Abstract
This article considers estimation of the unknown linear index coefficients of a model in which a number of nonparametrically identified reduced form parameters are assumed to be smooth and invertible function of one or more linear indices. The results extend the previous literature by allowing the number of reduced form parameters to exceed the number of indices (i.e., the indices are “overdetermined” by the reduced form parameters. The estimator of the unknown index coefficients (up to scale) is the eigenvector of a matrix (defined in terms of a first-step nonparametric estimator of the reduced form parameters) corresponding to its smallest (in magnitude) eigenvalue. Under suitable conditions, the proposed estimator is shown to be root-n-consistent and asymptotically normal, and under additional restrictions an efficient choice of a “weight matrix” is derived in the overdetermined case.
Original language | English |
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Pages (from-to) | 1-10 |
Number of pages | 10 |
Journal | Journal of Business and Economic Statistics |
Volume | 36 |
Issue number | 1 |
DOIs | |
State | Published - 2 Jan 2018 |
Keywords
- Invertible models
- Multinomial response
- Semiparametric estimation
- Single index models