Curve registration plays a major role in functional data analysis by separating amplitude and phase variation through warping functions and the accurate simulation of warping processes is essential for developing statistical methods that properly account for phase variability in functional data. In this paper, we focus on the simulation of continuous warping processes with a prescribed expectation and a controllable variance. We study and compare three procedures, including two existing methods and a new algorithm based on randomized empirical cumulative distribution functions. For each approach, we provide an operational description and establish theoretical results for the first two moments of the simulated processes. A numerical study illustrates the theoretical findings and highlights the respective merits of the three methods. Finally, we present an application to the analysis of temperature distributions in Montreal based on simulated realizations from a warping process estimated from temperature quantile functions.

翻译：曲线配准在函数数据分析中扮演着关键角色，它通过翘曲函数分离振幅变化与相位变化，而翘曲过程的精确模拟对于开发能恰当处理函数数据相位变异性的统计方法至关重要。本文聚焦于具有指定期望和可控方差的连续翘曲过程的模拟。我们研究并比较了三种方法，包括两种现有方法和一种基于随机化经验累积分布函数的新算法。针对每种方法，我们提供了操作描述，并建立了模拟过程前两阶矩的理论结果。一项数值研究验证了理论发现，并凸显了三种方法各自的优势。最后，我们展示了一个应用实例：基于从温度分位数函数估计出的翘曲过程进行模拟实现，以此分析蒙特利尔的温度分布。