The minimum sum of absolute errors regression: a robust alternative to the least squares regression

Narula, Subhash C.; Saldiva, Paulo Hilário Nascimento; André, Carmen Diva Saldiva de; Elian, Silvia Nagib; Ferreira, Aurea F.; Capelozzi, Vera Luíza

doi:10.1002/(sici)1097-0258(19990615)18:11<1401::aid-sim136>3.0.co;2-g

Cited by 19 publications

(10 citation statements)

References 44 publications

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“…The WAPE or the absolute errors are more robust against outliers comparing to the squared errors (Narula, Saldiva, Andre, Elian, Ferreira, & Capelozzi, 1999). We now empirically validate this claim with our data.…”

Section: Minimizing Wape Vs Minimizing Squared Errorssupporting

confidence: 70%

On the estimation of the true demand in call centers with redials and reconnects

Ding

Koole²,

Mei

2015

European Journal of Operational Research

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a b s t r a c tIn practice, in many call centers customers often perform redials (i.e., reattempt after an abandonment) and reconnects (i.e., reattempt after an answered call). In the literature, call center models usually do not cover these features, while real data analysis and simulation results show ignoring them inevitably leads to inaccurate estimation of the total inbound volume. Therefore, in this paper we propose a performance model that includes both features. In our model, the total volume consists of three types of calls: (1) fresh calls (i.e., initial call attempts), (2) redials, and (3) reconnects. In practice, the total volume is used to make forecasts, while according to the simulation results, this could lead to high forecast errors, and subsequently wrong staffing decisions. However, most of the call center data sets do not have customer-identity information, which makes it difficult to identify how many calls are fresh and what fractions of the calls are redials and reconnects.Motivated by this, we propose a model to estimate the number of fresh calls, and the redial and reconnect probabilities, using real call center data that has no customer-identity information. We show that these three variables cannot be estimated simultaneously. However, it is empirically shown that if one variable is given, the other two variables can be estimated accurately with relatively small bias. We show that our estimations of redial and reconnect probabilities and the number of fresh calls are close to the real ones, both via real data analysis and simulation.

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Section: Minimizing Wape Vs Minimizing Squared Errorssupporting

confidence: 70%

On the estimation of the true demand in call centers with redials and reconnects

Ding

Koole²,

Mei

2015

European Journal of Operational Research

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“…This “error normalized” target function was explored, as was a least absolute deviations target function that is less sensitive to outlier observations. (49)…”

Section: Methodsmentioning

confidence: 99%

Common Enzymological Experiments Allow Free Energy Profile Determination

Toney

2013

Biochemistry

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The determination of a complete set of rate constants (free energy profiles; FEPs) for a complex kinetic mechanism is challenging. Enzymologists have devised a variety of informative steady-state kinetic experiments (e.g., Michaelis-Menten kinetics, viscosity dependence of kinetic parameters, KIEs, etc.) that each provide distinct information regarding a particular kinetic system. A simple method for combining steady-state experiments in a single analysis is presented here, which allows microscopic rate constants and intrinsic kinetic isotope effects to be determined. It is first shown that Michaelis-Menten kinetic parameters (kcat and KM values), kinetic isotope efffets, solvent viscosity effects, and intermediate partitioning measurements are sufficient to define the rate constants for a reversible uni-uni mechanism with an intermediate, EZ, between the ES and EP complexes. Global optimization provides the framework to combine the independent experimental measurements, and the search for rate constants is performed using algorithms implemented in the biochemical software COPASI. This method is applied to the determination of FEPs for both alanine racemase and triosephosphate isomerase. The FEPs obtained from global optimization agree with those in the literature, with important exceptions. The method opens the door to routine and large-scale determination of FEPs for enzymes.

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“…with mean µ and variance 2λ 2 , usually referred to as location and scale parameters, respectively, and typically denoted as L(µ, λ). If we apply this probability distribution to model the observation and motion noise, we obtain an L1-norm loss function to optimize…”

Section: L1-normmentioning

confidence: 99%

“…It may be noted that the absolute error estimates are of maximum likelihood and hence asymptotically efficient when the errors follow the Laplace distribution. The minimum sum of the absolute error regression has been studied in different contexts and has received different names: minimum sum of absolute errors (MSAE) [1], least sum of absolute errors (LSAE) [2], minimum absolute deviation errors (MAD) [3], least absolute deviation errors (LAD) [3], L1-norm, etc. It has been successfully used in different fields.…”

Section: Introductionmentioning

confidence: 99%

L1–L2-norm comparison in global localization of mobile robots

Moreno

Blanco

Muñoz

et al. 2011

Robotics and Autonomous Systems

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Abstract:The global localization methods deal with the estimation of the pose of a mobile robot assuming no prior state information about the pose and a complete a priori knowledge of the environment where the mobile robot is going to be localized. Most existing algorithms are based on the minimization of an L2-norm loss function. In spite of the extended use of the L2-norm, the use of the L1-norm offers some alternative advantages. The present work compares the L1-norm and the L2-norm with the same basic optimization mechanism to determine the advantages of each norm when applied to the global localization problem.The algorithm has been tested subject to different noise levels to demonstrate the accuracy, effectiveness, robustness, and computational efficiency of both L1-norm and L2-norm approaches.

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The minimum sum of absolute errors regression: a robust alternative to the least squares regression

Cited by 19 publications

References 44 publications

On the estimation of the true demand in call centers with redials and reconnects

On the estimation of the true demand in call centers with redials and reconnects

Common Enzymological Experiments Allow Free Energy Profile Determination

L1–L2-norm comparison in global localization of mobile robots

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