In this paper we consider the problem of constructing non-asymptotic confidence regions for the parameters of Errors-In-Variables (EIV) systems where both inputs and outputs are observed in noise. The Leave-out Sign-dominant Correlation Regions (LSCR) and Sign-Perturbed Sums (SPS) approaches which are two methods for constructing confidence regions from a finite number of data points, are extended to EIV systems. An appropriate correlation sequence which is required for both LSCR and SPS, is computed by a Kalman filter, and accordingly, a state-space form of the EIV system where both input and output are regarded as outputs is utilized. The constructed confidence regions include the true parameter with a user-chosen probability, and parameter values different from the true ones will be left out of the confidence region as the number of data points increases. The theoretical results are illustrated in a simulation example.

在本文中，我们考虑为在误差中观察到输入和输出的变量误差（EIV）系统的参数构造非渐近置信区域的问题。省略符号主导相关区域（LSCR）和符号扰动和（SPS）方法是从有限数量的数据点构造置信区域的两种方法，现已扩展到EIV系统。通过卡尔曼滤波器来计算LSCR和SPS两者都需要的适当的相关序列，因此，利用了将输入和输出都视为输出的EIV系统的状态空间形式。构造的置信区域包括具有用户选择概率的真实参数，随着数据点数量的增加，与真实值不同的参数值将被排除在置信区域之外。在一个仿真示例中说明了理论结果。