Interpolation problem for periodically correlated stochastic sequences with missing observations

具有周期平稳乘性季节增量的序列的稳健插值

Robust interpolation of sequences with periodically stationary multiplicative seasonal increments

本文研究具有分数阶周期平稳广义多重增量且含多季节与积分模式的随机序列插值问题，在谱密度已知时给出最优插值误差公式，在谱密度不确定时提出极小极大稳健谱特性公式。

带噪声观测的具有周期相关增量的连续时间随机过程的极小极大插值

Minimax interpolation of continuous time stochastic processes with periodically correlated increments observed with noise

本文研究带周期平稳噪声观测下具有周期平稳增量的连续时间随机过程缺失值线性泛函的最优估计问题，通过构造平稳增量序列，在已知谱密度和给定可容许谱密度集合两种情形下分别给出了最优估计及极小极大稳健谱特征的计算公式。

Minimax extrapolation problem for periodically correlated stochastic sequences with missing observations

The problem of optimal estimation of the linear functionals which depend on the unknown values of a periodically correlated stochastic sequence $ζ(j)$ from observations of the sequence $ζ(j)+θ(j)$ at points $j\in\{\dots,-n,\dots,-2,-1,0\}\setminus S$, $S=\bigcup _{l=1}^{s-1}\{-M_l\cdot T+1,\dots,-M_{l-1}\cdot T-N_{l}\cdot T\}$, is considered, where $θ(j)$ is an uncorrelated with $ζ(j)$ periodically correlated stochastic sequence. Formulas for calculation the mean square error and the spectral characteristic of the optimal estimate of the functional $Aζ$ are proposed in the case where spectral …

多维平稳过程在缺失观测下的插值问题

Interpolation Problem for Multidimensional Stationary Processes with Missing Observations

研究多维连续时间平稳随机过程线性函数的均方最优线性估计问题，针对缺失观测和谱不确定性情况，提出计算最优估计的均方误差和谱特征的公式。

关于带记忆的缺失泛函数据的最优预测

On optimal prediction of missing functional data with memory

本文研究带记忆的缺失泛函数据重构问题，针对高斯过程及其双射变换给出$L^2$最优重构的理论表达式与离散近似收敛速率，在参数协方差情形下可逐函数估计且记忆下为非线性解，仿真显示其优于传统插值法。

从含缺失数据中无偏估计自协方差、互协方差及相应功率谱密度

Bias-Free Estimation of the Auto- and Cross-Covariance and the Corresponding Power Spectral Densities from Gappy Data

针对含随机异常值和相关缺口的平稳均匀采样数据，提出仅平均有效样本且不插值的非参数无偏协方差与功率谱密度估计方法。