A consistent local linear estimator of the covariate adjusted correlation coefficient

Danh V. Nguyen; Damla Şentürk

doi:10.1016/j.spl.2009.04.021

A consistent local linear estimator of the covariate adjusted correlation coefficient

Danh V. Nguyen, Damla Şentürk

Public Health Sciences

Research output: Contribution to journal › Article › peer-review

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, ̃) = ψ₁ (U) Y + ψ₂ (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)
Pages (from-to)	1684-1689
Number of pages	6
Journal	Statistics and Probability Letters
Volume	79
Issue number	15
DOIs	https://doi.org/10.1016/j.spl.2009.04.021
State	Published - Aug 1 2009

ASJC Scopus subject areas

Statistics, Probability and Uncertainty
Statistics and Probability

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10.1016/j.spl.2009.04.021

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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,{\~ }) = 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).",

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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).

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A consistent local linear estimator of the covariate adjusted correlation coefficient

Abstract

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