A Simple Proof of the Existence of the Best Estimator in a Quasilinear Regression Model

Jukić, Dragan

doi:10.1007/s10957-013-0434-1

Cited by 3 publications

(1 citation statement)

References 16 publications

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“…However, in practice, the probability that the NLS estimate does not exist cannot be ignored, see the following example. Only a handful of papers discuss the non‐existence of the NLS estimate either in terms of sufficient criteria Demidenko () or necessary and sufficient conditions for specific non‐linear regression models Hadeler et al (), Jukić & Markovic () & Jukić (), to name a few. The purpose of this section is to illustrate how the probability of non‐existence affects the density distribution using simplistic examples of non‐linear regression where this probability is tractable.…”

Section: Numerical Complicationsmentioning

confidence: 99%

Exact and Approximate Statistical Inference for Nonlinear Regression and the Estimating Equation Approach

Demidenko

2017

Scandinavian J Statistics

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The exact density distribution of the nonlinear least squares estimator in the one-parameter regression model is derived in closed form and expressed through the cumulative distribution function of the standard normal variable. Several proposals to generalize this result are discussed. The exact density is extended to the estimating equation (EE) approach and the nonlinear regression with an arbitrary number of linear parameters and one intrinsically nonlinear parameter. For a very special nonlinear regression model, the derived density coincides with the distribution of the ratio of two normally distributed random variables previously obtained by Fieller (1932), unlike other approximations previously suggested by other authors. Approximations to the density of the EE estimators are discussed in the multivariate case. Numerical complications associated with the nonlinear least squares are illustrated, such as nonexistence and/or multiple solutions, as major factors contributing to poor density approximation. The nonlinear Markov-Gauss theorem is formulated based on the near exact EE density approximation.

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Section: Numerical Complicationsmentioning

confidence: 99%

Exact and Approximate Statistical Inference for Nonlinear Regression and the Estimating Equation Approach

Demidenko

2017

Scandinavian J Statistics

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Parameter Identification of the Capillary Rising Process in Nanomaterials for Evaporative Cooling Applications

Levchenko¹,

Pavlenko

Shulumei

et al. 2020

Advances in Design, Simulation and Manufacturing III

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An existence level for the residual sum of squares of the power-law regression with an unknown location parameter

Jukić

Marošević

2021

Mathematica Slovaca

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In a recent paper [JUKIĆ, D.: A necessary and sufficient criterion for the existence of the global minima of a continuous lower bounded function on a noncompact set, J. Comput. Appl. Math. 375 (2020)], a new existence level was introduced and then was used to obtain a necessary and sufficient criterion for the existence of the global minima of a continuous lower bounded function on a noncompact set. In this paper, we determined that existence level for the residual sum of squares of the power-law regression with an unknown location parameter, and so we obtained a necessary and sufficient condition which guarantee the existence of the least squares estimate.

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A Simple Proof of the Existence of the Best Estimator in a Quasilinear Regression Model

Cited by 3 publications

References 16 publications

Exact and Approximate Statistical Inference for Nonlinear Regression and the Estimating Equation Approach

Exact and Approximate Statistical Inference for Nonlinear Regression and the Estimating Equation Approach

Parameter Identification of the Capillary Rising Process in Nanomaterials for Evaporative Cooling Applications

An existence level for the residual sum of squares of the power-law regression with an unknown location parameter

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