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摘要翻译：
对于具有单断点的线性回归模型中的部分结构变化，我们发展了一个连续记录渐近框架来建立断点日期的推理方法。在固定的时间范围[0,N]上，我们有T个采样频率为h的观测值，并且在保持时间跨度N不变的情况下，设T为h 0。我们对一个潜在的连续时间模型施加了非常温和的规律性条件，以产生数据。我们考虑了中断日期的最小二乘估计，并建立了一致性和收敛速度。我们提供了一个缩小位移量和局部增加方差的极限理论。渐近分布对应于回归方程的二次变分函数和高斯中心鞅过程在一定时间间隔内的极值位置。我们可以解释由断裂前和断裂后制度提供的不对称信息内容，并说明断裂的位置和转移幅度是如何形成分布的关键因素。我们考虑了一个基于插件估计的可行版本，它对有限样本分布提供了一个非常好的近似。我们使用最高密度区域的概念来构造置信度集。总体而言，我们的方法是可靠的，并提供准确的覆盖概率和相对较短的平均长度的置信度集。重要的是，无论中断的大小，它都这样做。
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英文标题：
《Continuous Record Asymptotics for Change-Points Models》
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作者：
Alessandro Casini and Pierre Perron
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最新提交年份：
2021
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
For a partial structural change in a linear regression model with a single break, we develop a continuous record asymptotic framework to build inference methods for the break date. We have T observations with a sampling frequency h over a fixed time horizon [0, N] , and let T with h 0 while keeping the time span N fixed. We impose very mild regularity conditions on an underlying continuous-time model assumed to generate the data. We consider the least-squares estimate of the break date and establish consistency and convergence rate. We provide a limit theory for shrinking magnitudes of shifts and locally increasing variances. The asymptotic distribution corresponds to the location of the extremum of a function of the quadratic variation of the regressors and of a Gaussian centered martingale process over a certain time interval. We can account for the asymmetric informational content provided by the pre- and post-break regimes and show how the location of the break and shift magnitude are key ingredients in shaping the distribution. We consider a feasible version based on plug-in estimates, which provides a very good approximation to the finite sample distribution. We use the concept of Highest Density Region to construct confidence sets. Overall, our method is reliable and delivers accurate coverage probabilities and relatively short average length of the confidence sets. Importantly, it does so irrespective of the size of the break.
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PDF链接：
https://arxiv.org/pdf/1803.10881
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