Local nonlinear least squares: Using parametric information in nonparametric regression

Journal of Econometrics

Volumn 99, Issue 1, 2000, Pages 63-106

  Gozalo, Pedro ^a   Linton, Oliver ^b  

^a BROWN UNIVERSITY   (United States)

^b LONDON SCHOOL OF ECONOMICS   (United Kingdom)

Author keywords

Binary choice; Kernel; Local regression; Nonparametric regression; Parametric regression

Indexed keywords

EID: 0041757246     PISSN: 03044076     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4076(00)00031-2     Document Type: Article

References (48)

1. Anand, S., Harris, C.J., Linton, O., 1993. On the concept of ultrapoverty. Harvard Center for Population Studies Working paper 93-02.
2. Andrews, D.W.K., 1993. Tests for parameter instability and structural change with unknown change point. Econometrica 61, 821-856.
3. Andrews, D.W.K., 1994. Empirical process methods in econometrics. In: Engle III, R.F., McFadden, D. (Eds.), The Handbook of Econometrics, Vol. IV. North-Holland, Amsterdam.
4. Ansley, C.F., Kohn, R., Wong, C., 1993. Nonparametric spline regression with prior information. Biometrika 80, 75-88.
5. Bierens, H.J., 1987. Kernel estimators of regression functions. In: Bewley, T.F. (Ed.), Advances in Econometrics: Fifth World Congress, Vol. 1. Cambridge University Press, Cambridge, MA.
6. Bierens, H.J., Pott-Buter, H.A., 1990. Specification of household Engel curves by nonparametric regression. Econometric Reviews 9, 123-184.
7. Copas, J.B., 1994. Local likelihood based on kernel censoring. Journal of the Royal Statistical Society, Series B 57, 221-235.
8. Cox, D.R., Reid, N., 1987. Parameter orthogonality and approximate conditional inference (with discussion). Journal of the Royal Statistical Society, Series B 49, 1-39.
9. Deaton, A., 1986. Demand analysis. In: Griliches, Z., Intriligator, M. (Eds.), The Handbook of Econometrics, Vol. III. North-Holland, Amsterdam.
10. Fan, J., 1992. Design-adaptive nonparametric regression. Journal of the American Statistical Association 87, 998-1004.
11. Fan, J., 1993. Local linear regression smoothers and their minimax efficiencies. The Annals of Statistics 21, 196-216.
12. Fan, J., Gijbels, I., 1992. Variable bandwidth and local linear regression smoothers. Annals of Statistics 20, 2008-2036.
13. Fan, J., Heckman, N., Wand, M., 1995. Local polynomial kernel regression for generalized linear models and quasi-likelihood functions. Journal of the American Statistical Association 90, 141-150.
14. Fenton, V.M., Gallant, A.R., 1996. Convergence rates for SNP density estimators. Econometrica 64, 719-727.
15. Gallant, A.R., White, H., 1988. A Unified Theory of Estimation for Nonlinear Dynamic Models. Blackwell, Oxford.
16. Giné, E., Zinn, J., 1984. Some limit theorems for empirical processes. Annals of Probability 12, 929-989.
17. Gourieroux, C., Monfort, A., Tenreiro, A., 1994. Kernel M-estimators: nonparametric diagnostics for structural models. Manuscript, CEPREMAP, Paris.
18. Härdle, W., 1990. Applied Nonparametric Regression. Cambridge University Press, Cambridge, MA.
19. Härdle, W., Linton, O.B., 1994. Applied nonparametric methods. In: Engle III, R.F., McFadden, D. (Eds.), The Handbook of Econometrics, Vol. IV. North-Holland, Amsterdam, pp. 2295-2339.
20. Hastie, T., Tibshirani, R., 1993. Varying-coefficient models (with discussion). Journal of the Royal Statistical Society, Series B 55, 757-796.
21. Hjort, N.L., 1993. Dynamic likelihood hazard estimation. Biometrika, to appear.
22. Hjort, N.L., Jones, M.C., 1994. Local fitting of regression models by likelihood: what is important? Institute of Mathematics, University of Oslo, Statistical Research Report No. 10.
23. Hjort, N.L., Jones, M.C., 1996. Locally parametric nonparametric density estimation. Annals of Statistics 24, 1619-1647.
24. Horowitz, J., 1992. A smoothed maximum score estimator for the binary response model. Econometrica 60, 505-531.
25. Horowitz, J., 1993. Semiparametric estimation of a work-trip mode choice model. Journal of Econometrics 58, 49-70.
26. Jennrich, R.I., 1969. Asymptotic properties of non-linear least squares estimators. The Annals of Mathematical Statistics 40, 633-643.
27. Klein, R.W., Spady, R.H., 1993. An efficient semiparametric estimator for discrete choice models. Econometrica 61, 387-421.
28. Loader, C.R., 1996. Local likelihood density estimation. Annals of Statistics 24, 1602-1618.
29. McManus, D.A., 1994. Making the Cobb-Douglas functional form an efficient nonparametric estimator through localization. Working Paper No. 94-31, Finance and Economics Discussion Series, Federal Reserve Board, Washington D.C.
30. Manski, C.F., 1975. The maximum score estimation of the stochastic utility model of choice. Journal of Econometrics 3, 205-228.
31. Masry, E., 1996. Multivariate regression estimation: local polynomial fitting for time series. Stochastic Processes and their Applications 65, 81-101.
32. Müller, H.G., 1988. Nonparametric Regression Analysis of Longitudinal Data. Springer, New York, NY.
33. Newey, W., McFadden, D., 1994. Large sample estimation and hypothesis testing. In: Engle III, R.F., McFadden, D. (Eds.), The Handbook of Econometrics, Vol. IV. North-Holland, Amterdam.
34. Nolan, D., Pollard, D., 1987. U-Processes: rates of convergence. Annals of Statistics 15, 780-799.
35. Pakes, A., Pollard, D., 1989. Simulation and the asymptotics of optimization estimators. Econometrica 57, 1027-1057.
36. Pollard, D., 1984. Convergence of Stochastic Processes. Springer, New York, NY.
37. Pötscher, B.M., Prucha, I.R., 1991. Basic structure of the asymptotic theory in dynamic nonlinear econometric models I: consistency and approximation concepts. Econometric Reviews 10, 125-216.
38. Robinson, P.M., 1989. Time varying nonlinear regression. In: Hackl, P., Westland, A. (Eds.), Statistical Analysis and Forecasting of Economic Structural Change. Springer, New York, NY.
39. Ruppert, D., Wand, M.P., 1994. Multivariate weighted least squares regression. The Annals of Statistics 22, 1346-1370.
40. Schuster, E.F., Yakowitz, S., 1979. Contributions to the theory of nonparametric regression with application to system identification. Annals of Statistics 7, 139-145.
41. Silverman, B.W., 1978. Weak and strong uniform consistency of the kernel estimate of a density and its derivatives. Annals of Statistics 6, 177-184.
42. Staniswalis, J.G., 1989. The kernel estimate of a regression function in likelihood based models. Journal of the American Statistical Association 84, 276-283.
43. Staniswalis, J.G., Severini, T.A., 1991. Diagnostics for assessing regression models. Journal of the American Statistical Association 86, 684-691.
44. Stoker, T.M., 1986. Consistent estimation of scaled coefficients. Econometrica 54, 1461-1481.
45. Stone, C.J., 1977. Consistent nonparametric regression. Annals of Statistics 5, 595-620.
46. Stone, C.J., 1982. Optimal global rates of convergence for nonparametric regression. Annals of Statistics 8, 1040-1053.
47. Tibshirani, R., 1984. Local Likelihood estimation. Ph.D. Thesis, Stanford University.
48. Wand, M.P., Jones, M.C., 1995. Kernel Smoothing. Chapman & Hall, London.