Quadratic Loss Research Articles

New Hybrid EWMA Charts for Efficient Process Dispersion Monitoring with Application in Automobile Industry

The EWMA charts are the well-known memory-type charts used for monitoring the small-to-intermediate shifts in the process parameters (location and/or dispersion). The hybrid EWMA (HEWMA) charts are enhanced version of the EWMA charts, which effectively monitor the process parameters. This paper aims to develop two new uppersided HEWMA charts for monitoring shifts in process variance, i.e., HEWMA1 and HEWMA2 charts. The design structures of the proposed HEWMA1 and HEWMA2 charts are based on the concept of integrating the features of two EWMA charts. The HEWMA1 and HEWMA2 charts plotting statistics are developed using one EWMA statistic as input for the other EWMA statistic. A Monte Carlo simulations method is used as a computational technique to determine the numerical results for the performance characteristics, such as average run length (ARL), median run length, and standard deviation run length (SDRL) for assessing the performance of the proposed HEWMA1 and HEWMA2 charts. In addition, to evaluate the overall performance of the proposed HEWMA1 and HEWMA2 charts, other numerical measures consisting of the extra quadratic loss (EQL), relative average run length (RARL), and performance comparison index (PCI) are also computed. The proposed HEWMA1 and HEWMA2 charts are compared to some existing charts, such as CH, CEWMA, HEWMA, AEWMA HHW1, HHW2, AIB-EWMA-I, and AIB-EWMA-II charts, on the basis aforementioned numerical measures. The comparison reveals that the proposed HEWMA1 and HEWMA2 charts achieve better detection ability against the existing charts. In the end, a real-life data application is also provided to enhance the implementation of the proposed HEWMA1 and HEWMA2 charts practically.

Assessing the Cost of Network Simplifications in Long-Term Hydrothermal Dispatch Planning Models

The sustainable utilization of hydro energy relies on accurate estimates of the opportunity cost of the water. This value is calculated through long-term hydrothermal dispatch problems (LTHDP), and the recent literature has raised awareness about the consequences of modeling simplifications in these problems. The inaccurate representation of Kirchhoff's voltage law under the premise of a DC power flow is an example. Under a non-linear AC model, however, the LTHDP becomes intractable, and the literature lacks an accurate evaluation method of different modeling alternatives. In this paper, we extend the state-of-the-art cost-assessment framework of network approximations for LTHDP and bring relevant and practical new insights. First, we increase the quality of the assessment by using an AC power flow to simulate and compare the performance of five policies based on different network approximations. Second, we find that the tightest network relaxation (based on semidefinite programming) is not the one exhibiting the best performance. Results show that the DC power flow with quadratic losses approximation exhibits the lowest expected cost and inconsistency gaps. Finally, its computational burden is lower than that exhibited by the semidefinite relaxation, whereas market distortions are significantly reduced in comparison to previously published benchmarks based on DC power flow.

Learning the Proximity Operator in Unfolded ADMM for Phase Retrieval

This paper considers the phase retrieval (PR) problem, which aims to reconstruct a signal from phaseless measurements such as magnitude or power spectrograms. PR is generally handled as a minimization problem involving a quadratic loss. Recent works have considered alternative discrepancy measures, such as the Bregman divergences, but it is still challenging to tailor the optimal loss for a given setting. In this paper we propose a novel strategy to automatically learn the optimal metric for PR. We unfold a recently introduced ADMM algorithm into a neural network, and we emphasize that the information about the loss used to formulate the PR problem is conveyed by the proximity operator involved in the ADMM updates. Therefore, we replace this proximity operator with trainable activation functions: learning these in a supervised setting is then equivalent to learning an optimal metric for PR. Experiments conducted with speech signals show that our approach outperforms the baseline ADMM, using a light and interpretable neural architecture.

Fully corrective gradient boosting with squared hinge: Fast learning rates and early stopping

In this paper, we propose an efficient boosting method with theoretical guarantees for binary classification. There are three key ingredients of the proposed boosting method: a fully corrective greedy (FCG) update, a differentiable squared hinge (also called truncated quadratic) loss function, and an efficient alternating direction method of multipliers (ADMM) solver. Compared with traditional boosting methods, on one hand, the FCG update accelerates the numerical convergence rate, and on the other hand, the squared hinge loss inherits the robustness of the hinge loss for classification and maintains the theoretical benefits of the square loss in regression. The ADMM solver with guaranteed fast convergence then provides an efficient implementation for the proposed boosting method. We conduct both theoretical analysis and numerical verification to show the outperformance of the proposed method. Theoretically, a fast learning rate of order O((m/logm)−1/2) is proved under certain standard assumptions, where m is the size of sample set. Numerically, a series of toy simulations and real data experiments are carried out to verify the developed theory.

Some results on quadratic credibility premium using the balanced loss function

PurposeThis paper generalizes the quadratic framework introduced by Le Courtois (2016) and Sumpf (2018), to obtain new credibility premiums in the balanced case, i.e. under the balanced squared error loss function. More precisely, the authors construct a quadratic credibility framework under the net quadratic loss function where premiums are estimated based on the values of past observations and of past squared observations under the parametric and the non-parametric approaches, this framework is useful for the practitioner who wants to explicitly take into account higher order (cross) moments of past data.Design/methodology/approachIn the actuarial field, credibility theory is an empirical model used to calculate the premium. One of the crucial tasks of the actuary in the insurance company is to design a tariff structure that will fairly distribute the burden of claims among insureds. In this work, the authors use the weighted balanced loss function (WBLF, henceforth) to obtain new credibility premiums, and WBLF is a generalized loss function introduced by Zellner (1994) (see Gupta and Berger (1994), pp. 371-390) which appears also in Dey et al. (1999) and Farsipour and Asgharzadhe (2004).FindingsThe authors declare that there is no conflict of interest and the funding information is not applicable.Research limitations/implicationsThis work is motivated by the following: quadratic credibility premium under the balanced loss function is useful for the practitioner who wants to explicitly take into account higher order (cross) moments and new effects such as the clustering effect to finding a premium more credible and more precise, which arranges both parts: the insurer and the insured. Also, it is easy to apply for parametric and non-parametric approaches. In addition, the formulas of the parametric (Poisson–gamma case) and the non-parametric approach are simple in form and may be used to find a more flexible premium in many special cases. On the other hand, this work neglects the semi-parametric approach because it is rarely used by practitioners.Practical implicationsThere are several examples of actuarial science (credibility).Originality/valueIn this paper, the authors used the WBLF and a quadratic adjustment to obtain new credibility premiums. More precisely, the authors construct a quadratic credibility framework under the net quadratic loss function where premiums are estimated based on the values of past observations and of past squared observations under the parametric and the non-parametric approaches, this framework is useful for the practitioner who wants to explicitly take into account higher order (cross) moments of past data.

On shrinkage estimators improving the positive part of James-Stein estimator

Abstract In this work, we study the estimation of the multivariate normal mean by different classes of shrinkage estimators. The risk associated with the quadratic loss function is used to compare two estimators. We start by considering a class of estimators that dominate the positive part of James-Stein estimator. Then, we treat estimators of polynomial form and prove if we increase the degree of the polynomial we can build a better estimator from the one previously constructed. Furthermore, we discuss the minimaxity property of the considered estimators.

A homogeneously weighted moving average control chart for monitoring time between events

AbstractIn high‐quality processes, non‐conforming events rarely occur, and the time between events (TBE) is more likely to follow a skewed distribution, such as gamma distribution. This paper proposes a gamma distribution‐based one‐sided homogeneously weighted moving average control chart for monitoring the TBE. The proposed control chart is known as the HWMA_TBE control chart. The HWMA_TBE control chart monitors the downward shifts in the process, that is, a decrease in inter‐arrival time that can lead to the process deterioration. The Monte Carlo simulation approach is used to compute specific performance indicators, such as average run length (), standard deviation run length , extra quadratic loss (), relative average run length (), and performance comparison index (). Based on these performance indicators, the HWMA_TBE control chart is compared to some competing control charts. The comparison suggests that the HWMA_TBE control chart is more efficient than the competing control charts. Moreover, this paper also investigates the robustness of the HWMA_TBE control chart, which indicates that the HWMA_TBE control chart is more robust than the competing control charts. In the end, two examples are provided, one with boring machine failure data and the other with breast cancer survival data, to evaluate the implementation of the HWMA_TBE control chart for practical situations.

A study on exponentiated Gompertz distribution under Bayesian discipline using informative priors

Abstract The exponentiated Gompertz (EGZ) distribution has been recently used in almost all areas of human endeavours, starting from modelling lifetime data to cancer treatment. Various applications and properties of the EGZ distribution are provided by Anis and De (2020). This paper explores the important properties of the EGZ distribution under Bayesian discipline using two informative priors: the Gamma Prior (GP) and the Inverse Levy Prior (ILP). This is done in the framework of five selected loss functions. The findings show that the two best loss functions are the Weighted Balance Loss Function (WBLF) and the Quadratic Loss Function (QLF). The usefulness of the model is illustrated by the use of real-life data in relation to simulated data. The empirical results of the comparison are presented through a graphical illustration of the posterior distributions.

Minimax Estimation Of The Parameter Of The Maxwell Distribution Under Quadratic Loss Function

This paper is concerned with the problem of finding the minimax estimators of the parameter θ of the Maxwell distribution (MW) for quadratic loss functions by applying the theorem of Lehmann [1950]. Through simulation study the performance of this method compared with the classical methods containing the Maximum Likelihood and moment Estimators with respect to Mean squared-errors (MSEs) .We reach to that the Minimax estimator with small positive values of c gives the best results, followed by the Maximum likelihood estimator

Semi- Minimax Estimations on the Exponential Distribution Under Symmetric and Asymmetric Loss Functions

In this paper the semi-minimax estimators of the scale parameter of the exponential distribution are presented by applying the theorem of Lehmann under symmetric (quadratic) loss function and asymmetric (entropy, mlinex , precautionary) loss functions .The results of comparison between these estimators are compared empirically using Monte-Carlo simulation study with respect to the mean square error(MSE) and the mean percentage error(MPE). In general, the results showed that the semi-minimax estimator under quadratic loss function is the best estimator by MSE and MPE for all sample sizes. We can notice that, when the values of the parameters β ,θ increasing the semi-minimax estimator under quadratic loss function is the best estimator by MSE while comparison by MPE showed that the semi-minimax estimator under mlinex loss function when the value of c positive is the best, but they both get worse as α ,θ increases. Also the results showed that when α, β together increase the semi-minimax estimator under entropy loss function is the best by MSE while by MPE the semi-minimax estimator under precautionary loss function is the best estimator.

Accelerating Federated Edge Learning

Transferring large models in federated learning (FL) networks is often hindered by clients’ limited bandwidth. We propose <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textsf {FedAA}$ </tex-math></inline-formula> , an FL algorithm which achieves fast convergence by exploiting the regularized Anderson acceleration (AA) on the global level. First, we demonstrate that FL can benefit from acceleration methods in numerical analysis. Second, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textsf {FedAA}$ </tex-math></inline-formula> improves the convergence rate for quadratic losses and improves the empirical performance for smooth and strongly convex objectives, compared to FedAvg, an FL algorithm using gradient descent (GD) local updates. Experimental results demonstrate that employing AA can significantly improve the performance of FedAvg, even when the objective is non-convex.

Bayesian estimation of the parameter of Maxwell-Mukherjee Islam distribution using assumptions of the Extended Jeffrey's, Inverse-Rayleigh and Inverse-Nakagami priors under the three loss functions

A three-parameter Maxwell-Mukherjee Islam distribution was proposed by applying Maxwell generalized family of distributions introduced by Ishaq and Abiodun [17]. The probability density and cumulative distribution functions of the proposed distribution were defined. The validity test was derived from its cumulative distribution function. The study aimed to obtain a Bayesian estimation of the scale parameter of Maxwell-Mukherjee Islam distribution by using assumptions of the Extended Jeffrey's (Uniform, Jeffrey's and Hartigan's), Inverse-Rayleigh and Inverse-Nakagami priors under the loss functions, namely, Squared Error Loss Function (SELF), Precautionary Loss Function (PLF) and Quadratic Loss Function (QLF), and their performances were compared. The posterior distribution under each prior and its corresponding loss functions was derived. The performance of the Bayesian estimation was illustrated from the basis of quantile function by using a simulation study and application to real life data set. For different sample sizes and parameter values, the QLF and SELF under Jeffrey's and Hartigan's priors produced the same estimates, bias and Mean Squared Error (MSE) just as we observed in their mathematical derivatives. Similarly, the SELF, PLF and QLF under Inverse-Rayleigh and Inverse-Nakagami priors provided the same performance when some parameter values are equal. For some parameter values, the QLF under Inverse-Nakagami and Inverse-Rayleigh priors produced the least values of MSE. In the application to real life data set, the QLF and SELF under Jeffrey's and Hartigan's priors; the SELF, PLF and QLF under Inverse-Rayleigh and Inverse-Nakagami priors provided similar results as observed in the simulation study. Therefore, the study concluded that the QLF under Inverse-Rayleigh and Inverse-Nakagami priors could effectively be used in the estimation of scale parameter of Maxwell-Mukherjee Islam distribution using Bayesian approach.

Bayesian Approaches for Poisson Distribution Parameter Estimation

The Bayesian approach, a non-classical estimation technique, is very widely used in statistical inference for real world situations. The parameter is considered to be a random variable, and knowledge of the prior distribution is used to update the parameter estimation. Herein, two Bayesian approaches for Poisson parameter estimation by deriving the posterior distribution under the squared error loss or quadratic loss functions are proposed. Their performances were compared with frequentist (maximum likelihood estimator) and Empirical Bayes approaches through Monte Carlo simulations. The mean square error was used as the test criterion for comparing the methods for point estimation; the smallest value indicates the best performing method with the estimated parameter value closest to the true parameter value. Coverage Probabilities (CPs) and average lengths (ALs) were obtained to evaluate the performances of the methods for constructing confidence intervals. The results reveal that the Bayesian approaches were excellent for point estimation when the true parameter value was small (0.5, 1 and 2). In the credible interval comparison, these methods obtained CP values close to the nominal 0.95 confidence level and the smallest ALs for large sample sizes (50 and 100), when the true parameter value was small (0.5, 1 and 2). Doi: 10.28991/esj-2021-01310 Full Text: PDF

Location charts based on concomitants of ranked set samples from Morgenstern family

This paper surveys the location chart based on concomitants of ranked set sampling (RSS), a triangular modification of RSS, which is known as maximum ranked set sampling with unequal sample (MRSSU) and the extreme ranked set sampling (ERSS) from the Farlie–Gumbel–Morgenstern bivariate family. We also remarked both heavy-tailed symmetric and skewed distributions throughout the paper. For the performance evaluation of the charts, extensive utilization of the Monte Carlo simulations is carried out using average run length (ARL), extra quadratic loss (EQL), relative ARL (RARL), and performance comparison index (PCI) measures, and finally, conclusion ends this research.

Monotone persuasion

We explore Bayesian persuasion environments in which the state and action spaces are ordered, allowing for complementarity between actions and types. Building on the literature on monotone comparative statics, we identify conditions that guarantee that these are optimal among all (possibly non-monotone) signal structures. When the action space is binary, supermodularity of the sender's and receiver's preferences suffices for the optimal signal to have a monotone structure. With a continuum of actions, the conditions are more intriguing. We identify a novel single-crossing condition using a virtual utility representation of the sender's payoff. We also provide a technique to compute the optimal monotone signal structure, even when this monotonicity is due to an exogenous constraint. Applications are given to quadratic loss functions with biases, capacity constraints, and credit ratings.

Fractionation of carbohydrates and proteins and in vitro rumen kinetics of corn silage under various storage durations

The experiment evaluated the effects on the chemical composition (fermentation, kinetic parameters, and protein and carbohydrate fractions) of corn silage after various storage durations (45, 90, 180, and 360 days). Experimental mini silos of the corn plants were made and opened after various storage periods. The experimental design was completely randomized with four treatments and four replications per treatment. Variables such as pH, lactic acid and acetic acid showed a quadratic effect, whereas effluent and gas losses increased linearly with prolonged storage. Proteolysis was observed with an increase in storage, resulting in a rise in ammonia-N, soluble N, and non-protein N concentration and reduction in true protein. The soluble carbohydrate fractions were reduced, and digestible and indigestible fibre were increased. For the kinetic degradation parameters of the silages obtained through in vitro gas methodology, the highest fermentation rate occurred in the first 12 hours of incubation, and the highest volume of gas produced within 96 hours was obtained for silages with shorter storage (45 days). The increase in storage resulted in greater losses and lower ruminal degradability in vitro, causing a decrease in protein quality and nutritional value.

Bayesian inference of bivariate Weibull geometric model based on LINEX and quadratic loss functions

Bayesian inference of bivariate Weibull geometric model based on LINEX and quadratic loss functions

Convergence rates of support vector machines regression for functional data

Support vector machines regression (SVMR) is an important part of statistical learning theory. The main difference between SVMR and the classical least squares regression (LSR) is that SVMR uses the ϵ-insensitive loss rather than quadratic loss to measure the empirical error. In this paper, we consider SVMR method in the field of functional data analysis under the framework of reproducing kernel Hilbert spaces. The main tool used in our theoretical analysis is the concentration inequalities for suprema of some appropriate empirical processes. As a result, we establish explicit convergence rates of the prediction risk for SVMR, which coincide with the minimax lower bound obtained recently in literature for LSR.

Smoothing quantile regression for a distributed system

Quantile regression has become a popular alternative to least squares regression for providing a comprehensive description of the response distribution, and robustness against heavy-tailed error distributions. However, the nonsmooth quantile loss poses new challenges to distributed estimation in both computation and theoretical development. To address this challenge, we use a convolution-type smoothing approach and its Taylor expression to transform the nondifferentiable quantile loss function into a convex quadratic loss function, which admits a fast and scalable algorithm to perform optimization under massive and high-dimensional data. The proposed distributed estimators are both computationally and communication efficient. Moreover, only the gradient information is communicated at each iteration. Theoretically, we show that, after a certain number of iterations, the resulting estimator is statistically as efficient as the global estimator without any restriction on the number of machines. Both simulations and data analysis are conducted to illustrate the finite sample performance of the proposed methods.

An Efficient Angle-based Universum Least Squares Twin Support Vector Machine for Classification

Universum-based support vector machine incorporates prior information about the distribution of data in training of the classifier. This leads to better generalization performance but with increased computation cost. Various twin hyperplane-based models are proposed to reduce the computation cost of universum-based algorithms. In this work, we present an efficient angle-based universum least squares twin support vector machine (AULSTSVM) for classification. This is a novel approach of incorporating universum in the formulation of least squares-based twin SVM model. First, the proposed AULSTSVM constructs a universum hyperplane, which is proximal to universum data points. Then, the classifying hyperplane is constructed by minimizing the angle with the universum hyperplane. This gives prior information about data distribution to the classifier. In addition to the quadratic loss, we introduce linear loss in the optimization problem of the proposed AULSTSVM, which leads to lesser computation cost of the model. Numerical experiments are performed on several benchmark synthetic, real-world, and large-scale datasets. The results show that proposed AULSTSVM performs better than existing algorithms w.r.t. generalization performance as well as computation time. Moreover, an application to Alzheimer’s disease is presented, where AULSTSVM obtains accuracy of 95% for classification of healthy and Alzheimers subjects. The results imply that the proposed AULSTSVM is a better alternative for classification of large-scale datasets and biomedical applications.