Classical Estimation Approaches Research Articles

Analyzing Burr-X competing risk model using adaptive progressive Type-II censored binomial removal data with application to electrodes and electronics

The aim of this paper is to investigate the Burr-X competing risks model in the context of adaptive progressively Type-II censored samples. In this scenario, the removal pattern is assumed to be a random variable that follows the binomial distribution, which is a more realistic assumption compared to assuming a fixed removal pattern. In this study, we explore both classical and Bayesian estimation approaches to estimate the parameters of the Burr-X competing risks model, as well as the reliability parameter and the parameter of the binomial distribution. The interval ranges of different parameters are determined by utilizing the asymptotic normality of the maximum likelihood estimators. Furthermore, the Bayes credible intervals are calculated by sampling from the joint posterior distribution using the Markov Chain Monte Carlo procedure. To assess the efficiency of the acquired estimators, a comprehensive simulation study that considered various types of experimental designs is conducted. Finally, two applications are considered by analyzing data sets of electrodes and electronics.

Parameter-Free State Estimation Based on Kalman Filter with Attention Learning for GPS Tracking in Autonomous Driving System.

GPS-based maneuvering target localization and tracking is a crucial aspect of autonomous driving and is widely used in navigation, transportation, autonomous vehicles, and other fields.The classical tracking approach employs a Kalman filter with precise system parameters to estimate the state. However, it is difficult to model their uncertainty because of the complex motion of maneuvering targets and the unknown sensor characteristics. Furthermore, GPS data often involve unknown color noise, making it challenging to obtain accurate system parameters, which can degrade the performance of the classical methods. To address these issues, we present a state estimation method based on the Kalman filter that does not require predefined parameters but instead uses attention learning. We use a transformer encoder with a long short-term memory (LSTM) network to extract dynamic characteristics, and estimate the system model parameters online using the expectation maximization (EM) algorithm, based on the output of the attention learning module. Finally, the Kalman filter computes the dynamic state estimates using the parameters of the learned system, dynamics, and measurement characteristics. Based on GPS simulation data and the Geolife Beijing vehicle GPS trajectory dataset, the experimental results demonstrated that our method outperformed classical and pure model-free network estimation approaches in estimation accuracy, providing an effective solution for practical maneuvering-target tracking applications.

An empirical analysis of economic growth in countries exposed to coastal risks: Implications for their ecosystems

Using a novel database on countries exposed to coastal risks (CR), this paper estimates an augmented neoclassical growth model that encompasses eight other new growth models. To account for uncertainty related to the number of models and choice of growth determinant proxies, we use a Bayesian averaging of classical estimates (BACE) approach. A preliminary examination of the data reveals that a country that faces coastal risks is likely to be a former British colony characterized by a common law legal framework, a parliamentary political system, a high degree of international trade openness, little language and ethnic fractionalization, a low level of public sector corruption, and a high rate of fertility. The BACE-based model selection procedure shows that, in CR countries, the growth determinant proxies typically used in the neoclassical, macroeconomic policy, natural resources, and institutions theories are significantly correlated with growth. These results suggest two implications related to these countries’ coastal ecosystems. First, because they are heavily dependent on natural resources and have high fertility rates, these countries might seek short-term economic gains at the expense of deterioration in their ecosystems. Second, these countries’ good institutions and low levels of ethnic division might be conducive to sustainable management of these ecosystems.

Statistical Inference of the Beta Binomial Exponential 2 Distribution with Application to Environmental Data

A new four-parameter lifetime distribution called the beta binomial exponential 2 (BBE2) distribution is proposed. Some mathematical features, including quantile function, moments, generating function and characteristic function, of the BBE2 distribution, are computed. When the life test is truncated at a predetermined time, acceptance sampling plans (ASP) are constructed for the BBE2 distribution. The truncation time is supposed to represent the median lifetime of the BBE2 distribution with predetermined factors for the smallest sample size required to guarantee that the prescribed life test is achieved at a given consumer’s risk. Some numerical results for a given consumer’s risk, BBE2 distribution parameters and truncation time are derived. Classical (maximum likelihood and maximum product of spacing estimation methods) and Bayesian estimation approaches are utilized to estimate the model parameters. The performance of the model parameters is examined through the simulation study by using the three different approaches of estimation. Subsequently, we examine real-world data applications to demonstrate the versatility and potential of the BBE2 model. A real-world application demonstrates that the new distribution can offer a better fit than other competitive lifetime models.

Properties and estimation approaches of the odd JCA family with applications

SummaryIn this article, we study a new generator of distributions called the odd JCA‐G family. We determine the main mathematical properties of the new family. Some special submodels of the odd JCA‐G family are presented. The special models of the JCA‐G family have tractable densities shapes which possess various kinds of asymmetric, reversed‐J, left‐skewed, right‐skewed, symmetrical shapes. Furthermore, special submodels exhibit flexible hazard rate shapes. Additionally, the parameters of the odd JCA Burr‐XII model are estimated using some classical estimation approaches. The performance and efficiency of these approaches are explored via numerical simulations. The applicability of the odd JCA‐G family is illustrated by fitting two real‐life datasets. The data analysis shows that the odd JCA Burr‐XII model outperforms some well‐known distributions for the selected data.

The effects of measurement errors on estimating and assessing the multivariate process capability with imprecise characteristic

In industrial environments, process capability indices are daily employed as numerical metrics to summarize the performance of a process according to a predefined set of specification limits. Neglecting gauge measurement errors is a common phenomenon in process capability evaluations by researchers in laboratory investigations and by practitioners in daily operations. However, this common negligence is far from reality regardless of the employment of highly modern measuring tools, and may notably influence the efficiency of the measuring method for assessing the performance of a manufacturing process. In this paper, a linear covariate error model is applied to investigate the effects of gauge measurement errors on the classical and fuzzy estimation approaches of the multivariate process capability index SpkT for univariate and multivariate normally distributed quality characteristics with precise specification limits. Moreover, lower confidence bounds are also derived for the yield index SpkT in the presence of measurement errors and based on a fuzzy approach. In addition to the theoretical results, extensive simulations have been conducted to analyze how the behavior of the test statistic and lower confidence bound (LCB) for assessing the performance of the process is affected by different sources of the measurement errors. The obtained results indicate that a serious underestimation of the process capability occurs when the data is contaminated with measurement errors. It is also shown that the underestimation problem is somewhat solved by taking multiple measurements from the identical item. Moreover, comparative analyses show that the proposed method is superior to Scagliarini’s method and Wang’s way such that the negative effects of errors on underestimating the LCB are reduced in the proposed plan. This paper also extends the application of the introduced method to correlated variables. Finally, three practical examples are discussed to demonstrate the use of the proposed method in industrial applications.

Detectability Conditions and State Estimation for Linear Time-Varying and Nonlinear Systems

This work proposes a detectability condition for linear time-varying systems based on the exponential dichotomy spectrum. The condition guarantees the existence of an observer, whose gain is determined only by the unstable modes of the system. This allows for an observer design with low computational complexity compared to classical estimation approaches. An extension of this observer design to a class of nonlinear systems is proposed and local convergence of the corresponding estimation error dynamics is proven. Numerical results show the efficacy of the proposed observer design technique.

Classical and Modern gain estimation approach of PID controller for the pitch control of the RCTA aircraft

In the current age of globalization, the development of autopilots is superficial as the standard of living is improved through aerial surveillance, defense applications, and door- to-door transportation. To design the PID controller, a mathematical model is created to address the system identification for estimating longitudinal derivatives and to study the handling qualities of aircraft in order to improve piloting performance. This paper exhibits a comparative assessment between the classical closed-loop PID tuning methods like ZN, Modified ZN, Tyreus-luyben, Astrom- Hagglund and the modern control techniques like pole placement, LQR for the pitch controller design. The simulation results are displayed in the time-domain, which demonstrates the effectiveness of the approach used to design a robust controller.

Deep homography estimation in dynamic surgical scenes for laparoscopic camera motion extraction

ABSTRACT Current laparoscopic camera motion automation relies on rule-based approaches or only focuses on surgical tools. Imitation Learning (IL) methods could alleviate these shortcomings, but have so far been applied to oversimplified setups. Instead of extracting actions from oversimplified setups, in this work we introduce a method that allows to extract a laparoscope holder’s actions from videos of laparoscopic interventions. We synthetically add camera motion to a newly acquired dataset of camera motion free da Vinci surgery image sequences through a novel homography generation algorithm. The synthetic camera motion serves as a supervisory signal for camera motion estimation that is invariant to object and tool motion. We perform an extensive evaluation of state-of-the-art (SOTA) Deep Neural Networks (DNNs) across multiple compute regimes, finding our method transfers from our camera motion free da Vinci surgery dataset to videos of laparoscopic interventions, outperforming classical homography estimation approaches in both, precision by , and runtime on a CPU by .

A Randles Circuit Parameter Estimation of Li-Ion Batteries With Embedded Hardware

Accurate modelling of electrochemical sources is very important to predict how a source will perform in specific applications related to the load or environmental parameters. A Randles circuit is considered as a reliable equivalent electrical circuit in studying and modelling various electrochemical systems and processes. The classical parameter estimation approach based on use of software packages (ZSim, MEISP, LEVMW, etc.) requires for the high computational performance processing units, decreasing the reliability as proper maintenance actions can be delayed because of offline analysis. Advancing the state of the art, we propose a low-complexity approach for embedded hardware-based parameter estimation of the Randles circuit. Our non-iterative method uses only the measured real and imaginary part of impedance, with numerical approximation of the first derivative of real/imaginary part quotient, to create closed-form expressions with a unique solution. The initial estimated values are available from partial dataset (after measurement at only 3 frequencies). Moreover, it is not software platform-specific, which enables a high level of portability. The presented method is verified with theoretical, numerical and experimental analysis, with more than 1000 datasets. We also demonstrated the applicability in parameter estimation of the Randles circuit of a Li-ion battery. Finally, we verified suitability for embedded hardware platforms, with deployment on a microcontroller-based platform with a clock speed of 16 MHz and 8 kB of SRAM. Reliable parameter estimation processing of a 100-points dataset was performed in just 106 milliseconds with 1% relative error, requiring less than 53 mJ of energy.

Combination of Stochastic State Estimation with Online Identification of the Open-Circuit Voltage of Lithium-Ion Batteries

Typical equivalent circuit models for Lithium-ion batteries are represented in the form of the so-called Thévenin form. These models comprise a state of charge (SOC) controlled voltage source as well as lumped elements such as series resistances as well as at least one RC subnetwork to describe dynamic effects by the terminal current and voltage as input and output of the battery. In classical state estimation approaches, these characteristics are assumed to be identified beforehand, while aging of battery cells is related to a loss of the total capacity, changes in the charging/discharging efficiency, an increase of the Ohmic cell resistance, and/or changes of the time constants of the above-mentioned RC networks. Such variations can be estimated by means of additional parameters that are included in the system's state vector. However, the typically applied approaches do not allow for a direct identification of the nonlinear dependencies of the circuit elements on the SOC and other influence factors such as currents or the cell temperature. Therefore, this paper proposes a real-time capable, two-stage identification of these dependencies on the example of the open-circuit voltage by means of an Unscented Kalman Filter (UKF) approach. In the first stage, the state variables of the dynamic system model are estimated together with a lumped disturbance term (an additive correction of the open-circuit voltage). In the second stage, this disturbance term is used to correct the a-priori knowledge of the open-circuit voltage and to simultaneously express the identification quality in terms of covariances for the coefficients of its piecewise polynomial approximation in each temporal discretization step. The efficiency of the proposed methodology is demonstrated in simulations for an experimentally validated system model.

Factors of Renewable Energy Consumption in the European Countries—The Bayesian Averaging Classical Estimates Approach

The paper aims to identify the most likely factors that determine the demand for energy consumption from renewable sources (renewable energy consumption—REC) in European countries. Although in Europe, a high environmental awareness is omnipresent, countries differ in scope and share of REC due to historical energetic policies and dependencies, investments into renewable and traditional energetic sectors, R&D development, structural changes required by energetic policy change, and many other factors. The study refers to a set of macroeconomic, institutional, and social factors affecting energetic renewable policy and REC in selected European countries in two points of time: i.e., before and after the Paris Agreement. The Bayesian Average Classical Estimates (BACE) is applied to indicate the most likely factors affecting REC in 2015 and 2018. The comparison of the results reveals that the Gross Domestic Product (GDP) level, nuclear and hydro energy consumption were the determinants significant in both analyzed years. Furthermore, it became clear that in 2015, the REC depended strongly on the energy consumption structure, while in 2018, the foreign direct investment and trade openness played their role in increasing renewable energy consumption. The direction of changes is gradual and positive. It complies with the Sustainable Development Goals (SDGs).

The Gamma–Gompertz distribution: Theory and applications

In this article, we explore a new model with three parameters called Gamma–Gompertz (GGo) distribution which is generated by the gamma-X family. The GGo distribution provides better fits than some competing distributions such as three-parameter Gompertz, Gompertz–Lindley, Gompertz–geometric, Gompertz–Poisson, and inverse Gompertz distributions. Some well-known distributions are included in the GGo distribution as special sub-models. The density function of the distribution can be decreasing, unimodal and decreasing–increasing–decreasing shaped while the failure rate function can be increasing and unimodal shaped. Various properties of the GGo distribution are obtained. An extensive simulation study is carried out to assess the effectiveness of some classical estimation approaches which are discussed to estimate the model parameters. To demonstrate the potentiality of the GGo distribution, two real data sets are used and the bootstrap percentile confidence intervals are also obtained by bootstrap resampling. In addition, a new regression model is proposed via re-parametrization of the GGo distribution, called the log-GGo distribution. The maximum likelihood method is considered to estimate the unknown parameters of re-parametrized log-GGo distribution. The potentiality of log-GGo regression model is analyzed for HIV+ censored data set.

Jointly Calibrating Hydrologic Model Parameters and State Adjustments

AbstractA method is presented to address model state uncertainty in hydrologic model simulation. This is achieved by introducing tuneable parameters that allow adjustments to the model states. Excessive dimensionality is avoided by introducing only a limited number of parameters that control the index (timing) and size of the state adjustments. The method is designed to compensate for issues with hydrologic model structures, particularly those relevant to the soil moisture state in a rainfall‐runoff model. In the context of water resource planning and management, errors in the model states have often been overlooked as an important source of uncertainty and have the potential to significantly degrade model simulations. A synthetic study shows that a classical parameter estimation approach will produce biased distributions when state errors exist, and that the proposed state and parameter uncertainty estimation (SPUE) can remove the bias in parameter estimates for improved model simulations. In a real case study, SPUE and the classical approach are implemented in 46 sites around Australia. The results show that hydrologic parameter distributions for a selected conceptual model can be significantly different when accounting for state uncertainty. This has large implications for scenario modeling since it puts into dispute how to determine appropriate parameters for such studies. SPUE outperforms the classical approach in a range of calibration and validation metrics, particularly for sites that contain zero flows. Future work involves testing SPUE with different hydrologic models and likelihood formulations, and enhancing rigor by explicitly accounting for observational data uncertainty.

Bayesian inference for the Birnbaum–Saunders autoregressive conditional duration model with application to high-frequency financial data

Autoregressive conditional duration (ACD) models have been preponderant when the subject is the modeling of high-frequency financial data. A prominent model that has demonstrated great adjustment capacity is the ACD model based on the Birnbaum–Saunders distribution (BS-ACD). Recent works have shown that this model outperforms the existing models in the literature. Nevertheless, these works explore only classical estimation approaches. In this article, we perform a Bayesian approach of the BS-ACD model. The scale parameter was modeled considering a dynamic linear model. Estimation of posterior distribution of parameters was approximated through Markov chain Monte Carlo methods. A simulation study is conducted to evaluate the performance of Bayesian estimators and two applications to real high frequency data illustrate the proposed methodology.

Narrow Money Demand in Indonesia and in Other Transitional Economies – Model Selection and Forecasting

Purpose: This paper aims to incorporate model uncertainty in variable selection and forecasting in the monetarist money demand model and check whether the emerging economies such as the Czech Republic, Poland, Hungary, Russia, Mexico, Brazil, Turkey, India, Republic of South Africa, and Indonesia follow this model in the long-run. The case of the United Kingdom serves as a benchmark for the study. Design/Methodology/Approach: In dynamic econometric modeling, the number of potential explanatory variables increases rapidly, and model uncertainty grows very fast. Consequently, empirical modeling of money demand needs a comprehensive strategy for model selection and forecasting. We use Bayesian averaging of classical estimates (BACE) as an appropriate model reduction strategy. The monetary model serves as the theoretical basis for empirical equilibrium error-correction models (EqCM) and employing the Bayesian averaging of classical estimates (BACE) approach for variable and model selection and forecasting. Findings: Four theoretical and competitive model specifications are proposed and empirically tested. We found that monetary systems in Indonesia and other analyzed economies are both stable and theory consistent. The forecasts generated for Indonesia are accurate. The robustness of the model selection based on the BACE procedure was strongly confirmed. Practical Implications: The proposed procedure is valid for practical application, particularly in dynamic model selection and forecasting. Originality/Value: The novelty of this research lies in employing the BACE approach to model the demand for money with the equilibrium error correction (EqCM) mechanism.

Using a sequential latent class approach for model averaging: Benefits in forecasting and behavioural insights

Abstract Despite the frequent use of model averaging in many disciplines from weather forecasting to health outcomes, it is not yet an idea often considered in travel behaviour or choice modelling. The idea behind model averaging is that a single model can be created by calculating contribution weights for a set of candidate models, depending on their relative performance, thus creating an ‘average’. There are different ways of doing this, with a clear distinction between looking at the overall performance of each model or by doing this at the level of individual agents or observations. In this paper, we demonstrate that a relatively straightforward adaptation of latent class models can be used for the latter approach and show how this can be an effective method for travel behaviour modelling. We identify two key opportunities for model averaging. The first is the situation where an analyst faces the difficult choice between a number of advanced models, all with some desirable properties. The second is the situation where advanced models cannot be used due to the size of the data and/or choice sets. Our tests demonstrate that in both cases, model averaging using a sequential latent class framework results in a consistent improvement in model fit for both estimation and in forecasting with subsets of validation samples. Additionally, we demonstrate that model averaging can be used to obtain more reliable elasticities and welfare measures by averaging across outputs obtained from the set of candidate models. In terms of actual implementation of model averaging, we present a simple expectation–maximisation (EM) algorithm which can deal with very large numbers of candidate models within the same model averaging structure, unlike the typical case with classical estimation approaches for latent class.

Model simplification and variable selection: A replication of the UK inflation model by Hendry (2001)

SummaryIn this paper, we revisit the well‐known UK inflation model by Hendry (Journal of Applied Econometrics, 2001, 16, 255–275. We replicate the results in a narrow sense using the gretl and PcGive programs. In a wide sense, we extend the study of model uncertainty using the Bayesian averaging of classical estimates (BACE) approach as an automatic model reduction strategy. We consider three different specifications to compare BACE variable selection with Hendry's reduction. We find that the BACE method can recover the path of nontrivial reduction strategy.

Forecasting the crude oil prices based on Econophysics and Bayesian approach

In view of the importance and complexity of crude oil price, we investigate the dynamic forecasting of crude oil prices via Bayesian and Econophysics approaches. We propose information entropy to measure the predictability of crude oil prices and employ the rolling window approach to forecast the dynamic price of crude oil. In this article, Bayesian approach is applied to estimate the parameters, at the same time, the classic estimate approach is also adopted. Finally, we compare the forecasting results of the two methods. The results of this paper indicates that (1) both estimate approaches can effectively estimate the parameters of Heston model; (2) under a specific loss function, Bayesian approach has advantage over classical estimation approach when estimated sample size is small, while the estimate sample size increases, classical method slightly outperforms Bayesian method; (3) the predicted entropy of the estimated interval of 200 days under the Bayesian method are closest to the actual information entropy, while the estimated interval of 600 days under the maximum likelihood method is closest to the information entropy; (4) except for the estimation interval of 200 days, the predicted entropy under the maximum likelihood estimation is more representative of the predictability of the crude oil price. we also consider the more general case, we test this two methods of different steps ahead and compare the stability of the two methods.

Application of an improved parameter estimation approach to characterize enhanced heat exchangers

The main goals of this paper are twofold: to provide an improved parameter estimation procedure that enables the accurate evaluation of heat transfer correlations for the Nusselt number and to present a new procedure for identifying the presence of transition in the flow regime.In the first goal, it needs to be pointed out that although this kind of approach is based on temperature measurements, in the literature, the classical parameter estimation approach uses the overall heat transfer coefficient. To reduce uncertainty in the evaluation of internal and external heat transfer coefficients, in the improved procedure, the measured temperature data were directly used without any intermediate elaboration.The validation of the new procedure, carried out by means of synthetic data, highlighted that both the relative error on each estimated parameter and the amplitude of the confidence intervals were reduced by minimizing the objective function expressed in terms of outlet temperature of the tube side of the heat exchanger.With regard to the transition regime, the numerical outcomes revealed that both in the laminar and turbulent regimes, the amplitude of the confidence intervals of the estimated parameters was very small; in the transition regime, the amplitude became wide. Therefore, this parameter served as a useful indicator to identify the presence of transition in the flow regime. This finding enabled a new indirect methodology, called the transition alert procedure, to be developed for identifying the Reynolds number value at which transition of the flow regime occurred. This method is an iterative subsampling of the dataset based on the observation of the amplitude of the confidence intervals.To assess the robustness of the methodologies proposed here, the improved parameter estimation procedure and the transition alert procedure were applied to the obtained experimental data by analyzing a counter-flow heat exchanger with double corrugated tubes. In this kind of tube, the condition when the transition from the laminar to the turbulent flow regime occurs is not known a priori.