论文标题
关于线性过程小波密度估计的集成平方误差
On the integrated mean squared error of wavelet density estimation for linear processes
论文作者
论文摘要
令$ \ {x_n：n \ in \ n \} $为线性过程，密度函数$ f（x）\ in l^2（\ r）$。我们研究$ f（x）$的小波密度估计。在某些规则条件下，我们基于线性过程中的非零系数的数量，实现了密度估计的集成平均平方误差的最小值最佳收敛速率。被认为的小波具有紧凑的支撑，并且连续两次可区分。母小波的消失力矩数量与线性过程中的非零系数的数量以及创新功能的特征功能的衰减率成正比。理论上的结果通过在高斯，库奇和卡方分布之后进行创新的模拟研究来说明。
Let $\{X_n: n\in \N\}$ be a linear process with density function $f(x)\in L^2(\R)$. We study wavelet density estimation of $f(x)$. Under some regular conditions on the characteristic function of innovations, we achieve, based on the number of nonzero coefficients in the linear process, the minimax optimal convergence rate of the integrated mean squared error of density estimation. Considered wavelets have compact support and are twice continuously differentiable. The number of vanishing moments of mother wavelet is proportional to the number of nonzero coefficients in the linear process and to the rate of decay of characteristic function of innovations. Theoretical results are illustrated by simulation studies with innovations following Gaussian, Cauchy and chi-squared distributions.
