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自相关误差下的加性非参数回归AI 解读

Summary A Bayesian approach is presented for nonparametric estimation of an additive regression model with autocorrelated errors. Each of the potentially non-linear components is modelled as a regression spline using many knots, while the errors are modelled by a high order stationary autoregressive process parameterized in terms of its autocorrelations. The distribution of significant knots and partial autocorrelations is accounted for using subset selection. Our approach…

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结合先验信息的非参数样条回归AI 解读

By using prior information about the regression curve we propose new nonparametric regression estimates. We incorporate two types of information. First, we suppose that the regression curve is similar in shape to a family of parametric curves characterized as the solution to a linear differential equation. The regression curve is estimated by penalized least squares with the differential operator defining the smoothness penalty. We discuss in particular growth and decay…

利用先验信息的非参数样条回归AI 解读

SUMMARY By using prior information about the regression curve we propose new nonparametric regression estimates. We incorporate two types of information. First, we suppose that the regression curve is similar in shape to a family of parametric curves characterized as the solution to a linear differential equation. The regression curve is estimated by penalized least squares with the differential operator defining the smoothness penalty. We discuss in particular growth and…

具有自回归移动平均误差的非参数样条回归AI 解读

We estimate by spline nonparametric regression an unknown function observed with autocorrelated errors when the errors are modelled by an autoregressive moving average model. Unknown parameters are estimated by either maximum likelihood, cross-validation or generalized cross-validation. By expressing the problem in state space form we obtain O(n) algorithms to estimate the function and its derivatives and evaluate the marginal likelihood and cross-validation functions. The…

具有 ARMA 误差的非参数样条回归AI 解读

We estimate by spline nonparametric regression an unknown function observed with autocorrelated errors when the errors are modelled by an autoregressive moving average model. Unknown parameters are estimated by either maximum likelihood, cross-validation or generalized cross-validation. By expressing the problem in state space form we obtain O(n) algorithms to estimate the function and its derivatives and evaluate the marginal likelihood and cross-validation functions. The…