### 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 |

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Statistics and Probability

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## Cite this

Nguyen, D. V., & Şentürk, D. (2009). A consistent local linear estimator of the covariate adjusted correlation coefficient.

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