We propose a new nonparametric test of stochastic monotonicity which adapts to the unknown smoothness of the conditional distribution of interest, possesses desirable asymptotic properties, is conceptually easy to implement, and computationally attractive. In particular, we show that the test asymptotically controls size at a polynomial rate, is nonconservative, and detects certain smooth local alternatives that converge to the null with the fastest possible rate. Our test is based on a data-driven bandwidth value and the critical value for the test takes this randomness into account. Monte Carlo simulations indicate that the test performs well in finite samples. In particular, the simulations show that the test controls size and, under some alternatives, is significantly more powerful than existing procedures.

中文翻译：

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随机单调性的自适应检验

我们提出了一种新的随机单调性非参数测试，它适应感兴趣的条件分布的未知平滑度，具有理想的渐近特性，在概念上易于实现，并且在计算上具有吸引力。特别是，我们表明该测试以多项式速率渐近控制大小，是非保守的，并检测到某些平滑的局部替代方案，这些替代方案以最快的速度收敛到零值。我们的测试基于数据驱动的带宽值，测试的临界值考虑了这种随机性。蒙特卡罗模拟表明该测试在有限样本中表现良好。特别是，模拟表明测试控制大小，并且在某些替代方案下，比现有程序更强大。