Estimation Of Nonlinear Models Research Articles

Uncertain statistics models for characterizing annual total energy production

In the field of annual total energy production, it is hard to determine whether the experimental data is linear or nonlinear growth characteristics. Therefore, different regression models are used to test the properties of the observed data. This article uses actual data to perform parameter estimation and residual analysis of linear and nonlinear regression models. In addition, uncertain nonlinear time series model is used to fit the experimental data in order to find a more suitable statistics model after obtaining the growth properties of the observed data. A test is introduced to prove that the disturbance terms presented in the regression and time series models are actually uncertain variables, not random variables. Moreover, the uncertain hypothesis tests show that the uncertain time series model is in better agreement with the real data of the annual total energy production.

Enhancing the health benefits of air quality improvement: a comparative study across diverse scenarios.

In many studies, linear methods were used to calculate health benefits of air quality improvement, but the relationship between air pollutants and diseases may be complex and nonlinear. In addition, previous studies using reference number as average number of diseases may overestimate the health benefits. Therefore, the nonlinear model estimation and resetting of the reference number were very important. Hospital admission data for coronary heart disease (CHD), meteorological data, and air pollutant data of Zibo City from 2015 to 2019 were collected. The generalized additive model (GAM) was used to explore the association between air pollutants and hospital admission for CHD, and to evaluate the effects on health benefits under different reference number settings. A total of 21,105 hospitalized cases for CHD were reported in Zibo during the study period. The results of the GAM showed there was a log-linear exposure-response relationship between O3 and hospital admissions for CHD, with RR (relative risk) of 1.0143 (95% CI: 1.0047 ~ 1.0239). There were log-nonlinear exposure-response relationships between PM10, PM2.5, SO2, and hospital admissions for CHD. With the increase of pollutants concentrations, the risk for hospital admission showed a trend of increasing first and then decreasing. Compared with the average hospital admissions as the reference number, health benefits calculated by hospital admissions predicted by the GAM model yielded lower. Using the World Health Organization air quality guidelines as reference, attributable fractions of O3, PM10, and PM2.5 were 1.97% (95% CI: 0.63 ~ 3.40%), 11.82% (95% CI: 8.60 ~ 15.24%), and 11.82% (95% CI: 8.79 ~ 15.04%), respectively. When quantifying health benefits brought by improving air quality, corresponding calculation methods should first be determined according to the exposure-response relationships between air pollutants and outcomes. Then, applying the average hospital admissions as reference number may overestimate health benefits resulting from improved air quality.

Determining the parameters of the functioning for a nonlinear ballistic system in a real external environment

Determining the parameters of the functioning for a nonlinear ballistic system in a real external environment

Two-dimensional (2D) axis-pin force sensor and its characterization on the shear force direction

The characterization of the shear force direction is an imperative technical problem to be solved for the axis-pin force sensor. In the present work, a two-dimensional axis-pin force sensor has been designed. The layout of the sensor is to open horizontal blind holes and vertical blind holes at intervals of 90 degrees along the circular direction on the surface of the axis-pin. Then the variation law of the circumferential strain of blind holes along with the shear force direction is first studied through the FEA simulation. It is found that the sum of the circumferential strains of two horizontal blind holes or vertical blind holes varies in sine and cosine pattern with the shear force direction. On this basis, the mathematical model of shear force direction characterized by circumferential strains of blind holes is derived. Eventually, the prototype of the axis-pin force sensor was made to verify this law. The experimental results showed that the accuracy of the shear force and direction measured by the sensor can reach ± 8% and ± 5% respectively, which meet the requirements of the practical application. This method eliminates the theoretical error caused by the use of correction coefficients and nonlinear model approximation, which provides a theoretical basis for the development of two-dimensional axis-pin force sensors.

Least square estimation of non-linear structural models

A new method for estimating a wide class of structural equation models (SEM) is proposed and evaluated. A weighted least squares approach is used that estimates parameters and latent variables. This new approach is flexible enough to handle non-linear and non-smooth models and allows us to model various constraints. The method includes various strategies to deal with the problem of choosing weights. The principle strengths and weaknesses of this approach are discussed, and simulation studies are performed to reveal the problems and potential of this approach.

Indirect inference approach for parameter estimation of non linear manoeuvring models of a ROV based on model basin trials

ABSTRACT In this work, indirect inference (II) techniques are applied to estimate the parameters of a non-linear manoeuvring model of a remotely operated vehicle (ROV). In the application of this method, a set of auxiliary statistics is established in the optimisation process in order to improve the efficiency of the estimated parameters. For the parameter estimation, data from different tests are available, which were carried out with a ROV in the facilities of the Centro de Experiencias Hidrodinámicas del Pardo INTA/CEHIPAR, Madrid. The model obtained is validated by means of graphical and statistical methods with the acquired data and the statistical properties of the estimated parameters are evaluated by means of a Monte Carlo study.

Nonlinear Time-Delayed Quorum Sensing System: State Estimation Via a Robust Observer

This paper proposes an innovative method to estimate the states in a nonlinear time-delayed quorum sensing (QS) model using an extended Kalman filter (EKF) observer. By addressing the inherent time delays in QS system which arise as a delayed response of bacteria to population fluctuations, the study introduces variable structure dynamical estimators, specifically the EKF, to approximate missing states based on available measurements. The EKF observer is applied to estimate four out of five internal non-measurable nonlinear states in a time-delayed QS model. This is the first attempt to utilize the EKF state estimation in nonlinear time delay QS models. The research contributes to the understanding of QS systems, provides insights into the communication dynamics inside biological systems, and offers a practical solution for estimating states in realistic scenarios.

The Concavity of Conditional Maximum Likelihood Estimation for Logit Panel Data Models with Imputed Covariates

In estimating logistic regression models, convergence of the maximization algorithm is critical; however, this may fail. Numerous bias correction methods for maximum likelihood estimates of parameters have been conducted for cases of complete data sets, and also for longitudinal models. Balanced data sets yield consistent estimates from conditional logit estimators for binary response panel data models. When faced with a missing covariates problem, researchers adopt various imputation techniques to complete the data and without loss of generality; consistent estimates still suffice asymptotically. For maximum likelihood estimates of the parameters for logistic regression in cases of imputed covariates, the optimal choice of an imputation technique that yields the best estimates with minimum variance is still elusive. This paper aims to examine the behaviour of the Hessian matrix with optimal values of the imputed covariates vector, which will make the Newton–Raphson algorithm converge faster through a reduced absolute value of the product of the score function and the inverse fisher information component. We focus on a method used to modify the conditional likelihood function through the partitioning of the covariate matrix. We also confirm that the positive moduli of the Hessian for conditional estimators are sufficient for the concavity of the log-likelihood function, resulting in optimum parameter estimates. An increased Hessian modulus ensures the faster convergence of the parameter estimates. Simulation results reveal that model-based imputations perform better than classical imputation techniques, yielding estimates with smaller bias and higher precision for the conditional maximum likelihood estimation of nonlinear panel models.

Develop a Nonlinear Regression Model Using Box-Cox Transformation with Application

This article introduces an algorithm designed for utilizing power transformations in the estimation of nonlinear regression models. The algorithm outlines a series of steps for selecting the most suitable power parameter estimate through a combination of the conventional Maximum Likelihood Estimation technique and specific criteria for enhancing statistical modeling effectiveness. Supplementary decision guidelines involve the utilization of the determination coefficient and the p-value from the errors normality test. The algorithm's application was demonstrated using actual data. The article's conclusion highlighted the ability to identify a range of feasible solutions for selecting the optimal power parameter. However, it was acknowledging the challenge of identifying a single optimal value that satisfies the requirements of all estimation and decision methodologies.

Parameter estimation in nonlinear mixed effect models based on ordinary differential equations: an optimal control approach

Parameter estimation in nonlinear mixed effect models based on ordinary differential equations: an optimal control approach

Estimation of nonlinear mixed-effects continuous-time models using the continuous-discrete extended Kalman filter.

Many intensive longitudinal measurements are collected at irregularly spaced time intervals, and involve complex, possibly nonlinear and heterogeneous patterns of change. Effective modelling of such change processes requires continuous-time differential equation models that may be nonlinear and include mixed effects in the parameters. One approach of fitting such models is to define random effect variables as additional latent variables in a stochastic differential equation (SDE) model of choice, and use estimation algorithms designed for fitting SDE models, such as the continuous-discrete extended Kalman filter (CDEKF) approach implemented in the dynr R package, to estimate the random effect variables as latent variables. However, this approach's efficacy and identification constraints in handling mixed-effects SDE models have not been investigated. In the current study, we analytically inspect the identification constraints of using the CDEKF approach to fit nonlinear mixed-effects SDE models; extend a published model of emotions to a nonlinear mixed-effects SDE model as an example, and fit it to a set of irregularly spaced ecological momentary assessment data; and evaluate the feasibility of the proposed approach to fit the model through a Monte Carlo simulation study. Results show that the proposed approach produces reasonable parameter and standard error estimates when some identification constraint is met. We address the effects of sample size, process noise variance, and data spacing conditions on estimation results.

System error estimation for sensor network with integrated sensing and communication application

The integrated sensing and communication base station can perform both communication and sensing tasks simultaneously. The key premise of accurate localization and tracking of targets is sensor registration process. If system errors of multi-sensor system are not corrected properly, it can lead to significant sensing errors and reduce the overall system performance. In this paper, we propose a system error estimation method for a 3-dimensional asynchronous base station network to achieve satisfactory localization and tracking performance. Specifically, by making use of the priori information of the cooperative targets, we propose to minimize the sum of squares of the position mismatch errors of the targets, this leads to a nonlinear error estimation model for the system errors. To handle the high nonlinearity and ensure fast convergence of online registration, an efficient inexact block coordinate descent optimization algorithm incorporating the proximal method is proposed. The algorithm divides the estimation problem into a linear least square subproblem and several quadratic constrained quadratic program subproblems, enabling different kinds of system errors to be alternatively updated. Finally, the effectiveness and feasibility of the proposed estimation algorithm are demonstrated through numerical simulation.

Observer-Based Approximate Affine Nonlinear Model Predictive Controller for Hydraulic Robotic Excavators with Constraints

Given the highly nonlinear and strongly constrained nature of the electro-hydraulic system, we proposed an observer-based approximate nonlinear model predictive controller (ANMPC) for the trajectory tracking control of robotic excavators. A nonlinear non-affine state space equation with identified parameters is employed to describe the dynamics of the electro-hydraulic system. Then, to mitigate the plant-model mismatch caused by the first-order linearization, an approximate affine nonlinear state space model is utilized to represent the explicit relationship between the output and input and an ANMPC is designed based on the approximate nonlinear model. Meanwhile, the Extended Kalman Filter was introduced for state observation to deal with the unmeasurable velocity information and heavy measurement noises. Comparative experiments are conducted on a 1.7-ton hydraulic robotic excavator, where ANMPC and linear model predictive control are used to track a typical excavation trajectory. The experimental results provide evidence of convincing trajectory tracking performance.

Smoothed simulated pseudo-maximum likelihood estimation for nonlinear mixed effects models with censored responses.

Nonlinear mixed effects models have been widely applied to analyses of data that arise from biological, agricultural, and environmental sciences. Estimation of and inference on parameters in nonlinear mixed effects models are often based on the specification of a likelihood function. Maximizing this likelihood function can be complicated by the specification of the random effects distribution, especially in the presence of multiple random effects. The implementation of nonlinear mixed effects models can be further complicated by left-censored responses, representing measurements from bioassays where the exact quantification below a certain threshold is not possible. Motivated by the need to characterize the nonlinear human immunodeficiency virus RNA viral load trajectories after the interruption of antiretroviral therapy, we propose a smoothed simulated pseudo-maximum likelihood estimation approach to fit nonlinear mixed effects models in the presence of left-censored observations. We establish the consistency and asymptotic normality of the resulting estimators. We develop testing procedures for the correlation among random effects and for testing the distributional assumptions on random effects against a specific alternative. In contrast to the existing variants of expectation-maximization approaches, the proposed methods offer flexibility in the specification of the random effects distribution and convenience in making inference about higher-order correlation parameters. We evaluate the finite-sample performance of the proposed methods through extensive simulation studies and illustrate them on a combined dataset from six AIDS Clinical Trials Group treatment interruption studies.

Bayesian optimal sensor placement for parameter estimation under modeling and input uncertainties

A Bayesian optimal sensor placement (OSP) framework for parameter estimation in nonlinear structural dynamics models is proposed, based on maximizing a utility function built from appropriate measures of information contained in the input–output response time history data. The information gain is quantified using Kullback–Leibler divergence (KL-div) between the prior and posterior distribution of the model parameters. The design variables may include the type and location of sensors. Asymptotic approximations, valid for large number of data, provide valuable insight into the measure of information. Robustness to uncertainties in nuisance (non-updatable) parameters associated with modeling and excitation uncertainties is considered by maximizing the expected information gain over all possible values of the nuisance parameters. In particular, the framework handles the case where the excitation time history is measured by installed sensors but remains unknown at the experimental design phase. Introducing stochastic excitation models, the expected information gain is taken over the large number of uncertain parameters used to model the random variability in the input time histories. Monte Carlo or sparse grid methods estimate the multidimensional probability integrals arising in the formulation. Heuristic algorithms are used to solve the optimization problem. The effectiveness of the method is demonstrated for a multi-degree of freedom (DOF) spring–mass chain system with restoring elements that exhibit hysteretic nonlinearities.

Multi-fidelity nonlinear unsteady aerodynamic modeling and uncertainty estimation based on Hierarchical Kriging

By fusing aerodynamic data from multiple sources, multi-fidelity methods can well balance model accuracy and computational cost. To extend multi-fidelity models for predicting unsteady aerodynamics with uncertainty estimation, an improved modelling framework based on the Hierarchical Kriging (HK) is proposed for nonlinear aerodynamic reduced-order modelling. This aerodynamic modelling framework is achieved by a two-stage modelling strategy. In the first stage, using the current and time-delayed low-fidelity aerodynamic load and pitching motion as input, a linear regression model is built to achieve preliminary aerodynamic prediction. In the second stage, the current and time-delayed preliminary prediction, as well as pitching motion history are used as the input of the Hierarchical Kriging model to predict the high-fidelity aerodynamic loads. The generalization capability of this improved modelling framework is firstly verified by several analytical examples. Furthermore, with three sets of training samples taken from harmonic pitching motions of an airfoil in transonic flow, the proposed model achieves accurate prediction on unsteady aerodynamics of other harmonic and random motions, and provides reliable uncertainty estimation of the predicted unsteady aerodynamics. In addition, the computational cost and prediction errors of multi-fidelity and the single-fidelity aerodynamic model are compared. Even with the same computational cost, the proposed multi-fidelity model still shows improved accuracy. Finally, using the uncertainty estimation of the proposed model, an active learning task is performed, which actively selects and incrementally adds the required training samples. With active learning, a good balance between model accuracy and cost of data acquisition is maintained, while avoiding over-fitting problems of the proposed model.

Dynamic State Estimation of Nonlinear Differential Algebraic Equation Models of Power Networks

This paper investigates the joint problems of dynamic state estimation of algebraic variables (voltage and phase angle) and generator states (rotor angle and frequency) of nonlinear differential algebraic equation (NDAE) power network models, under uncertainty. Traditionally, these two problems have been decoupled due to complexity of handling NDAE models. In particular, this paper offers the first attempt to solve the aforementioned problem in a coupled approach where the algebraic and generator states estimates are simultaneously computed. The proposed estimation algorithm herein is endowed with the following properties: <i>(i)</i> it is fairly simple to implement and based on well-understood Lyapunov theory; <i>(ii)</i> considers various sources of uncertainty from generator control inputs, loads, renewables, process and measurement noise; <i>(iii)</i> models phasor measurement unit installations at arbitrary buses; and <i>(iv)</i> is computationally less intensive than the decoupled approach in the literature.

On the robustness/replication of econometric analyses from nonlinear models using various commonplace software packages

AbstractBecause replicability is an important part of every scientific endeavor, this research deals with comparing and contrasting parameter estimates, standard errors, and p‐values from the estimation of five commonly encountered nonlinear models in applied econometrics. Commonplace software packages indigenous to econometrics and statistics are used, namely EVIEWS 11.0, SAS 9.4, Stata 17, and R 4.1.2 in five replication exercises to determine potential differences, if any, in empirical results. The hypothesis that mainstream software packages generate different empirical results in the estimation of nonlinear models is confirmed for the polynomial distributed lag (PDL) model and the GARCH(1,1) model. For the probit model and the Barten synthetic demand system model, the differences in parameter estimates, standard errors, and p‐values are less evident across the four commonly used software packages. For the Tobit model, the respective sets of parameter estimates, standard errors, and p‐values are nearly identical across the respective software packages. Economic analysts should not just accept estimation results uncritically, but instead, conduct sensitivity analyses involving the use of at least two software packages. The agricultural economics profession should adopt this recommendation as standard practice.

INTERCEPT ESTIMATION IN NONLINEAR SELECTION MODELS

We propose various semiparametric estimators for nonlinear selection models, where slope and intercept can be separately identified. When the selection equation satisfies a monotonic index restriction, we suggest a local polynomial estimator, using only observations for which the marginal cumulative distribution function of the instrument index is close to one. Data-driven procedures such as cross-validation may be used to select the bandwidth for this estimator. We then consider the case in which the monotonic index restriction does not hold and/or the set of observations with a propensity score close to one is thin so that convergence occurs at a rate that is arbitrarily close to the cubic rate. We explore the finite sample behavior in a Monte Carlo study and illustrate the use of our estimator using a model for count data with multiplicative unobserved heterogeneity.

Maximum Entropy Exploration in Contextual Bandits with Neural Networks and Energy Based Models.

Contextual bandits can solve a huge range of real-world problems. However, current popular algorithms to solve them either rely on linear models or unreliable uncertainty estimation in non-linear models, which are required to deal with the exploration-exploitation trade-off. Inspired by theories of human cognition, we introduce novel techniques that use maximum entropy exploration, relying on neural networks to find optimal policies in settings with both continuous and discrete action spaces. We present two classes of models, one with neural networks as reward estimators, and the other with energy based models, which model the probability of obtaining an optimal reward given an action. We evaluate the performance of these models in static and dynamic contextual bandit simulation environments. We show that both techniques outperform standard baseline algorithms, such as NN HMC, NN Discrete, Upper Confidence Bound, and Thompson Sampling, where energy based models have the best overall performance. This provides practitioners with new techniques that perform well in static and dynamic settings, and are particularly well suited to non-linear scenarios with continuous action spaces.