Speaker
Description
In the functional response model (FRM), where a functional response is explained by scalar predictors, inference becomes challenging when the design matrix is not full-rank, leading to an ill-conditioned model (ICFRM). Widely used methods for this problem, such as $L^2$-norm-based tests (Zhang, 2013), suffer from critical flaws such as poor control of the type I error rate, which can invalidate statistical conclusions. To address these gaps, we first introduce two new test statistics for the general linear hypothesis problem in ICFRM: the globalizing pointwise F-test ($G_n$) and the $F_{max}$-test (Smaga and Stefańska, 2025). We employ robust nonparametric and parametric bootstrap techniques to approximate their null distributions. Simulation studies confirm that our proposed tests successfully control the type I error rate and exhibit greater statistical power than existing methods across different scenarios. We apply our methods to the audible noise data. The practical problem behind this data set is the motivation for our studies as the regression model is ill-conditioned in this case. Our ongoing research introduces a novel, alternative methodology: projection-based testing. This approach addresses the same problem by demonstrating that the functional null hypothesis can be equivalently expressed in terms of its projection. Preliminary simulation studies are underway to compare the performance of these projection tests against our validated $G_n$ and $F_{max,n}$ procedures. Initial results suggest the projection methods are promising, but their effectiveness is not consistent across all settings, opening a clear avenue for further research.
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