observation error. Ecology 79, 1463–1466 (1998)CrossRef Solow, A.R.: On fitting a population model in the presence of observation error. Ecology 79, 1463–1466 (1998)CrossRef
Zurück zum Zitat Solow, A.R.: Observation error and the detection of delayed density dependence. Ecology 82, 3263–3264 (2001)CrossRef Solow, A.R.: Observation error and the detection of delayed density dependence. Ecology 82, 3263–3264 (2001)CrossRef
Zurück zum Zitat Staudenmayer, J., Buonaccorsi, J.P.: Measurement error in linear autoregressive models. J. Am. Stat. Assoc. 100, 841–852 (2005)MathSciNetMATHCrossRef Staudenmayer, J., Buonaccorsi, J.P.: Measurement error in linear autoregressive models. J. Am. Stat. Assoc. 100, 841–852 (2005)MathSciNetMATHCrossRef
Zurück zum Zitat Stefanski, L., Cook, J.: Simulation-extrapolation: the measurement error jackknife. J. Am. Stat. Assoc. 90, 1247–1256 (1995)MathSciNetMATHCrossRef Stefanski, L., Cook, J.: Simulation-extrapolation: the measurement error jackknife. J. Am. Stat. Assoc. 90, 1247–1256 (1995)MathSciNetMATHCrossRef
Zurück zum Zitat Stenseth, N.C., Viljugrein, H., Saitoh, T., Hansen, T.F., Kittilsen, M.O., Bolviken, E., Glockner, F.: Seasonality, density dependence, and population cycles in Hokkaido voles. Proc. Natl. Acad. Sci. USA. 100, 11478–11483 (2003)CrossRef Stenseth, N.C., Viljugrein, H., Saitoh, T., Hansen, T.F., Kittilsen, M.O., Bolviken, E., Glockner, F.: Seasonality, density dependence, and population cycles in Hokkaido voles. Proc. Natl. Acad. Sci. USA. 100, 11478–11483 (2003)CrossRef
Zurück zum Zitat Tripodis, Y., Buonaccorsi, J.P.: Prediction and forecasting in linear models with measurement error and unknown parameters. J. Stat. Plann. Infer. 139, 4039–4050 (2009)MathSciNetMATHCrossRef Tripodis, Y., Buonaccorsi, J.P.: Prediction and forecasting in linear models with measurement error and unknown parameters. J. Stat. Plann. Infer. 139, 4039–4050 (2009)MathSciNetMATHCrossRef
Zurück zum Zitat Viljugrein, H., Stenseth, N.C., Smith, G.W., Steinbakk, G.H.: Density dependence in North American ducks. Ecology 86, 245–254 (2005)CrossRef Viljugrein, H., Stenseth, N.C., Smith, G.W., Steinbakk, G.H.: Density dependence in North American ducks. Ecology 86, 245–254 (2005)CrossRef
Zurück zum Zitat Walker, A.M.: Some consequences of superimposed error in time series analysis. Biometrika 47, 33–43 (1960)MathSciNetMATH Walker, A.M.: Some consequences of superimposed error in time series analysis. Biometrika 47, 33–43 (1960)MathSciNetMATH
Zurück zum Zitat Wang, G.: On the latent state estimation of nonlinear population dynamics using Bayesian and non-Bayesian state-space models. Ecol. Model. 20, 521–528 (2007)CrossRef Wang, G.: On the latent state estimation of nonlinear population dynamics using Bayesian and non-Bayesian state-space models. Ecol. Model. 20, 521–528 (2007)CrossRef
Zurück zum Zitat Wang, G., Hobbs, N.T., Boone, R.B., Illius, A.W., Gordon, I.J., Gross, J.E., Hamlin, K.L.: Spatial and temporal variability modify density dependence in populations of large herbivores. Ecology 87(1), 95–102 (2006)CrossRef Wang, G., Hobbs, N.T., Boone, R.B., Illius, A.W., Gordon, I.J., Gross, J.E., Hamlin, K.L.: Spatial and temporal variability modify density dependence in populations of large herbivores. Ecology 87(1), 95–102 (2006)CrossRef
Zurück zum Zitat Williams, C.K., Ives, A.R., Applegate, R.D.: Population dynamics across geographical ranges, time-series analyses of three small game species. Ecology 84, 2654–2667 (2003)CrossRef Williams, C.K., Ives, A.R., Applegate, R.D.: Population dynamics across geographical ranges, time-series analyses of three small game species. Ecology 84, 2654–2667 (2003)CrossRef
Zurück zum Zitat Wong, W-K., Miller, R.B.: Repeated time series analysis of ARIMA-noise models. J. Bus. Econ. Stat. 8, 243–250 (1990) Wong, W-K., Miller, R.B.: Repeated time series analysis of ARIMA-noise models. J. Bus. Econ. Stat. 8, 243–250 (1990)
Zurück zum Zitat Wong, W-K., Miller, R.B., Shrestha, K.: Maximum likelihood estimation of ARMA models with error processes for replicated observations. J. Appl. Stat. Sci. 10, 287–297 (2001)MathSciNetMATH Wong, W-K., Miller, R.B., Shrestha, K.: Maximum likelihood estimation of ARMA models with error processes for replicated observations. J. Appl. Stat. Sci. 10, 287–297 (2001)MathSciNetMATH
Metadaten
Titel
Measurement Error in Dynamic Models
verfasst von
John P. Buonaccorsi
Copyright-Jahr
2013
Verlag
Springer New York
DOI
https://doi.org/10.1007/978-1-4614-6871-4_3