On Smoothed MWSD Estimation of Mixing Proportion

The problem considered in the present paper is estimation of mixing proportions of mixtures of two (known) distributions by using the minimum weighted square distance (MWSD) method. The two classes of smoothed and unsmoothed parametric estimators of mixing proportion proposed in a sense of MWSD due to Wolfowitz(1953) in a mixture model F(x)=p (x)+(1-p) (x) based on three independent and identically distributed random samples of sizes n and , =1,2 from the mixture and two component populations. Comparisons are made based on their derived mean square errors (MSE). The superiority of smoothed estimator over unsmoothed one is established theoretically and also conducting Monte-Carlo study in sense of minimum mean square error criterion. Large sample properties such as rates of a.s. convergence and asymptotic normality of these estimators are also established. The results thus established here are completely new in the literature.

On a new generalized lindley distribution: Properties, estimation and applications

In this study, an extension of the generalized Lindley distribution using the Marshall-Olkin method and its own sub-models is presented. This new model for modelling survival and lifetime data is flexible. Several statistical properties and characterizations of the subject distribution along with its reliability analysis are presented. Statistical inference for the new family such as the Maximum likelihood estimators and the asymptotic variance covariance matrix of the unknown parameters are discussed. A simulation study is considered to compare the efficiency of the different estimators based on mean square error criterion. Finally, a real data set is analyzed to show the flexibility of our proposed model compared with the fit attained by some other competitive distributions.

The Autoregressive Moving Average with Exogenous Excitation Model for Acoustic Scattering from Underwater Objects

This study aims to identify and predict objects underwater using the autoregressive moving average with exogenous excitation (ARMX) model in such a way that the outcome of the model is similar to actual measurements. It is used for parameter estimation. This model is validated by comparing results in actual model with ARMX model, autoregressive with an exogenous variables, and Box Jenkins (BJ) model. The results are analyzed in frequency and time domain by using mean square error criterion. Initial results show that ARMX predicts the acoustic scattering response with an accuracy of 96%, while ARX provides an accuracy of 78%, and BJ model poorly estimates the signal with an accuracy of 35%. ARMX also provides higher accuracy of detection by 7-8% as compared to the existing techniques.

Training Load Responses Modelling in Elite Sports: How to Deal with Generalisation?

This study aims to provide a transferable methodology in the context of sport performance modelling, with a special focus to the generalisation of models. Data were collected from seven elite Short track speed skaters over a three months training period. In order to account for training load accumulation over sessions, cumulative responses to training were modelled by impulse, serial and bi-exponential responses functions. The variable dose-response (DR) model was compared to elastic net (ENET), principal component regression (PCR) and random forest (RF) models, while using cross-validation within a time-series framework. ENET, PCR and RF models were fitted either individually (MI) or on the whole group of athletes (MG). Root mean square error criterion was used to assess performances of models. ENET and PCR models provided a significant greater generalisation ability than the DR model (p = 0.012, p < 0.001, p = 0.005 and p < 0.001 for ENETI, ENETG, PCRI and PCRG, respectively). Only ENETI, ENETG and RFI were significantly more accurate in prediction than DR (p = 0.020, p < 0.001 and p = 0.043, respectively). In conclusion, ENET achieved greater generalisation and predictive accuracy performances. Thus, building and evaluating models within a generalisation enhancing procedure is a prerequisite for any predictive modelling.

Post-combustion artificial neural network modeling of nickel-producing multiple hearth furnace

In a nickel-producing multiple hearth furnace, there is a problem associated to the automatic operation of the temperature control loops in two of the hearths, since the same flow of air is split into two branches. A neural model of the post-combustion sub-process is built and served to increase the process efficiency of the industrial furnace. Data was taken for a three-months operating time period to identify the main variables characterizing the process and a model of multilayer perceptron type is built. For the validation of this model, process data from a four-months operating time period in 2018 was used and prediction errors based on a measure of closeness in terms of a mean square error criterion measured through its weights for the temperature of two of the hearths (four and six) versus the air flow to these hearths. Based on a rigorous testing and analysis of the process, the model is capable of predicting the temperature of hearth four and six with errors of 0.6 and 0.3 °C, respectively. In addition, the emissions by high concentration of carbon monoxide in the exhaust gases are reduced, thus contributing to the health of the ecosystem.

THE PREDICTIVE PERFORMANCE EVALUATION AND NUMERICAL EXAMPLE STUDY FOR THE PRINCIPAL COMPONENT TWO-PARAMETERS ESTIMATOR

In this paper, detailed comparisons are given between those estimators that can be derived from the principal component two-parameter estimator such as the ordinary least squares estimator, the principal components regression estimator, the ridge regression estimator, the Liu estimator, the r-k estimator and the r-d estimator by the prediction mean square error criterion. In addition, conditions for the superiority of the principal component two-parameter estimator over the others are obtained. Furthermore, a numerical example study is conducted to compare these estimators under the prediction mean squared error criterion.

Performance analysis of global local mean square error criterion of stochastic linearization for nonlinear oscillator

The paper presents a performance analysis of global-local mean square error criterion of stochastic linearization for some nonlinear oscillators. This criterion of stochastic linearization for nonlinear oscillators bases on dual conception to the local mean square error criterion (LOMSEC). The algorithm is generally built to multi degree of freedom (MDOF) nonlinear oscillators. Then, the performance analysis is carried out for two applications which comprise a rolling ship oscillation and two degree of freedom one. The improvement on accuracy of the proposed criterion has been shown in comparison with the conventional Gaussian equivalent linearization (GEL).

A FULL DUAL MEAN SQUARE ERROR CRITERION FOR THE EQUIVALENT LINEARIZATION

Among approximate methods, the method of equivalent linearization proposed by N. Krylov and N. Bogoliubov and extended by Caughey has remained an effective tool for both deterministic and stochastic problems. The idea of the method is based on the replacement of a nonlinear oscillator by a linear one under the same excitation. The standard way of implementing this method is that the coefficients of linearization are to be found from a criterion of equivalence. When the difference between the nonlinear function and equivalent linear one is significant the replacement leads to unaccepted errors. In order to reduce the errors one may apply the dual approach. One of significant advantages of the dual conception is its consideration of two different aspects of a problem in question allowing the investigation to be more appropriate. In this paper a special case of the weighted full dual mean square error criterion is introduced and investigated in detail. Numerical results are carried out to show that this special full dual mean square error criterion can give more accurate approximate solutions for both deterministic and random nonlinear systems.

Optimizing Signal De-Noising Algorithm for Acoustic Emission Leakage of Wavelet

Traditional wavelet denoising method cannot eliminate complex high-pressure pipe signals effectively. In the updated wavelet adaptive algorithm, this thesis defines the constraints in order to reconstruct the signals accurately. According to the minimum mean square error criterion, the results predict the weight coefficient and get the optimal linear predictive value. Adopting the improved algorithm under the same condition, this thesis concluded that Db6 increased the complexity of wavelet algorithm by 50% by comparative experiments. It will be more conducive to the realization of hardware and the feasibility of real-time denoising. Dual adaptive wavelet denoising method improved SNR by 50%. This denoising method will play a key role in the detection rate of high-pressure pipe in the online leakage detection system.