### Abstract

Consider the correlation between two random variables (X, Y), both not directly observed. One only observes over(X, ̃) = φ{symbol}_{1} (U) X + φ{symbol}_{2} (U) and over(Y, ̃) = ψ_{1} (U) Y + ψ_{2} (U), where all four functions {φ{symbol}_{l} ({dot operator}), ψ_{l} ({dot operator}), l = 1, 2} are unknown/unspecified smooth functions of an observable covariate U. We consider consistent estimation of the correlation between the unobserved variables X and Y, adjusted for the above general dual additive and multiplicative effects of U, based on the observed data (over(X, ̃), over(Y, ̃), U).

Original language | English (US) |
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Pages (from-to) | 1684-1689 |

Number of pages | 6 |

Journal | Statistics and Probability Letters |

Volume | 79 |

Issue number | 15 |

DOIs | |

State | Published - Aug 1 2009 |

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### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Statistics and Probability

### Cite this

*Statistics and Probability Letters*,

*79*(15), 1684-1689. https://doi.org/10.1016/j.spl.2009.04.021

**A consistent local linear estimator of the covariate adjusted correlation coefficient.** / Nguyen, Danh V.; Şentürk, Damla.

Research output: Contribution to journal › Article

*Statistics and Probability Letters*, vol. 79, no. 15, pp. 1684-1689. https://doi.org/10.1016/j.spl.2009.04.021

}

TY - JOUR

T1 - A consistent local linear estimator of the covariate adjusted correlation coefficient

AU - Nguyen, Danh V.

AU - Şentürk, Damla

PY - 2009/8/1

Y1 - 2009/8/1

N2 - Consider the correlation between two random variables (X, Y), both not directly observed. One only observes over(X, ̃) = φ{symbol}1 (U) X + φ{symbol}2 (U) and over(Y, ̃) = ψ1 (U) Y + ψ2 (U), where all four functions {φ{symbol}l ({dot operator}), ψl ({dot operator}), l = 1, 2} are unknown/unspecified smooth functions of an observable covariate U. We consider consistent estimation of the correlation between the unobserved variables X and Y, adjusted for the above general dual additive and multiplicative effects of U, based on the observed data (over(X, ̃), over(Y, ̃), U).

AB - Consider the correlation between two random variables (X, Y), both not directly observed. One only observes over(X, ̃) = φ{symbol}1 (U) X + φ{symbol}2 (U) and over(Y, ̃) = ψ1 (U) Y + ψ2 (U), where all four functions {φ{symbol}l ({dot operator}), ψl ({dot operator}), l = 1, 2} are unknown/unspecified smooth functions of an observable covariate U. We consider consistent estimation of the correlation between the unobserved variables X and Y, adjusted for the above general dual additive and multiplicative effects of U, based on the observed data (over(X, ̃), over(Y, ̃), U).

UR - http://www.scopus.com/inward/record.url?scp=67649097077&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67649097077&partnerID=8YFLogxK

U2 - 10.1016/j.spl.2009.04.021

DO - 10.1016/j.spl.2009.04.021

M3 - Article

VL - 79

SP - 1684

EP - 1689

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

IS - 15

ER -