### Abstract

Generalizing the mode regression of Lee (1989) with the rectangular kernel (RME), we try a quadratic kernel (QME), smoothing the rectangular kernel. Like RME, QME is the most useful when the dependent variable is truncated. QME is better than RME in that it gives a N^{ 1 2}-consistent estimator and an asymptotic distribution which parallels that of Powell's (1986) symmetrically trimmed least squares (STLS). In general, the symmetry requirement of QME is weaker than that of STLS and stronger than that of RME. Estimation of the covariance matrices of both QME and STLS requires density estimation. But a variation of QME can provide an upper bound of the covariance matrix without the burden of density estimation. The upper bound can be made tight at the cost of computation time.

Original language | English |
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Pages (from-to) | 1-19 |

Number of pages | 19 |

Journal | Journal of Econometrics |

Volume | 57 |

Issue number | 1-3 |

Publication status | Published - 1993 May 1 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistics and Probability
- Finance
- Economics and Econometrics

### Cite this

**Quadratic mode regression.** / Lee, Myoung-jae.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Quadratic mode regression

AU - Lee, Myoung-jae

PY - 1993/5/1

Y1 - 1993/5/1

N2 - Generalizing the mode regression of Lee (1989) with the rectangular kernel (RME), we try a quadratic kernel (QME), smoothing the rectangular kernel. Like RME, QME is the most useful when the dependent variable is truncated. QME is better than RME in that it gives a N 1 2-consistent estimator and an asymptotic distribution which parallels that of Powell's (1986) symmetrically trimmed least squares (STLS). In general, the symmetry requirement of QME is weaker than that of STLS and stronger than that of RME. Estimation of the covariance matrices of both QME and STLS requires density estimation. But a variation of QME can provide an upper bound of the covariance matrix without the burden of density estimation. The upper bound can be made tight at the cost of computation time.

AB - Generalizing the mode regression of Lee (1989) with the rectangular kernel (RME), we try a quadratic kernel (QME), smoothing the rectangular kernel. Like RME, QME is the most useful when the dependent variable is truncated. QME is better than RME in that it gives a N 1 2-consistent estimator and an asymptotic distribution which parallels that of Powell's (1986) symmetrically trimmed least squares (STLS). In general, the symmetry requirement of QME is weaker than that of STLS and stronger than that of RME. Estimation of the covariance matrices of both QME and STLS requires density estimation. But a variation of QME can provide an upper bound of the covariance matrix without the burden of density estimation. The upper bound can be made tight at the cost of computation time.

UR - http://www.scopus.com/inward/record.url?scp=38249003273&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249003273&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:38249003273

VL - 57

SP - 1

EP - 19

JO - Journal of Econometrics

JF - Journal of Econometrics

SN - 0304-4076

IS - 1-3

ER -