Constrained spline regression in the presence of AR(p) errors
Constrained spline regression in the presence of AR(p) errors
复制标题
存在 AR(p) 误差时的约束样条回归
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
J. Opsomer
中科院分区：
文献类型：
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作者：
Huansha Wang;Mary C. Meyer;J. Opsomer
从观测模式中提取趋势总是困难的，特别是当趋势被相关误差所掩盖时。通常，对趋势的先验知识并不包括参数族，而是有效的假设是模糊的，例如“平滑”或“单调增加”。错误地将趋势指定为一些简单的参数形式可能会导致对相关性的高估。在存在平稳AR(P)误差的情况下，该方法使用带形状约束(如单调性或凸性)的样条回归进行估计和推断。选择惩罚参数的标准标准，如Akaike信息准则(AIC)、交叉验证和广义交叉验证，在误差相关和没有形状约束的情况下表现得很差。在本文中，利用相关调整的AIC同时选择相关结构和惩罚参数。研究了具有相关项的非惩罚样条回归的渐近性质。证明了在适当的条件下，即使相关估计不一致，回归函数的相应投影估计仍然是一致的，并且具有最优的渐近速度。在存在AR(P)误差的情况下，约束样条法的收敛速度达到了无约束样条法的收敛速度。仿真结果表明，如果真实趋势满足约束条件，约束估计器的性能通常要好于无约束估计器。
Extracting the trend from the pattern of observations is always difficult, especially when the trend is obscured by correlated errors. Often, prior knowledge of the trend does not include a parametric family, and instead the valid assumptions are vague, such as ‘smooth’ or ‘monotone increasing’. Incorrectly specifying the trend as some simple parametric form can lead to overestimation of the correlation. The proposed method uses spline regression with shape constraints, such as monotonicity or convexity, for estimation and inference in the presence of stationary AR(p) errors. Standard criteria for selection of penalty parameter, such as Akaike information criterion (AIC), cross-validation and generalised cross-validation, have been shown to behave badly when the errors are correlated and in the absence of shape constraints. In this article, correlation structure and penalty parameter are selected simultaneously using a correlation-adjusted AIC. The asymptotic properties of unpenalised spline regression in the presence of correlation are investigated. It is proved that even if the estimation of the correlation is inconsistent, the corresponding projection estimation of the regression function can still be consistent and have the optimal asymptotic rate, under appropriate conditions. The constrained spline fit attains the convergence rate of unconstrained spline fit in the presence of AR(p) errors. Simulation results show that the constrained estimator typically behaves better than the unconstrained version if the true trend satisfies the constraints.