Least‐squares problems for Michaelis–Menten kinetics

Hadeler, K. P.; Jukić, Dragan; Sabo, Kristian

doi:10.1002/mma.835

Cited by 22 publications

(11 citation statements)

References 18 publications

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“…The main purpose of this paper is to systematize the results from [12,17] about the existence of the least squares estimate and the total least squares estimate for the Michaelis-Menten function, which will be done in Sect. 3.…”

Section: Total Least Squares (Tls) Approachmentioning

confidence: 99%

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A review of existence criteria for parameter estimation of the Michaelis–Menten regression model

2007

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In this paper we consider the least squares (LS) and total least squares (TLS) problems for a Michaelis-Menten enzyme kinetic model f (x; a, b) = ax/(b + x), a, b > 0. In various applied research such as biochemistry, pharmacology, biology and medicine there are lots of different applications of this model. We will systematize some of our results pertaining to the existence of the LS and TLS estimate, which were proved in Hadeler et al. (Math Method Appl Sci 30:1231-1241 and Jukić et al. (J Comput Appl Math 201:230-246, 2007). Finally, we suggest a choice of good initial approximation and give one numerical example.

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Section: Total Least Squares (Tls) Approachmentioning

confidence: 99%

“…It also gives sufficient conditions which guarantee the existence of the LS estimate for the Michaelis-Menten function. Theorem 3.1 (see [12]) Let the data ( p i , x i , y i ), i = 1, . .…”

Section: )mentioning

confidence: 99%

A review of existence criteria for parameter estimation of the Michaelis–Menten regression model

2007

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“…It has been shown that property of preponderant increase/decrease, which will be described in more details in the next section, has an important role in analyzing the existence of the LSE (see e.g. [2,3,5,6,7,13,14]). Our main theoretical result is the useful Theorem 1 that describes increasing/decreasing data by preponderantly increasing/decreasing data.…”

Section: Introductionmentioning

confidence: 99%

Preponderantly increasing/decreasing data in regression analysis

Marković

2016

CRORR

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Abstract. For the given data (wi, xi, yi), i = 1, . . . , n, and the given model function f (x; θ), where θ is a vector of unknown parameters, the goal of regression analysis is to obtain estimator θ * of the unknown parameters θ such that the vector of residuals is minimized in some sense. The common approach to this problem of minimization is the least-squares method, that is minimizing the L2 norm of the vector of residuals. For nonlinear model functions, what is necessary is finding at least the sufficient conditions on the data that will guarantee the existence of the best least-squares estimator. In this paper we will describe and examine in detail the property of preponderant increase/decrease of the data, which ensures the existence of the best estimator for certain important nonlinear model functions.

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“…The nonlinear weighted LS fitting problem for the three-parameter Weibull CDF is considered in [11]. Results on the existence of the LSE for some special classes of functions other than the three-parameter Weibull density functions can be found in [3,4,7,8,[12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear weighted least squares estimation of a three-parameter Weibull density with a nonparametric start

Marković

Jukić

Benšić

2009

Journal of Computational and Applied Mathematics

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a b s t r a c tThis paper is concerned with the parameter estimation problem for the three-parameter Weibull density which is widely employed as a model in reliability and lifetime studies. Our approach is a combination of nonparametric and parametric methods. The basic idea is to start with an initial nonparametric density estimate which needs to be as good as possible, and then apply the nonlinear least squares method to estimate the unknown parameters. As a main result, a theorem on the existence of the least squares estimate is obtained. Some simulations are given to show that our approach is satisfactory if the initial density is of good enough quality.

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Least‐squares problems for Michaelis–Menten kinetics

Cited by 22 publications

References 18 publications

A review of existence criteria for parameter estimation of the Michaelis–Menten regression model

A review of existence criteria for parameter estimation of the Michaelis–Menten regression model

Preponderantly increasing/decreasing data in regression analysis

Nonlinear weighted least squares estimation of a three-parameter Weibull density with a nonparametric start

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