Gaussian process(GP)is a stochastic process that has been successfully applied in finance,black-box modeling of biosystems,machine learning,geostatistics,multitask learning or robotics and reinforcement learning.Effec...Gaussian process(GP)is a stochastic process that has been successfully applied in finance,black-box modeling of biosystems,machine learning,geostatistics,multitask learning or robotics and reinforcement learning.Effectively estimating the spectral density function(SDF)and degree of memory(DOM)of a long-memory stationary GP(LMSGP)is needed to get accurate information about the process.The practice demonstrated that the periodogram estimator(PE)and lag window estimator(LWE)that are the extremely used estimators of the SDF and DOM have some drawbacks,especially for LMSGPs.The behaviors of the PEs and LWEs are soundly investigated numerically;however,the theoretical justifications are limited and thus the challenge to improve them is still daunting.This paper gives a closer look at the theoretical justifications of the efficiency of the LWEs that provides new sufficient conditions(NSCs)for improving the LWEs of the SDF and DOM for LMSGPs.The precision,the convergence rate of the bias and variance,and the asymptotic distributions of the LWEs under the NSCs are studied.A comparison study among the LWEs under the NSCs,the LWEs without the NSCs and the PEs is given to investigate the significance of the NSCs.The main theoretical and simulation results show that:the LWEs under theNSCs are asymptotically unbiased and consistent and better than the LWEswithout the NSCs and the PEs,and the asymptotic distributions of the LWEs under the NSCs are chi-square for SDF and normal for DOM.展开更多
The foldover is a quick and useful technique in construction of fractional factorial designs, which typically releases aliased factors or interactions. The issue of employing the uniformity criterion measured by the c...The foldover is a quick and useful technique in construction of fractional factorial designs, which typically releases aliased factors or interactions. The issue of employing the uniformity criterion measured by the centered L2-discrepancy to assess the optimal foldover plans was studied for four-level design. A new analytical expression and a new lower bound of the centered L2-discrepancy for fourlevel combined design under a general foldover plan are respectively obtained. A necessary condition for the existence of an optimal foldover plan meeting this lower bound was described. An algorithm for searching the optimal four-level foldover plans is also developed. Illustrative examples are provided, where numerical studies lend further support to our theoretical results. These results may help to provide some powerful and efficient Mgorithms for searching the optimal four-level foldover plans.展开更多
Experimental design is an effective statistical tool that is extensively applied in modern industry,engineering,and science.It is proved that experimental design is a powerful and efficient means to screen the relatio...Experimental design is an effective statistical tool that is extensively applied in modern industry,engineering,and science.It is proved that experimental design is a powerful and efficient means to screen the relationships between input factors and their responses,and to distinguish significant and unimportant factor effects.In many practical situations,experimenters are faced with large experiments having four-level factors.Even though there are several techniques provided to design such experiments,the challenge faced by the experimenters is still daunting.The practice has demonstrated that the existing techniques are highly time-consuming optimization procedures,satisfactory outcomes are not guaranteed,and non-mathematicians face a significant challenge in dealing with them.A new technique that can overcome these defects of the existing techniques is presented in this paper.The results demonstrated that the proposed technique outperformed the current techniques in terms of construction simplicity,computational efficiency and achieving satisfactory results capability.For non-mathematician experimenters,the new technique is much easier and simpler than the current techniques,as it allows them to design optimal large experiments without the recourse to optimization softwares.The optimality is discussed from four basic perspectives:maximizing the dissimilarity among experimental runs,maximizing the number of independent factors,minimizing the confounding among factors,and filling the experimental domain uniformly with as few gaps as possible.展开更多
基金supported by the UIC Research Grants with No.of(R201810,R201912 and R202010)the Curriculum Development and Teaching Enhancement with No.of(UICR0400046-21CTL)+1 种基金the Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science,BNU-HKBU United International College with No.of(2022B1212010006)in part by Guangdong Higher Education Upgrading Plan(2021-2025)with No.of(UIC R0400001-22).
文摘Gaussian process(GP)is a stochastic process that has been successfully applied in finance,black-box modeling of biosystems,machine learning,geostatistics,multitask learning or robotics and reinforcement learning.Effectively estimating the spectral density function(SDF)and degree of memory(DOM)of a long-memory stationary GP(LMSGP)is needed to get accurate information about the process.The practice demonstrated that the periodogram estimator(PE)and lag window estimator(LWE)that are the extremely used estimators of the SDF and DOM have some drawbacks,especially for LMSGPs.The behaviors of the PEs and LWEs are soundly investigated numerically;however,the theoretical justifications are limited and thus the challenge to improve them is still daunting.This paper gives a closer look at the theoretical justifications of the efficiency of the LWEs that provides new sufficient conditions(NSCs)for improving the LWEs of the SDF and DOM for LMSGPs.The precision,the convergence rate of the bias and variance,and the asymptotic distributions of the LWEs under the NSCs are studied.A comparison study among the LWEs under the NSCs,the LWEs without the NSCs and the PEs is given to investigate the significance of the NSCs.The main theoretical and simulation results show that:the LWEs under theNSCs are asymptotically unbiased and consistent and better than the LWEswithout the NSCs and the PEs,and the asymptotic distributions of the LWEs under the NSCs are chi-square for SDF and normal for DOM.
基金Supported by National Natural Science Foundation of China(Grant Nos.11271147,11471135 and 11471136)
文摘The foldover is a quick and useful technique in construction of fractional factorial designs, which typically releases aliased factors or interactions. The issue of employing the uniformity criterion measured by the centered L2-discrepancy to assess the optimal foldover plans was studied for four-level design. A new analytical expression and a new lower bound of the centered L2-discrepancy for fourlevel combined design under a general foldover plan are respectively obtained. A necessary condition for the existence of an optimal foldover plan meeting this lower bound was described. An algorithm for searching the optimal four-level foldover plans is also developed. Illustrative examples are provided, where numerical studies lend further support to our theoretical results. These results may help to provide some powerful and efficient Mgorithms for searching the optimal four-level foldover plans.
基金partially supported by the UIC Grants(Nos.R201810,R201912 and R202010)the Zhuhai Premier Discipline Grant.
文摘Experimental design is an effective statistical tool that is extensively applied in modern industry,engineering,and science.It is proved that experimental design is a powerful and efficient means to screen the relationships between input factors and their responses,and to distinguish significant and unimportant factor effects.In many practical situations,experimenters are faced with large experiments having four-level factors.Even though there are several techniques provided to design such experiments,the challenge faced by the experimenters is still daunting.The practice has demonstrated that the existing techniques are highly time-consuming optimization procedures,satisfactory outcomes are not guaranteed,and non-mathematicians face a significant challenge in dealing with them.A new technique that can overcome these defects of the existing techniques is presented in this paper.The results demonstrated that the proposed technique outperformed the current techniques in terms of construction simplicity,computational efficiency and achieving satisfactory results capability.For non-mathematician experimenters,the new technique is much easier and simpler than the current techniques,as it allows them to design optimal large experiments without the recourse to optimization softwares.The optimality is discussed from four basic perspectives:maximizing the dissimilarity among experimental runs,maximizing the number of independent factors,minimizing the confounding among factors,and filling the experimental domain uniformly with as few gaps as possible.
