Semiparametric analysis of discrete response. Asymptotic properties of the maximum score estimator. (English) Zbl 0567.62096
This article considers the estimation and identification of the model \(MED(y| x)=x\beta\) from a random sample of observations on (sgn y, x). The author has shown that the parameter \(\beta\) is not identifiable (up to a scale factor) if the distribution of x has bounded support and the median regression function \(x\beta\) is uniformly bounded away from zero for all x. Identification can be achieved under infinite support conditions.
Least absolute deviations estimators are shown to be strongly consistent. Maximum score estimation is shown to be equivalent to the least absolute deviations estimation procedures. The author has also shown that the maximum score estimate lies outside any fixed neighborhood of the normalized true parameter vector with probability that goes to zero at exponential rate.
Least absolute deviations estimators are shown to be strongly consistent. Maximum score estimation is shown to be equivalent to the least absolute deviations estimation procedures. The author has also shown that the maximum score estimate lies outside any fixed neighborhood of the normalized true parameter vector with probability that goes to zero at exponential rate.
Reviewer: L.-F.Lee
MSC:
| 62P20 | Applications of statistics to economics |
| 62F12 | Asymptotic properties of parametric estimators |
| 62G05 | Nonparametric estimation |
| 62J99 | Linear inference, regression |
Keywords:
discrete response; strong consistency; semiparametric model; median regression; Identification; infinite support conditions; least absolute deviations estimation; maximum score estimateReferences:
| [1] | Bickel, P., On adaptive estimation, Annals of Statistics, 10, 647-671 (1982) · Zbl 0489.62033 |
| [2] | Chernoff, H., A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations, Annals of Mathematical Statistics, 23, 493-507 (1952) · Zbl 0048.11804 |
| [3] | Cosslett, S., Distribution-free maximum likelihood estimator of the binary choice model, Econometrica, 51, 765-782 (1983) · Zbl 0528.62096 |
| [4] | Dudley, R., Central limit theorems for empirical measures, Annals of Probability, 6, 899-929 (1978) · Zbl 0404.60016 |
| [5] | Hansen, L., Large sample properties of generalized method of moments estimators, Econometrica, 50, 1029-1054 (1982) · Zbl 0502.62098 |
| [6] | Hoeffding, W., Probability inequalities for sums of bounded random variables, Journal of the American Statistical Association, 58, 13-30 (1963) · Zbl 0127.10602 |
| [7] | Koenker, R.; Bassett, G., Regression quantiles, Econometrica, 46, 33-50 (1978) · Zbl 0373.62038 |
| [8] | Manski, C., Maximum score estimation of the stochastic utility model of choice, Journal of Econometrics, 3, 205-228 (1975) · Zbl 0307.62068 |
| [9] | Manski, C., Closest empirical distribution estimation, Econometrica, 51, 305-319 (1983) · Zbl 0541.62016 |
| [10] | McFadden, D., Conditional logit analysis of qualitative choice behavior, (Zarembka, P., Frontiers of econometrics (1974), Academic Press: Academic Press New York) |
| [11] | Powell, J., Generalizations of the censored and truncated least absolute deviations estimators, (Institute for Mathematical Studies in the Social Sciences report no. 398 (1983), Stanford University: Stanford University Stanford, CA) |
| [12] | Rao, R. R., Relations between weak and uniform convergence of measures with applications, Annals of Mathematical Statistics, 33, 659-680 (1962) · Zbl 0117.28602 |
| [13] | Revesz, P., The laws of large numbers (1968), Academic Press: Academic Press New York · Zbl 0203.50403 |
| [14] | Sethuraman, J., On the probability of large deviations of families of sample means, Annals of Mathematical Statistics, 35, 1304-1316 (1964) · Zbl 0147.18803 |
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