تقرير
A Ball Divergence Based Measure For Conditional Independence Testing
| العنوان: | A Ball Divergence Based Measure For Conditional Independence Testing |
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| المؤلفون: | Banerjee, Bilol, Bhattacharya, Bhaswar B., Ghosh, Anil K. |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Statistics Theory, Statistics - Methodology |
| الوصف: | In this paper we introduce a new measure of conditional dependence between two random vectors ${\boldsymbol X}$ and ${\boldsymbol Y}$ given another random vector $\boldsymbol Z$ using the ball divergence. Our measure characterizes conditional independence and does not require any moment assumptions. We propose a consistent estimator of the measure using a kernel averaging technique and derive its asymptotic distribution. Using this statistic we construct two tests for conditional independence, one in the model-${\boldsymbol X}$ framework and the other based on a novel local wild bootstrap algorithm. In the model-${\boldsymbol X}$ framework, which assumes the knowledge of the distribution of ${\boldsymbol X}|{\boldsymbol Z}$, applying the conditional randomization test we obtain a method that controls Type I error in finite samples and is asymptotically consistent, even if the distribution of ${\boldsymbol X}|{\boldsymbol Z}$ is incorrectly specified up to distance preserving transformations. More generally, in situations where ${\boldsymbol X}|{\boldsymbol Z}$ is unknown or hard to estimate, we design a double-bandwidth based local wild bootstrap algorithm that asymptotically controls both Type I error and power. We illustrate the advantage of our method, both in terms of Type I error and power, in a range of simulation settings and also in a real data example. A consequence of our theoretical results is a general framework for studying the asymptotic properties of a 2-sample conditional $V$-statistic, which is of independent interest. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.21456 |
| رقم الأكسشن: | edsarx.2407.21456 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |