• Title/Summary/Keyword: Approximate Estimates

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A Kullback-Leibler divergence based comparison of approximate Bayesian estimations of ARMA models

  • Amin, Ayman A
    • Communications for Statistical Applications and Methods
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    • v.29 no.4
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    • pp.471-486
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    • 2022
  • Autoregressive moving average (ARMA) models involve nonlinearity in the model coefficients because of unobserved lagged errors, which complicates the likelihood function and makes the posterior density analytically intractable. In order to overcome this problem of posterior analysis, some approximation methods have been proposed in literature. In this paper we first review the main analytic approximations proposed to approximate the posterior density of ARMA models to be analytically tractable, which include Newbold, Zellner-Reynolds, and Broemeling-Shaarawy approximations. We then use the Kullback-Leibler divergence to study the relation between these three analytic approximations and to measure the distance between their derived approximate posteriors for ARMA models. In addition, we evaluate the impact of the approximate posteriors distance in Bayesian estimates of mean and precision of the model coefficients by generating a large number of Monte Carlo simulations from the approximate posteriors. Simulation study results show that the approximate posteriors of Newbold and Zellner-Reynolds are very close to each other, and their estimates have higher precision compared to those of Broemeling-Shaarawy approximation. Same results are obtained from the application to real-world time series datasets.

Higher Order Moments of Record Values From the Inverse Weibull Lifetime Model and Edgeworth Approximate Inference

  • Sultan, K.S.
    • International Journal of Reliability and Applications
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    • v.8 no.1
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    • pp.1-16
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    • 2007
  • In this paper, we derive exact explicit expressions for the triple and quadruple moments of the lower record values from inverse the Weibull (IW) distribution. Next, we present and calculate the coefficients of the best linear unbiased estimates of the location and scale parameters of IW distribution (BLUEs) for different choices of the shape parameter and records size. We then use the higher order moments and the calculated BLUEs to compute the mean, variance, and the coefficients of skewness and kurtosis of certain linear functions of lower record values. By using the coefficients of the skewness and kurtosis, we develop approximate confidence intervals for the location and scale parameters of the IW distribution using Edgeworth approximate values and then compare them with the corresponding intervals constructed through Monte Carlo simulations. Finally, we apply the findings of the paper to some simulated data.

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APPROXIMATE REACHABLE SETS FOR RETARDED SEMILINEAR CONTROL SYSTEMS

  • KIM, DAEWOOK;JEONG, JIN-MUN
    • Journal of applied mathematics & informatics
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    • v.38 no.5_6
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    • pp.469-481
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    • 2020
  • In this paper, we consider a control system for semilinear differential equations in Hilbert spaces with Lipschitz continuous nonlinear term. Our method is to find the equivalence of approximate controllability for the given semilinear system and the linear system excluded the nonlinear term, which is based on results on regularity for the mild solution and estimates of the fundamental solution.

AUXILIARY PRINCEPLE AND ERROR ESTIMATES FOR VARIATIONAL INEQUALITIES

  • NOOR, MUHAMMED ASLAM
    • Honam Mathematical Journal
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    • v.15 no.1
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    • pp.105-120
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    • 1993
  • The auxiliary principle technique is used to prove the uniqueness and the existence of solutions for a class of nonlinear variational inequalities and suggest an innovative iterative algorithm for computing the approximate solution of variational inequalities. Error estimates for the finite element approximation of the solution of variational inequalities are derived, which refine the previous known results. An example is given to illustrate the applications of the results obtained. Several special cases are considered and studied.

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L^INFINITY ERROR ESTIMATES FOR FINITE DIFFERENCE SCHEMES FOR GENERALIZED CAHN-HILLIARD AND KURAMOTO-SIVASHINSKY EQUATIONS

  • Choo, S.M.
    • Journal of applied mathematics & informatics
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    • v.23 no.1_2
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    • pp.571-579
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    • 2007
  • Finite difference schemes are considered for a generalization of the Cahn-Hilliard equation with Neumann boundary conditions and the Kuramoto-Sivashinsky equation with a periodic boundary condition, which is of the type $ut+\frac{{\partial}^2} {{\partial}x^2}\;g\;(u,\;u_x,\;u_{xx})=f(u,\;u_x,\;u_{xx})$. Stability and $L^{\infty}$ error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.

PROCESS RESEARCH FOR DEVELOPMENT OF STRUCTURAL COST ESTIMATING MODEL BASED QUANTITY - FOCUSED ON PUBLIC OFFICE BUILDING PROJECT -

  • Soo-Min Kim;Jung-Kyu Seo;Sung-Uk Kim;Chang-Hyun Shin;Yung-Jin Kim;Jae-Youl Chun
    • International conference on construction engineering and project management
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    • 2009.05a
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    • pp.1170-1175
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    • 2009
  • When managers estimate exact construction cost at early stage and design phase, they can reduce construction cost in a more efficient way than to predict at construction stage. But, the current of public construction cost estimation and management is concentrated almost after detailed design phase. Therefore, construction cost management in design development phase to generally use approximate estimating is not correct. Also, the existing construction cost used the method that estimated by gross floor area-based cost estimates at design development phase. So, it is difficult to show the specific amount of materials and basis about the estimated cost of the construction. This study derived problems and limits of construction management at design development phase in case of public office building project through review of literature and current survey, and suggested estimating process model process of structural construction cost go improve these matters.

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Integrating Deep Learning with Web-Based Price Analysis to Support Cost Estimation

  • Musa, Musa Ayuba;Akanbi, Temitope
    • International conference on construction engineering and project management
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    • 2022.06a
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    • pp.253-260
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    • 2022
  • Existing web-based cost databases have proved invaluable for construction cost estimating. These databases have been utilized to compute approximate cost estimates using assembly rates, unit rates, and etc. These web-based databases can be used independently with traditional cost estimation methods (manual methods) or used to support BIM-based cost estimating platforms. However, these databases are rigid, costly, and require a lot of manual inputs to reflect recent trends in prices or prices relative to a construction project's location. To address this gap, this study integrated deep learning techniques with web-based price analysis to develop a database that incorporates a project's location cost estimating standards and current cost trends in generating a cost estimate. The proposed method was tested in a case study project in Lagos, Nigeria. A cost estimate was successfully generated. Comparison of the experimental results with results using current industry standards showed that the proposed method achieved a 98.16% accuracy. The results showed that the proposed method was successful in generating approximate cost estimates irrespective of project's location.

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SOBOLEV TYPE APPROXIMATION ORDER BY SCATTERED SHIFTS OF A RADIAL BASIS FUNCTION

  • Yoon, Jung-Ho
    • Journal of applied mathematics & informatics
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    • v.23 no.1_2
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    • pp.435-443
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    • 2007
  • An important approach towards solving the scattered data problem is by using radial basis functions. However, for a large class of smooth basis functions such as Gaussians, the existing theories guarantee the interpolant to approximate well only for a very small class of very smooth approximate which is the so-called 'native' space. The approximands f need to be extremely smooth. Hence, the purpose of this paper is to study approximation by a scattered shifts of a radial basis functions. We provide error estimates on larger spaces, especially on the homogeneous Sobolev spaces.

FINITE DIFFERENCE SCHEMES FOR CALCIUM DIFFUSION EQUATIONS

  • Choo, S.M.
    • Journal of applied mathematics & informatics
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    • v.26 no.1_2
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    • pp.299-306
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    • 2008
  • Finite difference schemes are considered for a $Ca^{2+}$ diffusion equations, which discribe $Ca^{2+}$ buffering by using stationary and mobile buffers. Stability and $L^\infty$ error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.

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Two Queue Single Server Model for the DQDB Man

  • Noh, Seung J.
    • Journal of the Korean Operations Research and Management Science Society
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    • v.22 no.2
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    • pp.31-44
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    • 1997
  • This paper presents an approximate analytical model to estimate the mean packet walting times at the stations in the IEEE 802, 6 subnetwork of a metropolitan area network. Each station is modeled as a two queue single server system, which serves data packets and requests from downstream stations according to the DQDB protocol. The model estimates the mean waiting time of the requests and in turn, using the discrete time work conservation law, estimates the mean waiting time for packets. Simulation experiments shows that the model accurately works even under very high traffic loads.

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