Multivariate Regression Estimation : Local Polynomial Fitting for Time Series
نویسنده
چکیده
We consider the estimation of the multivariate regression function m (x 1 , . . . ,xd) = E [ψ (Yd) | X 1 = x 1 , . . . ,Xd = xd], and its partial derivatives, for stationary random processes {Yi ,Xi} using local higher-order polynomial fitting. Particular cases of ψ yield estimation of the conditional mean, conditional moments and conditional distributions. Joint asymptotic normality is established for estimates of the regression function and its partial derivatives for strongly mixing and ρ mixing processes. Expressions for the bias and variance/covariance matrix (of the asymptotically normal distribution) for these estimators are given. Short Title: Multivariate Regression Estimation.
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MULTIVARIATE LOCAL POLYNOMIAL REGRESSION FOR TIME SERIES: UNIFORM STRONG CONSISTENCY AND RATES by
Local high-order polynomial fitting is employed for the estimation of the multivariate regression function m (x 1 , . . . ,xd) = E [ψ (Yd) | X 1 = x 1 , . . . ,Xd = xd], and of its partial derivatives, for stationary random processes {Yi , Xi}. The function ψ may be selected to yield estimates of the conditional mean, conditional moments and conditional distributions. Uniform strong consistency...
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