Correlation coefficients and linear regression values computed from group averages can differ from correlation coefficients and linear regression values computed using individual scores. This observation known as the ecological fallacy often assumes that all the individual scores are available from a population. In many situations, one must use a sample from the larger population. In such cases, the computed correlation coefficient and linear regression values will depend on the sample that is chosen and the underlying sampling distribution. The sampling distribution of correlation coefficients and linear regression values for group averages will be identical to the sampling distribution for individuals for normally distributed variables for random samples drawn from infinitely large continuous distributions. However, data that is acquired in practice is often acquired when sampling without replacement from a finite population. Our objective is to demonstrate through Monte Carlo simulations that the sampling distributions for correlation and linear regression will also be similar for individuals and group averages when sampling without replacement from normally distributed variables. These simulations suggest that when a random sample from a population is selected, the correlation coefficients and linear regression values computed from individual scores will not be more accurate in estimating the entire population values compared to samples when group averages are used as long as the sample size is the same.
{"title":"Investigating the ecological fallacy through sampling distributions constructed from finite populations","authors":"David J. Torres, Damain Rouson","doi":"10.1515/mcma-2024-2013","DOIUrl":"https://doi.org/10.1515/mcma-2024-2013","url":null,"abstract":"\u0000 Correlation coefficients\u0000and linear regression values computed from group averages can differ from correlation coefficients and linear regression values computed using individual scores. This observation known as the ecological fallacy often assumes that all the individual scores are available from a population. In many situations, one must use a sample from the larger population. In such cases, the computed correlation coefficient and linear regression values will depend on the sample that is chosen and the underlying sampling distribution.\u0000The sampling distribution of correlation coefficients and linear regression values for group averages will be identical to the sampling distribution for individuals for normally distributed variables for random samples drawn from infinitely large continuous distributions.\u0000However, data that is acquired in practice is often acquired when sampling without replacement from a finite population. Our objective is to demonstrate through Monte Carlo simulations that the\u0000sampling distributions for\u0000correlation and linear regression will also be similar for individuals and group averages when sampling without replacement from normally distributed variables. These simulations suggest that when a random sample from a population is selected, the correlation coefficients and linear regression values computed from individual scores will not be more accurate in estimating the entire population values compared to samples when group averages are used as long as the sample size is the same.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141927085","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}
Abstract In this paper, we suggest joint application of computational probabilistic analysis and the Monte Carlo method for numerical stochastic modeling problems. We use all the capabilities of computational probabilistic analysis while maintaining all the advantages of the Monte Carlo method. Our approach allows us to efficiently implement a computational hybrid scheme. In this way, we reduce the computation time and present the results in the form of distributions. The crucial new points of our method are arithmetic operations on probability density functions and procedures for constructing on the probabilistic extensions. Relying on specific numerical examples of solving systems of linear algebraic equations with random coefficients, we present the advantages of our approach.
{"title":"Joint application of the Monte Carlo method and computational probabilistic analysis in problems of numerical modeling with data uncertainties","authors":"B. Dobronets, O. Popova","doi":"10.1515/mcma-2024-2006","DOIUrl":"https://doi.org/10.1515/mcma-2024-2006","url":null,"abstract":"Abstract In this paper, we suggest joint application of computational probabilistic analysis and the Monte Carlo method for numerical stochastic modeling problems. We use all the capabilities of computational probabilistic analysis while maintaining all the advantages of the Monte Carlo method. Our approach allows us to efficiently implement a computational hybrid scheme. In this way, we reduce the computation time and present the results in the form of distributions. The crucial new points of our method are arithmetic operations on probability density functions and procedures for constructing on the probabilistic extensions. Relying on specific numerical examples of solving systems of linear algebraic equations with random coefficients, we present the advantages of our approach.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141334980","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}
Viktor Bryzgalov, Nurlibay Shlimbetov, Anton Voytishek
This paper considers three approaches to choosing the constant H in the expression H𝐃ζ/n{Hsqrt{{mathbf{D}}zeta}/sqrt{n}} for the error of the Monte Carlo method for numerical calculation of mathematical expectation 𝐄ζ{{mathbf{E}}zeta} of a random variable ζ: in probability, in mean square and in mean.In practical studies using the Monte Carlo method, when estimating the calculation error, it is recommended to use the “in mean” approach with the constant H=2π
This paper considers three approaches to choosing the constant H in the expression H 𝐃 ζ / n {Hsqrt{{mathbf{D}}zeta}/sqrt{n}} for the error of the Monte Carlo method for numerical calculation of mathematical expectation 𝐄 ζ {{mathbf{E}}zeta} of a random variable ζ: in probability, in mean square and in mean.In practical studies using the Monte Carlo method, when estimating the calculation error, it is recommended to use the “in mean” approach with the constant H = 2 π = 0.79788456079 … {H=sqrt{frac{2}{pi}}=0.79788456079dots} .
{"title":"Choice of a constant in the expression for the error of the Monte Carlo method","authors":"Viktor Bryzgalov, Nurlibay Shlimbetov, Anton Voytishek","doi":"10.1515/mcma-2024-2004","DOIUrl":"https://doi.org/10.1515/mcma-2024-2004","url":null,"abstract":"\u0000 <jats:p>This paper considers three approaches to choosing the constant <jats:italic>H</jats:italic> in the expression <jats:inline-formula id=\"j_mcma-2024-2004_ineq_9999\">\u0000 <jats:alternatives>\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:mrow>\u0000 <m:mrow>\u0000 <m:mi>H</m:mi>\u0000 <m:mo></m:mo>\u0000 <m:msqrt>\u0000 <m:mrow>\u0000 <m:mi>𝐃</m:mi>\u0000 <m:mo></m:mo>\u0000 <m:mi>ζ</m:mi>\u0000 </m:mrow>\u0000 </m:msqrt>\u0000 </m:mrow>\u0000 <m:mo>/</m:mo>\u0000 <m:msqrt>\u0000 <m:mi>n</m:mi>\u0000 </m:msqrt>\u0000 </m:mrow>\u0000 </m:math>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_mcma-2024-2004_eq_0044.png\" />\u0000 <jats:tex-math>{Hsqrt{{mathbf{D}}zeta}/sqrt{n}}</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula> for the error of the Monte Carlo method for numerical calculation of mathematical expectation <jats:inline-formula id=\"j_mcma-2024-2004_ineq_9998\">\u0000 <jats:alternatives>\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:mrow>\u0000 <m:mi>𝐄</m:mi>\u0000 <m:mo></m:mo>\u0000 <m:mi>ζ</m:mi>\u0000 </m:mrow>\u0000 </m:math>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_mcma-2024-2004_eq_0114.png\" />\u0000 <jats:tex-math>{{mathbf{E}}zeta}</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula> of a random variable ζ: in probability, in mean square and in mean.In practical studies using the Monte Carlo method, when estimating the calculation error, it is recommended to use the “in mean” approach with the constant <jats:inline-formula id=\"j_mcma-2024-2004_ineq_9997\">\u0000 <jats:alternatives>\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:mrow>\u0000 <m:mi>H</m:mi>\u0000 <m:mo>=</m:mo>\u0000 <m:msqrt>\u0000 <m:mfrac>\u0000 <m:mn>2</m:mn>\u0000 <m:mi>π</m:mi>\u0000 </m:mfrac>\u0000 ","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140665613","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 study linear regression models in which the error term has shape mixtures of skew-normal distribution. This type of distribution belongs to the skew-normal (SN) distribution class that can be used for heavy tails and asymmetry data. For the first time, for the classical (non-Bayesian) estimation of the parameters of the SN family, we apply the Markov chains Monte Carlo ECM (MCMC-ECM) algorithm where the samples are generated by Gibbs sampling, denoted by Gibbs-ECM, and also, we extend two other types of the EM algorithm for the above model. Finally, the proposed method is evaluated through a simulation and compared with the Numerical Math-ECM algorithm and Monte Carlo ECM (MC-ECM) using a real data set.
在本文中，我们研究了误差项具有偏态正态分布形状混合物的线性回归模型。这种分布属于偏态正态分布（SN）类，可用于重尾和不对称数据。对于 SN 系列参数的经典（非贝叶斯）估计，我们首次应用了马尔可夫链蒙特卡罗 ECM（MCMC-ECM）算法，其中样本由吉布斯抽样生成，称为吉布斯-ECM，同时，我们还针对上述模型扩展了 EM 算法的其他两种类型。最后，我们通过模拟对所提出的方法进行了评估，并使用真实数据集将其与 Numerical Math-ECM 算法和蒙特卡罗 ECM（MC-ECM）进行了比较。
{"title":"Estimation in shape mixtures of skew-normal linear regression models via ECM coupled with Gibbs sampling","authors":"Zakaria Alizadeh Ghajari, Karim Zare, Soheil Shokri","doi":"10.1515/mcma-2024-2003","DOIUrl":"https://doi.org/10.1515/mcma-2024-2003","url":null,"abstract":"\u0000 In this paper, we study linear regression models in which the error term has shape mixtures of skew-normal distribution.\u0000This type of distribution belongs to the skew-normal (SN) distribution class that can be used for heavy tails and asymmetry data.\u0000For the first time, for the classical (non-Bayesian) estimation of the parameters of the SN family, we apply the Markov chains Monte Carlo ECM (MCMC-ECM) algorithm where the samples are generated by Gibbs sampling, denoted by Gibbs-ECM, and also, we extend two other types of the EM algorithm for the above model.\u0000Finally, the proposed method is evaluated through a simulation and compared with the Numerical Math-ECM algorithm and Monte Carlo ECM (MC-ECM) using a real data set.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140712847","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}
We develop a Monte Carlo method to solve backward stochastic differential equations (BSDEs) in high dimensions. The proposed algorithm is based on the regression-later approach using multivariate Hermite polynomials and their gradients. We propose numerical experiments to illustrate its performance.
{"title":"A gradient method for high-dimensional BSDEs","authors":"Kossi Gnameho, M. Stadje, A. Pelsser","doi":"10.1515/mcma-2024-2002","DOIUrl":"https://doi.org/10.1515/mcma-2024-2002","url":null,"abstract":"\u0000 We develop a Monte Carlo method to solve backward stochastic differential equations (BSDEs) in high dimensions.\u0000The proposed algorithm is based on the regression-later approach using multivariate Hermite polynomials and their gradients.\u0000We propose numerical experiments to illustrate its performance.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139777899","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}
We develop a Monte Carlo method to solve backward stochastic differential equations (BSDEs) in high dimensions. The proposed algorithm is based on the regression-later approach using multivariate Hermite polynomials and their gradients. We propose numerical experiments to illustrate its performance.
{"title":"A gradient method for high-dimensional BSDEs","authors":"Kossi Gnameho, M. Stadje, A. Pelsser","doi":"10.1515/mcma-2024-2002","DOIUrl":"https://doi.org/10.1515/mcma-2024-2002","url":null,"abstract":"\u0000 We develop a Monte Carlo method to solve backward stochastic differential equations (BSDEs) in high dimensions.\u0000The proposed algorithm is based on the regression-later approach using multivariate Hermite polynomials and their gradients.\u0000We propose numerical experiments to illustrate its performance.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139837449","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}
Multi-stage models for cohort data are popular statistical models in several fields such as disease progressions, biological development of plants and animals, and laboratory studies of life cycle development. A Bayesian approach on adopting deterministic transformations in the Metropolis–Hastings (MH) algorithm was used to estimate parameters for these stage structured models. However, the biases in later stages are limitations of this methodology, especially the accuracy of estimates for the models having more than three stages. The main aim of this paper is to reduce these biases in parameter estimation. In particular, we conjoin insignificant previous stages or negligible later stages to estimate parameters of a desired stage, while an adjusted MH algorithm based on deterministic transformations is applied for the non-hazard rate models. This means that current stage parameters are estimated separately from the information of its later stages. This proposed method is validated in simulation studies and applied for a case study of the incubation period of COVID-19. The results show that the proposed methods could reduce the biases in later stages for estimates in stage structured models, and the results of the case study can be regarded as a valuable continuation of pandemic prevention.
{"title":"On bias reduction in parametric estimation in stage structured development models","authors":"Hoa Pham, Huong T. T. Pham, Kai Siong Yow","doi":"10.1515/mcma-2024-2001","DOIUrl":"https://doi.org/10.1515/mcma-2024-2001","url":null,"abstract":"\u0000 Multi-stage models for cohort data are popular statistical models in several fields such as disease progressions, biological development of plants and animals, and laboratory studies of life cycle development.\u0000A Bayesian approach on adopting deterministic transformations in the Metropolis–Hastings (MH) algorithm was used to estimate parameters for these stage structured models.\u0000However, the biases in later stages are limitations of this methodology, especially the accuracy of estimates for the models having more than three stages.\u0000The main aim of this paper is to reduce these biases in parameter estimation.\u0000In particular, we conjoin insignificant previous stages or negligible later stages to estimate parameters of a desired stage, while an adjusted MH algorithm based on deterministic transformations is applied for the non-hazard rate models.\u0000This means that current stage parameters are estimated separately from the information of its later stages.\u0000This proposed method is validated in simulation studies and applied for a case study of the incubation period of COVID-19.\u0000The results show that the proposed methods could reduce the biases in later stages for estimates in stage structured models, and the results of the case study can be regarded as a valuable continuation of pandemic prevention.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140477987","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}
Yasmina Djabali, Sedda Hakmi, Nabil Zougab, D. Aïssani
Abstract This paper proposes the nonparametric asymmetric kernel method in the study of strong stability of the PH/M/1 queuing system, after perturbation of arrival distribution to evaluate the proximity of the complex GI/M/1 system, where GI is a unknown general distribution. The class of generalized gamma (GG) kernels is considered because of its several interesting properties and flexibility. A simulation for several models illustrates the performance of the GG asymmetric kernel estimators in the study of strong stability of the PH/M/1, by computing the variation distance and the stability error.
{"title":"Asymmetric kernel method in the study of strong stability of the PH/M/1 queuing system","authors":"Yasmina Djabali, Sedda Hakmi, Nabil Zougab, D. Aïssani","doi":"10.1515/mcma-2023-2023","DOIUrl":"https://doi.org/10.1515/mcma-2023-2023","url":null,"abstract":"Abstract This paper proposes the nonparametric asymmetric kernel method in the study of strong stability of the PH/M/1 queuing system, after perturbation of arrival distribution to evaluate the proximity of the complex GI/M/1 system, where GI is a unknown general distribution. The class of generalized gamma (GG) kernels is considered because of its several interesting properties and flexibility. A simulation for several models illustrates the performance of the GG asymmetric kernel estimators in the study of strong stability of the PH/M/1, by computing the variation distance and the stability error.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138633054","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}
Abstract The Random Walk on Spheres (RWS) algorithm for solving anisotropic transient diffusion problems based on a stochastic learning procedure for calculation of the exit position of the anisotropic diffusion process on a sphere is developed. Direct generalization of the Random Walk on Spheres method to anisotropic diffusion equations is not possible, therefore, we have numerically calculated the probability density for the exit position on a sphere. The first passage time is then represented explicitly. The method can easily be implemented to solve diffusion problems with spatially varying diffusion coefficients for complicated three-dimensional domains. Particle tracking algorithm is highly efficient for calculation of fluxes to boundaries. We apply the developed algorithm for solving an exciton transport in a semiconductor material with a threading dislocation where the measured functions are the exciton fluxes to the semiconductor’s substrate and on the dislocation surface.
{"title":"Random walk on spheres method for solving anisotropic transient diffusion problems and flux calculations","authors":"Irina Shalimova, Karl Sabelfeld","doi":"10.1515/mcma-2023-2022","DOIUrl":"https://doi.org/10.1515/mcma-2023-2022","url":null,"abstract":"Abstract The Random Walk on Spheres (RWS) algorithm for solving anisotropic transient diffusion problems based on a stochastic learning procedure for calculation of the exit position of the anisotropic diffusion process on a sphere is developed. Direct generalization of the Random Walk on Spheres method to anisotropic diffusion equations is not possible, therefore, we have numerically calculated the probability density for the exit position on a sphere. The first passage time is then represented explicitly. The method can easily be implemented to solve diffusion problems with spatially varying diffusion coefficients for complicated three-dimensional domains. Particle tracking algorithm is highly efficient for calculation of fluxes to boundaries. We apply the developed algorithm for solving an exciton transport in a semiconductor material with a threading dislocation where the measured functions are the exciton fluxes to the semiconductor’s substrate and on the dislocation surface.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136226897","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}
Abstract The estimation of the frequency component is very interesting to study, considering its unique nature when these parameters are together in their amplitude. The periodicity of the frequency components is also thought to affect the convergence of these parameters. In this paper, we consider the problem of estimating the frequency component of a periodic continuous-time sinusoidal signal. Under the high-frequency sampling setting, we provide the frequency components’ consistency and asymptotic normality. It is observed that the convergence rate of the continuous-time sinusoidal signal of the diffusion process is the same as the continuous-time sinusoidal signal of the Ornstein–Uhlenbeck process, which is mentioned in [G. Pramesti, Parameter least-squares estimation for time-inhomogeneous Ornstein–Uhlenbeck process, Monte Carlo Methods Appl. 29 (2023), 1, 1–32]. The result of this study deduces that the convergence rate of the frequency is the same as long as the signal is periodic. In this case, the existence of the rate of reversion does not affect the convergence rate of the frequency components. Further, the result of the study, that is, the convergence rate of the frequency is (nh)3 sqrt{(nh)^{3}} , also revised the previous one in [G. Pramesti, The least-squares estimator of sinusoidal signal of diffusion process for discrete observations, J. Math. Comput. Sci. 11 (2021), 5, 6433–6443], which mentioned (nh)3h sqrt{(nh)^{3}h} . The proposed approach is demonstrated with a ten-minute sampling rate of real data on the energy consumption of light fixtures in one Belgium household.
{"title":"On the estimation of periodic signals in the diffusion process using a high-frequency scheme","authors":"Getut Pramesti, Ristu Saptono","doi":"10.1515/mcma-2023-2020","DOIUrl":"https://doi.org/10.1515/mcma-2023-2020","url":null,"abstract":"Abstract The estimation of the frequency component is very interesting to study, considering its unique nature when these parameters are together in their amplitude. The periodicity of the frequency components is also thought to affect the convergence of these parameters. In this paper, we consider the problem of estimating the frequency component of a periodic continuous-time sinusoidal signal. Under the high-frequency sampling setting, we provide the frequency components’ consistency and asymptotic normality. It is observed that the convergence rate of the continuous-time sinusoidal signal of the diffusion process is the same as the continuous-time sinusoidal signal of the Ornstein–Uhlenbeck process, which is mentioned in [G. Pramesti, Parameter least-squares estimation for time-inhomogeneous Ornstein–Uhlenbeck process, Monte Carlo Methods Appl. 29 (2023), 1, 1–32]. The result of this study deduces that the convergence rate of the frequency is the same as long as the signal is periodic. In this case, the existence of the rate of reversion does not affect the convergence rate of the frequency components. Further, the result of the study, that is, the convergence rate of the frequency is <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msqrt> <m:msup> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:mi>n</m:mi> <m:mo></m:mo> <m:mi>h</m:mi> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> <m:mn>3</m:mn> </m:msup> </m:msqrt> </m:math> sqrt{(nh)^{3}} , also revised the previous one in [G. Pramesti, The least-squares estimator of sinusoidal signal of diffusion process for discrete observations, J. Math. Comput. Sci. 11 (2021), 5, 6433–6443], which mentioned <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msqrt> <m:mrow> <m:msup> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:mi>n</m:mi> <m:mo></m:mo> <m:mi>h</m:mi> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> <m:mn>3</m:mn> </m:msup> <m:mo></m:mo> <m:mi>h</m:mi> </m:mrow> </m:msqrt> </m:math> sqrt{(nh)^{3}h} . The proposed approach is demonstrated with a ten-minute sampling rate of real data on the energy consumption of light fixtures in one Belgium household.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135041950","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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