Goodness-of-fit test for point processes first-order intensity

IF 1.5 3区数学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Computational Statistics & Data Analysis Pub Date : 2024-02-01 DOI:10.1016/j.csda.2024.107929

M.I. Borrajo , W. González-Manteiga , M.D. Martínez-Miranda

引用次数: 0

Abstract

Modelling the first-order intensity function is one of the main aims in point process theory. An appropriate model describes the first-order intensity as a nonparametric function of spatial covariates. A formal testing procedure is presented to assess the goodness-of-fit of this model, assuming an inhomogeneous Poisson point process. The test is based on a quadratic distance between two kernel intensity estimators. The asymptotic normality of the test statistic is proved and a bootstrap procedure to approximate its distribution is suggested. The proposal is illustrated with two applications to real data sets, and an extensive simulation study to evaluate its finite-sample performance.

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点过程一阶强度拟合优度检验

一阶强度函数建模是点过程理论的主要目标之一。一个合适的模型将一阶强度描述为空间协变量的非参数函数。假设有一个不均匀的泊松点过程，本文提出了一个正式的测试程序来评估该模型的拟合优度。该检验基于两个核强度估计值之间的二次距离。证明了检验统计量的渐近正态性，并提出了近似其分布的引导程序。该建议通过对真实数据集的两个应用进行了说明，并通过广泛的模拟研究对其有限样本性能进行了评估。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computational Statistics & Data Analysis 数学-计算机：跨学科应用

CiteScore

3.70

自引率

5.60%

发文量

167

审稿时长

60 days

期刊介绍： Computational Statistics and Data Analysis (CSDA), an Official Publication of the network Computational and Methodological Statistics (CMStatistics) and of the International Association for Statistical Computing (IASC), is an international journal dedicated to the dissemination of methodological research and applications in the areas of computational statistics and data analysis. The journal consists of four refereed sections which are divided into the following subject areas: I) Computational Statistics - Manuscripts dealing with: 1) the explicit impact of computers on statistical methodology (e.g., Bayesian computing, bioinformatics,computer graphics, computer intensive inferential methods, data exploration, data mining, expert systems, heuristics, knowledge based systems, machine learning, neural networks, numerical and optimization methods, parallel computing, statistical databases, statistical systems), and 2) the development, evaluation and validation of statistical software and algorithms. Software and algorithms can be submitted with manuscripts and will be stored together with the online article. II) Statistical Methodology for Data Analysis - Manuscripts dealing with novel and original data analytical strategies and methodologies applied in biostatistics (design and analytic methods for clinical trials, epidemiological studies, statistical genetics, or genetic/environmental interactions), chemometrics, classification, data exploration, density estimation, design of experiments, environmetrics, education, image analysis, marketing, model free data exploration, pattern recognition, psychometrics, statistical physics, image processing, robust procedures. [...] III) Special Applications - [...] IV) Annals of Statistical Data Science [...]

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