经典的变点分析旨在（1）检测可能非平稳时间序列平均值的突变，以及（2）识别平均值表现出分段常数行为的区域。然而，在许多应用中，更合理的做法是假设平均值以平稳的方式逐渐变化。这些渐进的变化可能是不相关的（即微小的），也可能与手头的特定问题相关，本论文提出了检测后者的统计方法。更准确地说，我们考虑常见的非参数回归模型${\mathit{<trans\; data-src="X">X（X）</trans>}}_{\mathit{<trans\; data-src="i">我</trans>}}<trans\; data-src="=">=</trans>\mathit{<trans\; data-src="\mu ">\mu </trans>}<trans\; data-src="(">(</trans>\mathit{<trans\; data-src="i">我</trans>}<trans\; data-src="/">/</trans>\mathit{<trans\; data-src="n">n个</trans>}<trans\; data-src=")">)</trans><trans\; data-src="+">+</trans>{\mathit{<trans\; data-src="\epsilon ">\epsilon </trans>}}_{\mathit{<trans\; data-src="i">我</trans>}}$并提出回归函数最大绝对偏差的零假设检验μ从函数$\mathit{<trans\; data-src="g">克</trans>}<trans\; data-src="(">(</trans>\mathit{<trans\; data-src="\mu ">\mu </trans>}<trans\; data-src=")">)</trans>$（例如值$\mathit{<trans\; data-src="\mu ">\mu </trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=")">)</trans>$或积分${<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="0">0</trans>}}^{\mathrm{<trans\; data-src="1">1</trans>}}\mathit{<trans\; data-src="\mu ">\mu </trans>}<trans\; data-src="(">(</trans>\mathit{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathit{<trans\; data-src="t">t吨</trans>}$)小于给定间隔上的给定阈值$<trans\; data-src="[">[</trans>{\mathit{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="0">0</trans>}}<trans\; data-src=",">,</trans>{\mathit{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="]">]</trans><trans\; data-src="\subseteq ">\subseteq </trans><trans\; data-src="[">[</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="]">]</trans>$这类假设的测试是使用适当的估计器进行的，例如${\stackrel{<trans\; data-src="ˆ">ˆ</trans>}{\mathit{<trans\; data-src="d">d日</trans>}}}_{\mathrm{<trans\; data-src="\infty ">\infty </trans>}<trans\; data-src=",">,</trans>\mathit{<trans\; data-src="n">n个</trans>}}$，表示最大偏差${\mathit{<trans\; data-src="d">d日</trans>}}_{\mathrm{<trans\; data-src="\infty ">\infty </trans>}}<trans\; data-src="=">=</trans>{<trans\; data-src="sup">啜饮</trans>}_{\mathit{<trans\; data-src="t">t吨</trans>}<trans\; data-src="\in ">\in </trans><trans\; data-src="[">[</trans>{\mathit{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="0">0</trans>}}<trans\; data-src=",">,</trans>{\mathit{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="]">]</trans>}<trans\; data-src="|">|</trans>\mathit{<trans\; data-src="\mu ">\mu </trans>}<trans\; data-src="(">(</trans>\mathit{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">-</trans>\mathit{<trans\; data-src="g">克</trans>}<trans\; data-src="(">(</trans>\mathit{<trans\; data-src="\mu ">\mu </trans>}<trans\; data-src=")">)</trans><trans\; data-src="|">|</trans>$。我们导出了适当标准化版本的${\stackrel{<trans\; data-src="ˆ">ˆ</trans>}{\mathit{<trans\; data-src="d">d日</trans>}}}_{\mathrm{<trans\; data-src="\infty ">\infty </trans>}<trans\; data-src=",">,</trans>\mathit{<trans\; data-src="n">n个</trans>}}$，其中标准化取决于函数极值点集的勒贝格测度$\mathit{<trans\; data-src="\mu ">\mu </trans>}<trans\; data-src="(">(</trans><trans\; data-src="·">·</trans><trans\; data-src=")">)</trans><trans\; data-src="-">-</trans>\mathit{<trans\; data-src="g">克</trans>}<trans\; data-src="(">(</trans>\mathit{<trans\; data-src="\mu ">\mu </trans>}<trans\; data-src=")">)</trans>$基于此集合的一个估计，提出了一种改进的方法，并证明了其一致性。通过仿真研究和数据示例说明了结果。