Min-max Estimation Research Articles

Psr Model with Intelligent Min-Max Estimation Deep Learning (Imin-Maxedl) for Public Service Evaluation of Sports Venues

Sports venues play a pivotal role in fostering athletic excellence, community engagement, and social cohesion. From local recreation centers to iconic stadiums hosting international events, these facilities serve as hubs of activity, bringing together athletes, spectators, and enthusiasts from diverse backgrounds. The evaluation of sports venues is crucial for ensuring optimal functionality, service quality, and reputation within the community.
 The Public Service Evaluation of Sports Venues, integrating the PSR (Psychological Skills Model) model, provides a comprehensive framework for assessing the effectiveness and quality of sports facilities. This paper presents a comprehensive framework for the public service evaluation of sports venues, integrating the PSR (Psychological Skills Model) model with Intelligent Min-Max Estimation Deep Learning (Imin-maxEDL). The PSR model serves as the foundation for assessing the effectiveness and quality of sports facilities across multiple dimensions, including performance, service quality, and reputation. Meanwhile, Imin-maxEDL employs advanced deep learning techniques to optimize the evaluation process, leveraging large datasets to extract nuanced insights and predictive analytics. Through simulated experiments and empirical validations, the efficacy of the proposed framework is assessed, demonstrating significant improvements in accuracy, efficiency, and predictive capabilities compared to traditional evaluation methods. the integration of Imin-maxEDL resulted in a 25% increase in accuracy in predicting service quality ratings, while also reducing evaluation time by 30%. Additionally, the PSR model combined with Imin-maxEDL achieved a 20% improvement in reputation assessment precision, leading to more informed decision-making by stakeholders.

Hygiene promotion might be better than serological screening to deal with Cytomegalovirus infection during pregnancy: a methodological appraisal and decision analysis

BackgroundCytomegalovirus infection is the most frequent viral congenital infection, with possible consequences such as deafness, or psychomotor retardation. In 2016, the French High Council of Public Health was mandated to update recommendations regarding prevention of cytomegalovirus infection in pregnant women. We summarize a critical appraisal of knowledge and deterministic decision analysis comparing the current no-screening situation to serological screening during pregnancy, and to hygiene promotion.MethodsScreening was defined as systematic serological testing, during the first trimester, with repeated tests as needed, to all pregnant women. Outcomes were: 1) severe sequela: intellectual deficiency with IQ ≤ 50 or hearing impairment < 70 dB or sight impairment (≤ 3/10 at best eye); 2) moderate sequela: any level of intellectual, hearing or sight deficiency; and 3) death or termination of pregnancy. We simulated the one-year course of cytomegalovirus infection in a cohort of 800,000 pregnant women. We developed a deterministic decision model, using best and min-max estimates, extracted from systematic reviews or original studies.ResultsRelevant data were scarce or imprecise. We estimated that 4352 maternal primary infections would result in 1741 foetal infections, and an unknown number of maternal reinfections would result in 1699 foetal infections. There would be 788 cytomegalovirus-related consequences, including 316 foetal deaths or terminations of pregnancy, and 424 moderate and 48 severe sequelae. Screening would result in a 1.66-fold increase of poor outcomes, mostly related to a 2.93-fold increase in deaths and terminations of pregnancy, not compensated by the decrease in severe symptomatic newborns. The promotion of hygiene would result in a 0.75-fold decrease of poor outcomes, related to both a decrease in severe sequelae among symptomatic newborns (RR = 0.75; min-max: 1.00–0.68), and in deaths and terminations of pregnancy (RR = 0.75; min-max: 0.97–0.68).ConclusionsPrevention of cytomegalovirus infection during pregnancy should promote hygiene; serological screening should not be recommended.

On the min–max estimation of mean daily temperatures

Modern data analyses of hourly temperature records reveal the existence, in addition to the daily cycle, of multiple forcings of different frequencies. As a result the routine approach of estimating daily local mean temperature directly from the average of the minimum and maximum is heavily compromised. A simple dynamical model subjected to two periodic forcings of different frequencies, amplitudes and phases is solved analytically and shown to induce substantial deviations from the min–max method that depend crucially on the values of the parameters involved.

Chemical and isotopic signatures of hot springs from east-central Sonora State, Mexico: a new prospection survey of promissory low-to-medium temperature geothermal systems

A promissory low-to-medium temperature geothermal system located in Sonora (Mexico) has been studied. In the present work, a detailed geochemical survey was carried out to understand the hydrogeochemical signatures of hot spring waters. A field work campaign was conducted for collecting water samples from twelve hot springs placed in four major zones (NW, NE, C, and S). The collected samples were analysed by chemical and isotopic methods for determining their chemical (major and trace elements) and isotopic (18O/16O and D/H) compositions. Using geochemometric analyses of the fluid composition and fractionation, depletion and enrichment processes exhibited by major and trace elements were analysed.&#x0D; Hydrogeochemical classification was used to indicate the presence of sodium-sulphate (Na-SO4) waters in the North (NW and NE) and South hydrothermal zones; whereas calcium-magnesium-bicarbonate (Ca-Mg-HCO3) waters were identified for the Central zone. Some hot spring waters located in the NE zone were also typified as sodium-bicarbonate (Na-HCO3). In relation to the isotopic signatures of 18O/16O and D/H, four water samples from NE and C zones lie near to the global meteoric water line; whereas the remaining eight samples showed a shift for both oxygen and deuterium isotopes. A mixing line with a small shift of δ18O was identified and used as a proxy to discriminate waters with different isotopic signatures.&#x0D; After applying a geochemometric outliers detection/rejection and an iterative ANOVA statistical test, the mean temperature inferred from the most reliable solute geothermometers was 149±40 °C, which suggests to be considered as the minimum value of the reservoir temperature. As most of the hot spring waters fall outside of the full equilibrium curve, the original reservoir conditions were corrected by using a mixing conductive model, which predicted a deep equilibrium temperature of 210±11 °C. As this temperature is considerably higher than the mean temperature inferred from the geothermometers, it was suggested as an optimistic maximum reservoir temperature of the Sonora geothermal system.&#x0D; Using 150 °C and 200 °C as rounded-off reservoir temperatures (or min-max estimates), geochemical equilibria modelling based on fluid-mineral stability diagrams was carried out. An equilibrium process among local hydrothermal waters and albite-potassium feldespar and muscovite-prehnite-laumontite mineral assemblages was found. These minerals were proposed as representative mineral assemblages of low-grade metamorphism, which seems to indicate that the geothermal fluid equilibria were probably reached within the intermediate to acidic volcanic rocks from the Tarahumara Formation.

Loop Feedback Maximization for Channel Estimation in MIMO Communication

Background: Signal estimation and its performance have always remained a challenge for wireless communication society. To achieve noise immunity, the conventional recursive least squares estimation needs information of the noise measurements of the filtered process. A new estimation approach has been proposed that does not take knowledge of the noise statistics. Statistical Methods: A new min-max channel estimation approach based on state stabilization is proposed to achieve the objective of noise mitigation and higher performance in MIMO systems, using time variant interference modelling. The approach proposed has been simulated using the MATLAB environment with random input data. Findings: The performance of the Bit Error Rate (BER) over the specific range of Signal to Noise ratio for the existing Recursive Least Squares estimation and proposed a Min-Max estimation approach of different noise densities and fading factors. Conclusion: The results obtained indicate that the bit error rate of Recursive Least Squares estimation is more when compared with the Min-Max approach. Therefore, it is concluded that the proposed Min-Max estimation approach is more efficient when compared with the Recursive Least Squares estimation.

A Semidefinite Programming Approach to Min-max Estimation of the Common Part of Acoustic Feedback Paths in Hearing Aids

The convergence speed and the computational complexity of adaptive feedback cancellation algorithms both depend on the number of adaptive parameters used to model the acoustic feedback paths. To reduce the number of adaptive parameters it has been proposed to decompose the acoustic feedback paths as the convolution of a time-invariant common part and time-varying variable parts. Instead of estimating all parameters of the common and variable parts by minimizing the misalignment using a least-squares cost function, in this paper we propose to formulate the parameter estimation problem as a min-max optimization problem aiming to maximize the maximum stable gain (MSG). We formulate the min-max optimization problem as a semidefinite program and use a constraint based on Lyapunov theory to guarantee stability of the estimated common pole-zero filter. Experimental results using measured acoustic feedback paths show that the proposed min-max optimization outperforms least-squares optimization in terms of the MSG. Furthermore, the results indicate that the proposed common part decomposition is able to increase the MSG and reduce the number of variable part parameters even for unknown feedback paths that were not included in the optimization. Simulation results using an adaptive feedback cancellation algorithm based on the prediction-error-method show that the convergence speed can be increased by using the proposed feedback path decomposition.

General properties of solutions to inhomogeneous Black–Scholes equations with discontinuous maturity payoffs

We provide representations of solutions to terminal value problems of inhomogeneous Black–Scholes equations and study such general properties as min–max estimates, gradient estimates, monotonicity and convexity of the solutions with respect to the stock price variable, which are important for financial security pricing. In particular, we focus on finding representation of the gradient (with respect to the stock price variable) of solutions to the terminal value problems with discontinuous terminal payoffs or inhomogeneous terms. Such terminal value problems are often encountered in pricing problems of compound-like options such as Bermudan options or defaultable bonds with discrete default barrier, default intensity and endogenous default recovery. Our results can be used in pricing real defaultable bonds under consideration of existence of discrete coupons or taxes on coupons.

Volume of minimal hypersurfaces in manifolds with nonnegative Ricci curvature

Abstract We establish a min-max estimate on the volume width of a closed Riemannian manifold with nonnegative Ricci curvature. More precisely, we show that every closed Riemannian manifold with nonnegative Ricci curvature admits a PL Morse function whose level set volume is bounded in terms of the volume of the manifold. As a consequence of this sweep-out estimate, there exists an embedded, closed (possibly singular) minimal hypersurface whose volume is bounded in terms of the volume of the manifold.

General Properties of Solutions to Inhomogeneous Black-Scholes Equations with Discontinuous Maturity Payoffs and Application

We provide representations of solutions to terminal value problems of inhomogeneous Black-Scholes equations and studied such general properties as min-max estimates, gradient estimates, monotonicity and convexity of the solutions with respect to the stock price variable, which are important for financial security pricing. In particular, we focus on finding representation of the gradient (with respect to the stock price variable) of solutions to the terminal value problems with discontinuous terminal payoffs or inhomogeneous terms. Such terminal value problems are often encountered in pricing problems of compound-like options such as Bermudan options or defaultable bonds with discrete default barrier, default intensity and endogenous default recovery. Our results are applied in pricing defaultable discrete coupon bonds.

Robust linear least squares regression

We consider the problem of robustly predicting as well as the best linear combination of d given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. For the ridge estimator and the ordinary least squares estimator, and their variants, we provide new risk bounds of order d/n without logarithmic factor unlike some standard results, where n is the size of the training data. We also provide a new estimator with better deviations in the presence of heavy-tailed noise. It is based on truncating differences of losses in a min–max framework and satisfies a d/n risk bound both in expectation and in deviations. The key common surprising factor of these results is the absence of exponential moment condition on the output distribution while achieving exponential deviations. All risk bounds are obtained through a PAC-Bayesian analysis on truncated differences of losses. Experimental results strongly back up our truncated min–max estimator.

Parameter Estimation of Differential-Algebraic Systems Using Accessible Measurement

Hybrid differential evolution is applied to estimate the kinetic parameters of batch polymerization described by differential-algebraic equations. The dynamic behavior of the system consisted of the concentrations of the first and second initiators, the monomer conversion, the zeroth, first and second moments of dead polymer distributions and the total concentration of live polymer. The moments of dead polymer distributions and the total concentration of live polymer were in general difficult to measure in a real process. In this study, we considered that the estimation criterion consisted of some measurable data such as the concentrations of the first and second initiators, the monomer conversion, and the degree of polymerization and polydispersity. We used the worst observed error for all experiments as an objective function so that the parameter estimation problem becomes a min-max estimation problem. Several techniques were also employed to handle the estimation of kinetic parameters for comparison. Hybrid differential evolution could use five individuals to obtain a more satisfactory solution.

The Size of the Membership-Set in a Probabilistic Framework

In this paper, we study the size of the membership-set for system identification in a probabilistic framework. Assuming that the regressors are persistently exciting and the measurement noise is a sequence of independent, identically distributed bounded randoln variables, tight lower and upper non-asymptotic probability bounds on the membership-set diameter are obtained. These bounds are used in the computation of the confidence intervals for interpolatory estimators including the Chebyshev center, the analytic center, the constrained least-squares estimator (projection estimator), and the minmax estimator.

Optimal control in unobservable integral Volterra systems

This paper presents solution of the optimal linear-quadratic controller problem for unobservable integral Volterra systems with continuous/discontinuous states under deterministic uncertainties, over continuous/discontinuous observations. Due to the separation principle for integral systems, the initial continuous problem is split into the optimal minmax filtering problem for integral Volterra systems with deterministic uncertainties over continuous/discontinuous observations and the optimal linear-quadratic control (regulator) problem for observable deterministic integral Volterra systems with continuous/discontinuous states. As a result, the system of the optimal controller equations are obtained, including the linear equation for the optimally controlled minmax estimate and two Riccati equations for its ellipsoid matrix (optimal gain matrix of the filter) and the optimal regulator gain matrix. Then, in the discontinuous problems, the equation for the optimal controller and the equations for the optimal filter and regulator gain matrices are obtained using the filtering procedure for deriving the filtering equations over discontinuous observations proceeding from the known filtering equations over continuous ones and the dual results in the optimal control problem for integral systems. The technical example illustrating application of the obtained results is finally given.

Kinetic parameter estimation of an ethanol fermentation by hybrid differential evolution

Hybrid differential evolution is applied to estimate the kinetic model parameters of batch fermentation for ethanol and glycerol production usingSaccharomyces diastaticus LORRE 316. In this study, we consider the worst observed error for all experiments as an objective function so that the parameter estimation problem becomes the min-max estimation problem. Several numerical methods have employed to solve the min-max estimation problem for comparison. The hybrid differential evolution can use a small population size to obtain a more satisfied solution as compared from these computations.

Minmax estimation theory for solutions of abstract parabolic equations

Minmax estimation theory for solutions of abstract parabolic equations

Minmax estimation of functionals of solutions of initial-boundary-value problems for parabolic equations

Minmax estimation of functionals of solutions of initial-boundary-value problems for parabolic equations

An Extension of Estimation Theory on Unknown but Bounded Uncertainty

For a practical estimation problem with unknown but bounded uncertainty, there almost always exists an interval, in which any value can't be determined to be an upper bound or not. This causes difficulty in taking a suitable value as an upper bound, for a greater upper bound leads to a poorer estimation result, while a smaller value is less reliable to be an upper bound. This problem is considered in this paper. Firstly a new min-max estimation criterion is advanced, with which each component of the estimated vector is independently estimated .Then a concept of indefinite upper bound is introduced into unknown but bounded error description and an extension of the new criterion is made to adapt it to the new situation. On the base of this extended criterion an estimation algorithm is proposed to determine a suitable indefinite upper bound and corresponding estimate for each component of the estimated vector. This new approach is applied to study a practical example of China's national economy. The results of this application are satisfactory.

Fuzzy linear regression analysis

In this paper, a generalized fuzzy linear regression model Y = β 1 X 1 + β 2 X 2 + … + β m X m where all β j and X j ( j = 1, …, m) are fuzzy is considered. A new principle of estimating parameters, which is called Minmax principle, is introduced via the possibility distribution. The Minmax estimation of the regression model parameters and the LS estimation of the approximation model parameters are discussed. Procedures of estimating these parameters are given.

Min-Max Bias Robust Regression

This paper considers the problem of minimizing the maximum asymptotic bias of regression estimates over $\varepsilon$-contamination neighborhoods for the joint distribution of the response and carriers. Two classes of estimates are treated: (i) $M$-estimates with bounded function $\rho$ applied to the scaled residuals, using a very general class of scale estimates, and (ii) bounded influence function type generalized $M$-estimates. Estimates in the first class are obtained as the solution of a minimization problem, while estimates in the second class are specified by an estimating equation. The first class of $M$-estimates is sufficiently general to include both Huber Proposal 2 simultaneous estimates of regression coefficients and residuals scale, and Rousseeuw-Yohai $S$-estimates of regression. It is shown than an $S$-estimate based on a jump-function type $\rho$ solves the min-max bias problem for the class of $M$-estimates with very general scale. This estimate is obtained by the minimization of the $\alpha$-quantile of the squared residuals, where $\alpha = \alpha(\varepsilon)$ depends on the fraction of contamination $\varepsilon$. When $\varepsilon \rightarrow 0.5, \alpha(\varepsilon) \rightarrow 0.5$ and the min-max estimator approaches the least median of squared residuals estimator introduced by Rousseeuw. For the bounded influence class of $GM$-estimates, it is shown the sign type nonlinearity yields the min-max estimate. This estimate coincides with the minimum gross-error sensitivity $GM$-estimate. For $p = 1$, the optimal $GM$-estimate is optimal among the class of all equivariant regression estimates. The min-max $S$-estimator has a breakdown point which is independent of the number of carriers $p$ and tends to 0.5 as $\varepsilon$ increases to 0.5, but has a slow rate of convergence. The min-max $GM$-estimate has the usual rate of convergence, but a breakdown point which decreases to zero with increasing $p$. Finally, we compare the min-max biases for both types of estimates, for the case where the nominal model is multivariate normal.

Identification and prediction propagation of uncertainty in models with bounded noise

Abstract The identification of measurement, parametric, and structural model uncertainty is considered for models from observations with bounded noise. A min-max estimate for the upper bound of the structural model uncertainty is presented. The propa- gation of the parametric and structural model uncertainty, as a result of the obser- vation uncertainty bounds to the model prediction error, is examined. A simple water quality model is used to illustrate the different steps.