Existence of optimal solution for exponential model by least squares

Jukić, Dragan; Scitovski, Rudolf

doi:10.1016/s0377-0427(96)00160-4

Cited by 33 publications

(11 citation statements)

References 7 publications

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“…. , n, have the property of preponderant increase, and similarly, condition (7) means that the data (w i x…”

Section: Remark 1 the Following Results Which Was Used In [3] For Promentioning

confidence: 99%

“…It has been shown that for these models the property of preponderant increase/ decrease is crucial for the existence of the LSE. In [7], it was shown that the LSE exists, provided the data satisfy either the condition of preponderant increase or the condition of preponderant decrease.…”

Section: Some Applications Of Preponderant Increase Property In Regrementioning

confidence: 99%

“…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%

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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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“…. , n, have the property of preponderant increase, and similarly, condition (7) means that the data (w i x…”

Section: Remark 1 the Following Results Which Was Used In [3] For Promentioning

confidence: 99%

Section: Some Applications Of Preponderant Increase Property In Regrementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Preponderantly increasing/decreasing data in regression analysis

Marković

2016

CRORR

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“…In the case of nonlinear LS problems it is still extremely difficult to answer this question. Some theorems about the existence of the LSE for some special function can be found in e.g., [2,[5][6][7]15,16,18,19]. …”

Section: Least Squares (Ls) Approachmentioning

confidence: 99%

“…. , m, have the property of preponderant decrease, i.e., the slope of the associated weighted linear regression is negative (see [19]). …”

Section: Some Properties Of Rectangular Hyperbolamentioning

confidence: 99%

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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Least‐squares problems for Michaelis–Menten kinetics

Hadeler

Jukić

Sabo

2007

Math Methods in App Sciences

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SUMMARYThe Michaelis-Menten kinetics is fundamental in chemical and physiological reaction theory. The problem of parameter identification, which is not well posed for arbitrary data, is shown to be closely related to the Chebyshev sum inequality. This inequality yields sufficient conditions for existence of feasible solutions both for nonlinear and for linear least-squares problems. The conditions are natural and practical as they are satisfied if the data show the expected monotone and concave behaviour.

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Existence of optimal solution for exponential model by least squares

Cited by 33 publications

References 7 publications

Preponderantly increasing/decreasing data in regression analysis

Preponderantly increasing/decreasing data in regression analysis

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

Least‐squares problems for Michaelis–Menten kinetics

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