A criterion is proposed for testing the hypothesis about the nature of the error variance in the dependent variable in a linear model, which separates correctly and incorrectly specified models. In the former one, only the measurement errors determine the variance (i.e., the dependent variable is correctly explained by the independent ones, up to measurement errors), while the latter model lacks some independent covariates (or has a nonlinear structure). The proposed MEMV (Measurement Error Model Validity) test checks the validity of the model when both dependent and independent covariates are measured with errors. The criterion has an asymptotic character, but numerical simulations outlined approximate boundaries where estimates make sense. A practical example of the test’s implementation is discussed in detail – it shows the test’s ability to detect wrong specifications even in seemingly perfect models. Estimations of the errors due to the omission of the variables in the model are provided in the simulation study. The relation between measurement errors and model specification has not been studied earlier, and the proposed criterion may stimulate future research in this important area.
{"title":"A validity test for a multivariate linear measurement error model","authors":"Alexander Kukush, Igor Mandel","doi":"10.3233/mas-231494","DOIUrl":"https://doi.org/10.3233/mas-231494","url":null,"abstract":"A criterion is proposed for testing the hypothesis about the nature of the error variance in the dependent variable in a linear model, which separates correctly and incorrectly specified models. In the former one, only the measurement errors determine the variance (i.e., the dependent variable is correctly explained by the independent ones, up to measurement errors), while the latter model lacks some independent covariates (or has a nonlinear structure). The proposed MEMV (Measurement Error Model Validity) test checks the validity of the model when both dependent and independent covariates are measured with errors. The criterion has an asymptotic character, but numerical simulations outlined approximate boundaries where estimates make sense. A practical example of the test’s implementation is discussed in detail – it shows the test’s ability to detect wrong specifications even in seemingly perfect models. Estimations of the errors due to the omission of the variables in the model are provided in the simulation study. The relation between measurement errors and model specification has not been studied earlier, and the proposed criterion may stimulate future research in this important area.","PeriodicalId":35000,"journal":{"name":"Model Assisted Statistics and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140242742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The problem of buildings and structures durability during their long-term operation in aggressive environments is discussed. It is closely connected with the problem of destruction of composite materials as a random process of birth, development, and death of defects at chemical corrosion. The content of the study is to analyze the influence of non-stationary chemical reactions occurring in real conditions on these processes. The analysis is carried out taking into account the incidental physical phenomena affecting corrosion, the most important of which is the diffusion of initial substances and reaction products occurring under different hydrodynamic conditions, i.e., the nature of fluid motion and its pressure which stimulates corrosion. The synthesis of three processes – chemical kinetics, diffusion, and hydrodynamics – allows us to study one of the possible scenarios of corrosion process development as a Markov process based on the statistical theory of the “weakest” link and the joint distribution of the random material and geometric parameters. Numerical analysis of changes in elastic and electrical properties of composite materials under these conditions allows us to substantiate the technology of non-destructive control of changes in the state of the structure. The research results are based on mathematical and statistical modeling.
{"title":"Random processes in modeling durability of building and structure","authors":"Boris I. Vilge","doi":"10.3233/mas-231489","DOIUrl":"https://doi.org/10.3233/mas-231489","url":null,"abstract":"The problem of buildings and structures durability during their long-term operation in aggressive environments is discussed. It is closely connected with the problem of destruction of composite materials as a random process of birth, development, and death of defects at chemical corrosion. The content of the study is to analyze the influence of non-stationary chemical reactions occurring in real conditions on these processes. The analysis is carried out taking into account the incidental physical phenomena affecting corrosion, the most important of which is the diffusion of initial substances and reaction products occurring under different hydrodynamic conditions, i.e., the nature of fluid motion and its pressure which stimulates corrosion. The synthesis of three processes – chemical kinetics, diffusion, and hydrodynamics – allows us to study one of the possible scenarios of corrosion process development as a Markov process based on the statistical theory of the “weakest” link and the joint distribution of the random material and geometric parameters. Numerical analysis of changes in elastic and electrical properties of composite materials under these conditions allows us to substantiate the technology of non-destructive control of changes in the state of the structure. The research results are based on mathematical and statistical modeling.","PeriodicalId":35000,"journal":{"name":"Model Assisted Statistics and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140242177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we critically reevaluate Koch and Okamura’s (2020) conclusions on the conformity of Chinese COVID-19 data with Benford’s Law. Building on Figueiredo et al. (2022), we adopt a framework that combines multiple tests, including Chi-square, Kolmogorov-Smirnov, Euclidean Distance, Mean Absolute Deviation, Distortion Factor, and Mantissa Distribution. The primary rationale behind employing multiple tests is to enhance the robustness of our inference. The main finding of the study indicates that COVID-19 infections in China do not adhere to the distribution expected under Benford’s Law, nor does it align with the figures observed in the U.S. and Italy. The usefulness of deviations from Benford’s Law in detecting misreported or fraudulent data remains controversial. However, addressing this question requires a more careful statistical analysis than what is presented in the Koch and Okamura (2020) paper. By employing a combination of several tests using fully transparent procedures, we establish a more reliable approach to evaluating conformity to the Newcomb-Benford Law in applied research.
{"title":"Multiple conformity tests to assess deviations from the Newcomb-Benford Law (NBL): A replication of Koch and Okamura (2020)","authors":"Dalson Figueiredo, Lucas Silva","doi":"10.3233/mas-231459","DOIUrl":"https://doi.org/10.3233/mas-231459","url":null,"abstract":"In this paper, we critically reevaluate Koch and Okamura’s (2020) conclusions on the conformity of Chinese COVID-19 data with Benford’s Law. Building on Figueiredo et al. (2022), we adopt a framework that combines multiple tests, including Chi-square, Kolmogorov-Smirnov, Euclidean Distance, Mean Absolute Deviation, Distortion Factor, and Mantissa Distribution. The primary rationale behind employing multiple tests is to enhance the robustness of our inference. The main finding of the study indicates that COVID-19 infections in China do not adhere to the distribution expected under Benford’s Law, nor does it align with the figures observed in the U.S. and Italy. The usefulness of deviations from Benford’s Law in detecting misreported or fraudulent data remains controversial. However, addressing this question requires a more careful statistical analysis than what is presented in the Koch and Okamura (2020) paper. By employing a combination of several tests using fully transparent procedures, we establish a more reliable approach to evaluating conformity to the Newcomb-Benford Law in applied research.","PeriodicalId":35000,"journal":{"name":"Model Assisted Statistics and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140242700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper proposes a new logistic smooth transition autoregressive (LSTAR) cointegration test by combining the Fourier function to catch the structural changes that occur over time and the LSTAR model to consider the nonlinearity. Logistic and exponential functions are the main transition functions defining the nonlinearity in STAR models since the exponential smooth transition autoregressive (ESTAR) and LSTAR models can explain the different structures of economic variables. The Fourier approach is a simple and effective way to model the structural changes in time series as an alternative to dummy variables. The most significant advantage of the method is that it does not require prior knowledge about the date, number of breaks, or forms. Monte Carlo simulation results show that the proposed test has good size and power properties for different sample sizes and parameters. The results also revealed that the power performance of the proposed test and the Fourier ESTAR test offered by Güriş and Sedefoğlu (2022) are close to each other. The steps of the Fourier-based tests are illustrated by providing an empirical example of testing the validity of the purchasing power parity (PPP) hypothesis in Türkiye.
{"title":"The Fourier approach and testing for cointegration in LSTAR model","authors":"Gülşah Sedefoğlu, Burak Güriş","doi":"10.3233/mas-231468","DOIUrl":"https://doi.org/10.3233/mas-231468","url":null,"abstract":"This paper proposes a new logistic smooth transition autoregressive (LSTAR) cointegration test by combining the Fourier function to catch the structural changes that occur over time and the LSTAR model to consider the nonlinearity. Logistic and exponential functions are the main transition functions defining the nonlinearity in STAR models since the exponential smooth transition autoregressive (ESTAR) and LSTAR models can explain the different structures of economic variables. The Fourier approach is a simple and effective way to model the structural changes in time series as an alternative to dummy variables. The most significant advantage of the method is that it does not require prior knowledge about the date, number of breaks, or forms. Monte Carlo simulation results show that the proposed test has good size and power properties for different sample sizes and parameters. The results also revealed that the power performance of the proposed test and the Fourier ESTAR test offered by Güriş and Sedefoğlu (2022) are close to each other. The steps of the Fourier-based tests are illustrated by providing an empirical example of testing the validity of the purchasing power parity (PPP) hypothesis in Türkiye.","PeriodicalId":35000,"journal":{"name":"Model Assisted Statistics and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140244185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article presents a comparison of multivariate normal mean vectors under covariance positive definite matrices. We introduce an improved parametric bootstrap (IPB) approach for addressing the multivariate Behrens-Fisher problem, specifically focusing on cases with unequal covariance matrices. Additionally, we evaluate the performance of the IPB test by comparing it with three existing tests: the parametric bootstrap (PB) test, the generalized variable (GV) test, and the Johansen test. Through Monte Carlo simulation, our results demonstrate that both the IPB test and the PB test exhibit superior control over Type I error rates compared to the GV and Johansen tests. Notably, the IPB test outperforms the PB test in terms of controlling Type I error rates. Consequently, our study concludes that the IPB test represents a preferred statistical method for testing the equality of mean vectors in the multivariate Behrens-Fisher problem.
{"title":"Parametric test based on the bootstrapping approach for the MANOVA under a Behrens-Fisher problem","authors":"Jatsada Singthongchai, Noppakun Thongmual, Nirun Nitisuk","doi":"10.3233/mas-231449","DOIUrl":"https://doi.org/10.3233/mas-231449","url":null,"abstract":"This article presents a comparison of multivariate normal mean vectors under covariance positive definite matrices. We introduce an improved parametric bootstrap (IPB) approach for addressing the multivariate Behrens-Fisher problem, specifically focusing on cases with unequal covariance matrices. Additionally, we evaluate the performance of the IPB test by comparing it with three existing tests: the parametric bootstrap (PB) test, the generalized variable (GV) test, and the Johansen test. Through Monte Carlo simulation, our results demonstrate that both the IPB test and the PB test exhibit superior control over Type I error rates compared to the GV and Johansen tests. Notably, the IPB test outperforms the PB test in terms of controlling Type I error rates. Consequently, our study concludes that the IPB test represents a preferred statistical method for testing the equality of mean vectors in the multivariate Behrens-Fisher problem.","PeriodicalId":35000,"journal":{"name":"Model Assisted Statistics and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140244709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
At its core, copula theory focuses on constructing a copula function, which characterizes the structure of dependence between random variables. In particular, the creation of extreme value copulas is crucial because they allow accurate modeling of extreme dependence that traditional copulas can ignore. In this article, we propose theoretical developments on this subject by proposing two new extreme value copulas. They aim to extend the functionalities of the so-called Tawn copula. This is of interest because the Tawn copula is known to be a powerful tool in modeling joint distributions, particularly in capturing asymmetric and upper tail dependences, making it valuable for analyzing extreme events and tail risk. The proposed copulas are designed to go beyond these attractive features. On the mathematical side, they are derived from new Pickands dependence functions; one modifies the Pickands dependence function of the Tawn copula by using a polynomial-exponential function, and the other does the same but by introducing a power function. The proofs are based on diverse differentiation, arrangement, and inequality techniques. Overall, the created copulas are attractive because (i) they possess modulable levels of asymmetry, (ii) they depend on several tuning parameters, making them very flexible in terms of upper tail dependence in particular, and (iii) they benefit from interesting correlation ranges of values. Several figures and value tables support the theoretical findings.
{"title":"On two new modified tawn copulas","authors":"Christophe Chesneau","doi":"10.3233/mas-231451","DOIUrl":"https://doi.org/10.3233/mas-231451","url":null,"abstract":"At its core, copula theory focuses on constructing a copula function, which characterizes the structure of dependence between random variables. In particular, the creation of extreme value copulas is crucial because they allow accurate modeling of extreme dependence that traditional copulas can ignore. In this article, we propose theoretical developments on this subject by proposing two new extreme value copulas. They aim to extend the functionalities of the so-called Tawn copula. This is of interest because the Tawn copula is known to be a powerful tool in modeling joint distributions, particularly in capturing asymmetric and upper tail dependences, making it valuable for analyzing extreme events and tail risk. The proposed copulas are designed to go beyond these attractive features. On the mathematical side, they are derived from new Pickands dependence functions; one modifies the Pickands dependence function of the Tawn copula by using a polynomial-exponential function, and the other does the same but by introducing a power function. The proofs are based on diverse differentiation, arrangement, and inequality techniques. Overall, the created copulas are attractive because (i) they possess modulable levels of asymmetry, (ii) they depend on several tuning parameters, making them very flexible in terms of upper tail dependence in particular, and (iii) they benefit from interesting correlation ranges of values. Several figures and value tables support the theoretical findings.","PeriodicalId":35000,"journal":{"name":"Model Assisted Statistics and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140243916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
C. Chapman-Wardy, Eric Ocran, Samuel Iddi, L. Asiedu
Solid waste management has become a challenge for developing countries mainly because of surging economic activities, rapid urbanisation and rise in community living standards. Many researchers have identified its related problems and have recommended solutions while others have established models to forecast the amount of solid waste generated over a period. However, an efficient and effective management of solid waste requires adequate categorisation of solid waste generation areas to aid in the provision of area-specific or targeted solutions for each categorised area. In this study, we used primary data on some important socio-demographic variables (household size, house type, predominant religion of household, age and educational level of household head, residency type household waste disposal method, frequency of waste collection etc) and the amount of solid waste generated from 2102 households in Greater Accra Region, Ghana. We assessed the classification performances of a traditional statistical classifiers and some selected machine learning algorithms in classifying the surveyed areas in Greater Accra into low, medium, and high solid waste generation areas. The Support Vector Machine with the Cubic Kernel was found to be the best performing classifier with a Specificity of 86%, Sensitivity, Precision and Accuracy of 73% and Area under the curve (AUC) of 0.90. The Support Vector Machine with the Cubic Kernel is therefore recommended as a suitable algorithm for the categorisation of solid waste generation areas. Stakeholders responsible for solid waste management could leverage on the evidence from this study to categorise their waste generation areas and to proffer targeted community-based interventions.
{"title":"Classification of solid waste generation areas in the greater accra region using machine learning algorithms","authors":"C. Chapman-Wardy, Eric Ocran, Samuel Iddi, L. Asiedu","doi":"10.3233/mas-231440","DOIUrl":"https://doi.org/10.3233/mas-231440","url":null,"abstract":"Solid waste management has become a challenge for developing countries mainly because of surging economic activities, rapid urbanisation and rise in community living standards. Many researchers have identified its related problems and have recommended solutions while others have established models to forecast the amount of solid waste generated over a period. However, an efficient and effective management of solid waste requires adequate categorisation of solid waste generation areas to aid in the provision of area-specific or targeted solutions for each categorised area. In this study, we used primary data on some important socio-demographic variables (household size, house type, predominant religion of household, age and educational level of household head, residency type household waste disposal method, frequency of waste collection etc) and the amount of solid waste generated from 2102 households in Greater Accra Region, Ghana. We assessed the classification performances of a traditional statistical classifiers and some selected machine learning algorithms in classifying the surveyed areas in Greater Accra into low, medium, and high solid waste generation areas. The Support Vector Machine with the Cubic Kernel was found to be the best performing classifier with a Specificity of 86%, Sensitivity, Precision and Accuracy of 73% and Area under the curve (AUC) of 0.90. The Support Vector Machine with the Cubic Kernel is therefore recommended as a suitable algorithm for the categorisation of solid waste generation areas. Stakeholders responsible for solid waste management could leverage on the evidence from this study to categorise their waste generation areas and to proffer targeted community-based interventions.","PeriodicalId":35000,"journal":{"name":"Model Assisted Statistics and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139153193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Network data arises naturally in a wide variety of applications in different fields. In this article we discuss in detail the statistical modeling of financial networks. The structure of such networks red has not been studied thoroughly in the past, mainly due to limited accessible data. We explore the structure of a real trading network corresponding to transactions within the natural gas future market over a four-year period. The detection of meaningful communities of actors within networks is particularly relevant to understand the topology of a complex system like this. We explore the usage of stochastic block models in conjunction with a nonparametric Bayesian approach in order to identify clusters of traders in a flexible modeling framework. Our findings strongly indicate that the proposed models are highly reliable at detecting community structures.
{"title":"Bayesian inference of financial networks","authors":"Juan Sosa, Brenda Betancourt","doi":"10.3233/mas-231456","DOIUrl":"https://doi.org/10.3233/mas-231456","url":null,"abstract":"Network data arises naturally in a wide variety of applications in different fields. In this article we discuss in detail the statistical modeling of financial networks. The structure of such networks red has not been studied thoroughly in the past, mainly due to limited accessible data. We explore the structure of a real trading network corresponding to transactions within the natural gas future market over a four-year period. The detection of meaningful communities of actors within networks is particularly relevant to understand the topology of a complex system like this. We explore the usage of stochastic block models in conjunction with a nonparametric Bayesian approach in order to identify clusters of traders in a flexible modeling framework. Our findings strongly indicate that the proposed models are highly reliable at detecting community structures.","PeriodicalId":35000,"journal":{"name":"Model Assisted Statistics and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139154694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Laplace probability density function with additional shape parameter that regulates the degree of skewness is a skew Laplace distribution. The various forms of skew Laplace distribution are found in the literature, the distributions defined by Mc Gill (1962), Holla and Bhattacharya (1968), Lingappaiah (1988), Fernandez and Steel (1998). The skew log Laplace distribution is the probability distribution of a random variable whose logarithm follows a skew Laplace distribution. In this paper, the classical optimum tests for skewness parameter of skew log Laplace distribution (SLLD) derived from Lingappaiah (1988) distribution are discussed. Uniformly most powerful test, uniformly most powerful unbiased test and Wald’s sequential probability ratio test for skewness parameter are compared. The exact likelihood ratio test and Neyman structure test for testing skewness parameter when scale parameter is known are derived. Finally, the underreported income of Road Transport Company is analysed on the basis of the tests derived in this paper.
{"title":"Tests for skewness parameter of skew log Laplace distribution","authors":"Pradnya P. Khandeparkar, Vaijayanti Dixit","doi":"10.3233/mas-221423","DOIUrl":"https://doi.org/10.3233/mas-221423","url":null,"abstract":"Laplace probability density function with additional shape parameter that regulates the degree of skewness is a skew Laplace distribution. The various forms of skew Laplace distribution are found in the literature, the distributions defined by Mc Gill (1962), Holla and Bhattacharya (1968), Lingappaiah (1988), Fernandez and Steel (1998). The skew log Laplace distribution is the probability distribution of a random variable whose logarithm follows a skew Laplace distribution. In this paper, the classical optimum tests for skewness parameter of skew log Laplace distribution (SLLD) derived from Lingappaiah (1988) distribution are discussed. Uniformly most powerful test, uniformly most powerful unbiased test and Wald’s sequential probability ratio test for skewness parameter are compared. The exact likelihood ratio test and Neyman structure test for testing skewness parameter when scale parameter is known are derived. Finally, the underreported income of Road Transport Company is analysed on the basis of the tests derived in this paper.","PeriodicalId":35000,"journal":{"name":"Model Assisted Statistics and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139154553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Alex Paparas, S. Fotopoulos, V. Jandhyala, Dimitris Paparas
In this study we develop a change point methodology to identify and estimate changes in the parameter of a Poisson distribution. The proposed methodology considers the case when the Poisson parameter changes abruptly at an unknown point of time. For this case, the maximum likelihood estimate of the change point and its asymptotic distribution are pursued. Mainly, we carry out a large scale simulation study for evaluating the appropriateness of the asymptotic distribution of the mle from the view point of finite samples, and also for evaluating the closeness under known and unknown parameters. The simulations study also compares the mle with that of a Bayesian estimate. Then, the methodology is applied to three examples. First, we uncover changes in the number of homicides in California using monthly data from January 2002 until December 2020. Secondly, data about deaths of females caused by stomach cancer is considered to detect possible changes in the numbers recorded from 1930 to 2011. Thirdly, British coal mining disasters from 1851 to 1962 in which more than 10 men were killed are analyzed.
{"title":"Maximum likelihood estimation of a change point for Poisson distributed data","authors":"Alex Paparas, S. Fotopoulos, V. Jandhyala, Dimitris Paparas","doi":"10.3233/mas-231448","DOIUrl":"https://doi.org/10.3233/mas-231448","url":null,"abstract":"In this study we develop a change point methodology to identify and estimate changes in the parameter of a Poisson distribution. The proposed methodology considers the case when the Poisson parameter changes abruptly at an unknown point of time. For this case, the maximum likelihood estimate of the change point and its asymptotic distribution are pursued. Mainly, we carry out a large scale simulation study for evaluating the appropriateness of the asymptotic distribution of the mle from the view point of finite samples, and also for evaluating the closeness under known and unknown parameters. The simulations study also compares the mle with that of a Bayesian estimate. Then, the methodology is applied to three examples. First, we uncover changes in the number of homicides in California using monthly data from January 2002 until December 2020. Secondly, data about deaths of females caused by stomach cancer is considered to detect possible changes in the numbers recorded from 1930 to 2011. Thirdly, British coal mining disasters from 1851 to 1962 in which more than 10 men were killed are analyzed.","PeriodicalId":35000,"journal":{"name":"Model Assisted Statistics and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139153237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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