Semiparametric least squares (SLS) and weighted SLS estimation of single-index models. (English) Zbl 0816.62079
Summary: For the class of single-index models the author constructs a semiparametric estimator of coefficients up to a multiplicative constant that exhibits \(1/\sqrt{n}\)-consistency and asymptotic normality. This class of models includes censored and truncated Tobit models, binary choice models, and duration models with unobserved individual heterogeneity and random censoring. He also investigates a weighting scheme that achieves the semiparametric efficiency bound.
MSC:
| 62P20 | Applications of statistics to economics |
| 62G07 | Density estimation |
| 62G05 | Nonparametric estimation |
Keywords:
consistency; single-index models; semiparametric estimator; asymptotic normality; censored and truncated Tobit models; binary choice models; duration models; weighting scheme; semiparametric efficiency boundReferences:
| [1] | Andrews, Donald W. K.: Consistency in nonlinear econometric models: A generic uniform law of large numbers. Econometrica 55, 1465-1471 (1987) · Zbl 0646.62101 |
| [2] | Basmann, Robert L.: A generalized classical method of linear estimation of coefficients in a structural equation. Econometrica 25, 77-83 (1957) · Zbl 0078.34004 |
| [3] | Brillinger, David R.: A generalized linear model with ’Gaussian regressor variables. A festschrift for erich L. Lehmann (1983) · Zbl 0519.62050 |
| [4] | Cosslett, Stephen R.: Distribution-free maximum likelihood estimator of the binary choice model. Econometrica 51, 765-782 (1983) · Zbl 0528.62096 |
| [5] | Feller, William: 3rd ed. An introduction to probability theory and its applications. An introduction to probability theory and its applications 1 (1968) · Zbl 0155.23101 |
| [6] | Haerdle, Wolfgang; Hall, Peter; Ichimura, Hidehiko: Optimal smoothing in single index models. Discussion paper no. 9107 (1991) · Zbl 0770.62049 |
| [7] | Hall, Peter; Ichimura, Hidehiko: Optimal semi-parametric estimation in single-index models. (1991) · Zbl 0770.62049 |
| [8] | Han, Aaron K.: Non-parametric analysis of a generalized regression model. Journal of econometrics 35, 303-316 (1987) · Zbl 0638.62063 |
| [9] | Ichimura, Hidehiko; Lee, Lung-Fei: Semiparametric least squares estimation of multiple index models: single equation estimation. Nonparametric and semiparametric methods in econometrics and statistics (1991) · Zbl 0766.62065 |
| [10] | Ichimura, Hidehiko; Newey, Whitney K.: Efficiency of conditional expectation estimators in index models. (1990) |
| [11] | Manski, Charles F.: The maximum score estimation of the stochastic utility model of choice. Journal of econometrics 3, 205-228 (1975) · Zbl 0307.62068 |
| [12] | Manski, Charles F.: Semiparametric analysis of discrete response: asymptotic properties of the maximum score estimator. Journal of econometrics 27, 313-333 (1985) · Zbl 0567.62096 |
| [13] | Mccullagh, P.; Nelder, J.: Generalized linear models. (1983) · Zbl 0588.62104 |
| [14] | Nadaraja, N.: On regression estimator. Theory of probability and its applications 9, 157-159 (1964) |
| [15] | Newey, Whitney K.: Efficient estimation of semiparametric models via moment restrictions. (1990) · Zbl 0728.62107 |
| [16] | Parzen, Emanuel: On estimation of a probability density function and mode. Annals of mathematical statistics 33, 1065-1076 (1962) · Zbl 0116.11302 |
| [17] | Rao, B. L. S. Prakasa: Nonparametric functional estimation. (1983) · Zbl 0542.62025 |
| [18] | Ruud, Paul A.: Sufficient conditions for the consistency of maximum likelihood estimation despite misspecification of distribution. Econometrica 51, 225-228 (1983) · Zbl 0513.62071 |
| [19] | Stoker, Thomas M.: Consistent estimation of scaled coefficients. Econometrica 54, 1461-1481 (1986) · Zbl 0628.62105 |
| [20] | Theil, Henri: Estimation and simultaneous correlation in complete equation systems. (1953) |
| [21] | Theil, Henri: Repeated least-squares applied to complete equation systems. (1953) |
| [22] | Watson, G. S.: Smooth regression analysis. Sankha series A 26, 101-116 (1964) · Zbl 0138.13906 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
