Under the condition of non-classical distributed errors, the test for spatial dependence in spatial panel data models is still a problem waiting to be solved. In this paper, we apply the FDB (Fast Double Bootstrap) method to spatial panel data models to test spatial dependence. In order to research the validity of the Bootstrap LM-Error test in spatial random effect models under the condition that the error term obeys a normal distribution, heteroscedasticity, or time-series correlation, we construct Bootstrap LM-Error statistics and make use of Monte Carlo simulation from size distortion and power aspects to carry out our research. The Monte Carlo simulation results show that the asymptotic LM-Error test in the spatial random effects model has a large size of distortion when the error term disobeys classical distribution. However, the FDB LM-Error test can effectively correct the size distortion of the asymptotic test with the precondition that there is nearly no loss of power in the FDB test. Obviously, compared to the asymptotic LM-Error test, the FDB LM-Error test is a more valid method to test spatial dependence in a spatial random effects model.

Enterprise financial risk prediction is a fundamental task in financial risk management, yet its performance is often hindered by severe class imbalance, cross-enterprise heterogeneity, and the limited availability of labeled risky samples. These challenges are particularly pronounced in few-shot settings, where conventional machine learning and deep classification models tend to suffer from unstable representation learning, feature collapse, and weak decision boundaries. To address this issue, this study proposes a hierarchical metric learning framework for few-shot enterprise financial risk prediction on imbalanced tabular data. The framework integrates a state-space feature embedding network, an Adaptive Spectral Decomposition and Multi-Scale State Embedding module, and a Hierarchical Metric Manifold Alignment mechanism to enhance risk-sensitive representation learning, preserve geometric consistency across embedding levels, and improve prototype-based discrimination in the metric space. Experiments are conducted on three public datasets, namely American Bankruptcy, Corporate Financial Risk Assessment, and Enterprise Financial Network, under a unified 2-way 20-shot setting. The proposed method consistently achieves the best overall performance across Precision, Recall, Accuracy, F1-score, and AUC, with AUC values of 0.9526, 0.9687, and 0.9716 on the three datasets, respectively. Ablation studies and visual analyses further show that the proposed framework improves intra-class compactness, inter-class separability, and classification robustness under highly imbalanced conditions. These findings indicate that the proposed method provides an effective and robust machine learning solution for enterprise financial risk prediction and early warning in data-scarce financial scenarios.