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Weighted least squares estimators in possibly misspecified nonlinear regression

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Abstract

The behavior of estimators for misspecified parametric models has been well studied. We consider estimators for misspecified nonlinear regression models, with error and covariates possibly dependent. These models are described by specifying a parametric model for the conditional expectation of the response given the covariates. This is a parametric family of conditional constraints, which makes the model itself close to nonparametric. We study the behavior of weighted least squares estimators both when the regression function is correctly specified, and when it is misspecified and also involves possible additional covariates.

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References

  • Aguirre–Torres V, Domínguez MA (2004) Efficient method of moments in misspecified i.i.d. models. Econom Theory 20:513–534

    Article  MATH  Google Scholar 

  • Andrews DWK, Pollard D (1994) An introduction to functional central limit theorems for dependent stochastic processes. Int Stat Rev 62:119–132

    Article  MATH  Google Scholar 

  • Bickel PJ, Klaassen CAJ, Ritov Y, Wellner JA (1998) Efficient and adaptive estimation for semiparametric models. Springer, Berlin Heidelberg New York

    MATH  Google Scholar 

  • Gould A, Lawless JF (1988) Consistency and efficiency of regression coefficient estimates in location-scale models. Biometrika 75:535–540

    MATH  MathSciNet  Google Scholar 

  • Greenwood PE, Wefelmeyer W (1997) Maximum likelihood estimator and Kullback–Leibler information in misspecified Markov chain models. Teor. Veroyatnost. i Primenen. 42:169–178

    MATH  MathSciNet  Google Scholar 

  • Hájek J (1970) A characterization of limiting distributions of regular estimates. Z Wahrsch Verw Gebiete 14:323–330

    Article  MATH  Google Scholar 

  • Le Cam L (1960) Locally asymptotically normal families of distributions. Univ Calif Publ Stat 3:37–98

    MathSciNet  Google Scholar 

  • Lindsay B, Qu A (2003) Inference functions and quadratic score tests. Stat Sci 18:394–410

    Article  MATH  MathSciNet  Google Scholar 

  • McKean JW, Sheather SJ, Hettmansperger TP (1993) The use and interpretation of residuals based on robust estimation. J Am Stat Assoc 88:1254–1263

    Article  MATH  MathSciNet  Google Scholar 

  • Michaelis L, Menten ML (1913) Kinetik der Invertinwirkung. Biochemische Zeitschrift 49:333–369

    Google Scholar 

  • Müller UU, Wefelmeyer W (2002a) Estimators for models with constraints involving unknown parameters. Math Methods Stat 11:221–235

    MATH  Google Scholar 

  • Müller UU, Wefelmeyer W (2002b) Autoregression, estimating functions, and optimality criteria. In: Gulati C, Lin YX, Rayner J and Mishra S (eds) Advances in statistics, combinatorics and related areas. World Scientific Publishing, Singapore, pp. 180–195

    Google Scholar 

  • Qu A, Lindsay BG, Li B (2000) Improving generalised estimating equations using quadratic inference functions. Biometrika 87:823–836

    Article  MATH  MathSciNet  Google Scholar 

  • Ruppert D, Cressie N, Carroll RJ (1989) A transformation/weighting model for estimating Michaelis–Menten parameters. Biometrics 45:637–656

    Article  Google Scholar 

  • Sarkar N (1989) Comparisons among some estimators in misspecified linear models with multicollinearity. Ann Inst Stat Math 41:717–724

    Article  MATH  MathSciNet  Google Scholar 

  • Severini TA (1998) Some properties of inferences in misspecified linear models. Stat Probab Lett 40:149–153

    Article  MATH  MathSciNet  Google Scholar 

  • Shi P, Ye JJ, Zhou J (2003) Minimax robust designs for misspecified regression models. Can J Stat 31:397–414

    Article  MATH  MathSciNet  Google Scholar 

  • Struthers CA, Kalbfleisch JD (1986) Misspecified proportional hazard models. Biometrika 73:363–369

    Article  MATH  MathSciNet  Google Scholar 

  • White H (1981) Consequences and detection of misspecified nonlinear regression models. J Am Stat Assoc 76:419–433

    Article  MATH  Google Scholar 

  • White H (1982) Maximum likelihood estimation of misspecified models. Econometrica 50:1–26

    Article  MATH  MathSciNet  Google Scholar 

  • Zhang J and Liu A (2003) Local polynomial fitting based on empirical likelihood. Bernoulli 9:579–605

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Statistics, Texas A&M Univeristy, College Station, TX, 77843-3143, USA

    Ursula U. Müller

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  1. Ursula U. Müller
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Correspondence to Ursula U. Müller.

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Müller, U.U. Weighted least squares estimators in possibly misspecified nonlinear regression. Metrika 66, 39–59 (2007). https://doi.org/10.1007/s00184-006-0092-5

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  • DOI: https://doi.org/10.1007/s00184-006-0092-5

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