In two pervious papers \cite{dndiep3}, \cite{dndiep4}, the first author constructed the least square quantum neural networks (LS-QNN), and ploynomial interpolation quantum neural networks ( PI-QNN), parametrico-stattistical QNN like: leanr regrassion quantum neural networks (LR-QNN), polynomial regression quantum neural networks (PR-QNN), chi-squared quantum neural netowrks ($\chi^2$-QNN). We observed that the method works also in the cases by using nonparametric statistics. In this paper we analyze and implement the nonparametric tests on QNN such as: linear nonparametric regression quantum neural networks (LNR-QNN), polynomial nonparametric regression quantum neural networks (PNR-QNN). The implementation is constructed through the Gauss-Jordan Elimination quantum neural networks (GJE-QNN).The training rule is to use the high probability confidence regions or intervals.

中文翻译：

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非参数回归量子神经网络

在之前的两篇论文\cite{dndiep3}、\cite{dndiep4}中，第一作者构建了最小二乘量子神经网络（LS-QNN）和多项式插值量子神经网络（PI-QNN），参数统计QNN如：精简回归量子神经网络 (LR-QNN)、多项式回归量子神经网络 (PR-QNN)、卡方量子神经网络 ($\chi^2$-QNN)。我们观察到该方法在使用非参数统计的情况下也有效。在本文中，我们分析并实现了对 QNN 的非参数测试，例如：线性非参数回归量子神经网络 (LNR-QNN)、多项式非参数回归量子神经网络 (PNR-QNN)。该实现是通过高斯-乔丹消除量子神经网络（GJE-QNN）构建的。