Error Estimation Technique Research Articles

Fast standard error estimation for joint models of longitudinal and time-to-event data based on stochastic EM algorithms.

Maximum likelihood inference can often become computationally intensive when performing joint modeling of longitudinal and time-to-event data, due to the intractable integrals in the joint likelihood function. The computational challenges escalate further when modeling HIV-1 viral load data, owing to the nonlinear trajectories and the presence of left-censored data resulting from the assay's lower limit of quantification. In this paper, for a joint model comprising a nonlinear mixed-effect model and a Cox Proportional Hazards model, we develop a computationally efficient Stochastic EM (StEM) algorithm for parameter estimation. Furthermore, we propose a novel technique for fast standard error estimation, which directly estimates standard errors from the results of StEM iterations and is broadly applicable to various joint modeling settings, such as those containing generalized linear mixed-effect models, parametric survival models, or joint models with more than two submodels. We evaluate the performance of the proposed methods through simulation studies and apply them to HIV-1 viral load data from six AIDS Clinical Trials Group studies to characterize viral rebound trajectories following the interruption of antiretroviral therapy (ART), accounting for the informative duration of off-ART periods.

FDI, industrialisation and environmental quality in SSA—the role of institutional quality towards environmental sustainability

In light of the quest to achieve economic development without compromising environmental quality, we empirically examine whether institutional quality (INSQY) can help moderate the possible harmful effects of foreign direct investments (FDI) and industrialisation on environmental quality in sub-Saharan Africa (SSA). We utilise the Driscoll and Kraay standard error estimation technique on a panel of 45 SSA countries from 2000 to 2019. The results indicate that FDI and industrialisation generally have a significant harmful effect on the environment. Our findings reveal that INSQY directly promotes environmental quality. Notably, the results confirm that INSQY plays a stimulating role in mitigating the adverse effects of FDI and industrialisation on environmental quality. The results further validate the environmental Kuznets curve (EKC) hypothesis in SSA. These findings contribute to environmental sustainability literature and offer policymakers insights on how INSQY can enhance environmental quality. Our empirical results are also robust to different estimation techniques, such as the two-stage least squares. We recommend SSA leaders strengthen institutional capacities, enforce environmental regulations, and implement strict policies to ensure environmental quality while promoting industrialisation and FDI inflows.

Multifractal analysis of fractal interpolation functions

This paper presents a novel algorithm to utilize multifractal spectrum as a quantitative measure for the fractal interpolation functions with respect to scaling factor and fractional order. As of yet, there were no error estimation techniques to interpret the fractal interpolation functions in the literature. To bridge this gap, this paper sketches multifractality as a quantitative measure for inquiring and comparing the effects of different scaling factors. The proposed algorithm for analyzing the multifractal measure depends on the probability measure of data points, which fractal function passes through, enabling to effectively discuss the heterogeneity of fractal interpolation functions. In addition, the impact of fractional orders on the fractional derivative (integral) of fractal interpolation functions is also discussed tailoring the multifractal measure.

A cross country analysis of financial development, trade openness, population and digitalization’s impact on sustainable development

This study employs the Standard Error Estimation technique to investigate the connections between the digitalization of economy, population, trade openness, financial development, and sustainable development across 127 countries from 1990 to 2019. The findings revealed associations between financial development, population growth, trade openness, economic growth, Digitalization development, foreign direct investment (FDI), and sustainable development. Financial development negatively impacts sustainable development, suggesting that countries with advanced financial systems may struggle to maintain sustainability. Trade openness exhibits a negative association with sustainable development, implying that countries with open trade policies may face challenges in maintaining sustainability, possibly due to heightened competition or resource exploitation. These findings highlight the multifaceted relationship between economic factors and sustainable development, underscoring the importance of comprehensive policies and governance mechanisms in fostering sustainability amidst global economic dynamics.

An approaching method based on integral for linear neutral delay differential equations by using Hermite polynomials

AbstractThis article presents a approximation method for linear neutral delay differential equations using Hermite polynomials. The method ensures the unknown function to be found by approximating the first derivative with the help of the finite Hermite series. This method reduces the problem to a linear algebraic system using the first derivative approach, matrix operations and collocation points. Also error of the solution is estimated by constructing an error problem. Numerical examples are solved to explain the method and error estimation technique. The results demonstrate the effectiveness and accuracy of the current study. Calculations have been made using MATLAB.

Effect of Governance and Social Sustainability Reporting on the Financial Performance of Listed Manufacturing Firms in Nigeria

The study investigated the effect of governance and social sustainability reporting on the financial performance of listed manufacturing firms in Nigeria. The study covered a sample of 32 listed manufacturing firms in Nigeria from 2014 to 2021. The descriptive statistics and the pool OLS with robust standard error estimation technique were used to analyze the data. The result showed that governance reporting has significant effect on financial performance; also, social reporting has a negative significant effect on financial performance. The implication of this finding underscores the value of strong governance frameworks in enhancing investor confidence and ensuring effective management, which collectively contribute to better financial performance. The study recommends that manufacturing firms should prioritize strengthening their governance reporting practices as transparent and effective governance mechanisms can lead to enhanced financial performance and greater trust from investors and also assess their social reporting strategies and expenditures.

Sustainability Committee, Audit Firm Type and Corporate Sustainability Reporting of Non-Financial Firms in Nigeria

In spite of the detrimental consequences, such as pollution and other environmental risks arising from corporate activities, there has been a noticeable lack of transparency in disclosing social, environmental, and economic information. In light of this, the research aims to present empirical evidence regarding the impact of sustainability committees and the type of audit firm on the reporting of corporate sustainability information by companies. The study utilized an Ex-post facto research design, considering a population of one hundred and fifteen (115) listed non-financial firms. Ninety-two (92) companies were selected as the sample. Both descriptive and inferential (Panel Corrected Standard Error) estimation techniques were employed to analyze data collected from the annual reports and accounts of the sampled listed manufacturing companies over a seven-year period (2016-2022). The findings revealed that the presence of a sustainability committee and audit type significantly predict corporate sustainability reporting among listed non-financial firms at a 5% level of significance. In conclusion, the study determined that sustainability committees and audit types play a crucial and meaningful role in shaping corporate sustainability reporting practices among listed non-financial firms in Nigeria. As a result, the study recommends that listed companies should establish sustainability committees to proactively address sustainability issues and enhance disclosure. Additionally, non-Big Four audit firms are encouraged to enhance their services by providing their staff with up-to-date audit skills.

Towards Efforts to Equalize Income in Africa: The Role of Tourism Development

ABSTRACT A vast literature has investigated the nexus between tourism and income inequality in developing and developed countries. Unfortunately, the literature on the impact of tourism on income inequality in Africa is sparse. Hence, this study examines the influence of tourism on income inequality in 30 African countries over the period 1996–2020. In addition to international tourism arrivals and international tourism receipts which have been widely used by previous studies, this study uses a plethora of tourism indicators, namely business tourism spending, leisure tourism spending, internal travel and tourism consumption, domestic tourism spending, and visitor exports. Moreover, unlike previous studies that have extensively used the Gini index with its inadequacy as a measurement of income inequality; this study uses the Atkinson index and Palma ratio to capture extreme points of the inequality distribution. The empirical evidence is based on the panel-corrected standard error (PCSE) estimation technique. The results reveal that tourism contributes to the equalization of income in Africa, contingent on the type of tourism. Policy implications are discussed.

Application of Regularized Meshless Method with Error Estimation Technique for Water–Wave Scattering by Multiple Cylinders

In this manuscript, we will apply the regularized meshless method, coupled with an error estimation technique, to tackle the challenge of modeling oblique incident waves interacting with multiple cylinders. Given the impracticality of obtaining an exact solution in many real engineering problems, we introduce an error estimation technique designed to achieve reliable solutions. This technique excels in providing dependable solutions that closely approximate analytical solutions. An additional advantage is its capacity to identify the optimal number of points for both source and collocating points, thereby enhancing computational efficiency. The validity of the proposed method will be demonstrated through three numerical cases, presenting results that exhibit substantial agreement.

A second order numerical method for singularly perturbed Volterra integro-differential equations with delay

Abstract This study deals with singularly perturbed Volterra integro-differential equations with delay. Based on the properties of the exact solution, a hybrid difference scheme with appropriate quadrature rules on a Shishkin-type mesh is constructed. By using the truncation error estimate techniques and a discrete analogue of Grönwall’s inequality it is proved that the hybrid finite difference scheme is almost second order accurate in the discrete maximum norm. Numerical experiments support these theoretical results and indicate that the estimates are sharp.

DAEM: A Data- and Application-Aware Error Analysis Methodology for Approximate Adders

Approximate adders are some of the fundamental arithmetic operators that are being employed in error-resilient applications, to achieve performance/energy/area gains. This improvement usually comes at the cost of some accuracy and, therefore, requires prior error analysis, to select an approximate adder variant that provides acceptable accuracy. Most of the state-of-the-art error analysis techniques for approximate adders assume input bits and operands to be independent of one another, while some also assume the operands to be uniformly distributed. In this paper, we analyze the impact of these assumptions on the accuracy of error estimation techniques, and we highlight the need to address these assumptions, to achieve better and more realistic quality estimates. Based on our analysis, we propose DAEM, a data- and application-aware error analysis methodology for approximate adders. Unlike existing error analysis models, we neither assume the adder operands to be uniformly distributed nor assume them to be independent. Specifically, we use 2D joint input probability mass functions (PMFs), populated using sample data, in order to incorporate the data and application knowledge in the analysis. These 2D joint input PMFs, along with 2D error maps of approximate adders, are used to estimate the error PMF of an adder network. The error PMF is then utilized to compute different error measures, such as the mean squared error (MSE) and mean error distance (MED). We evaluate the proposed error analysis methodology on audio and video processing applications, and we demonstrate that our methodology provides error estimates having a better correlation with the simulation results, as compared to the state-of-the-art techniques.

Condition-number-based measurement configuration optimization for nanostructure reconstruction by optical scatterometry

The quality of the measured signature is influenced not only by the instrument’s precision but also by the selected measurement configuration. In optical scatterometry, the purpose of measurement configuration optimization (MCO) is to select an optimal or suboptimal combination of measurement conditions, such as the angles of incidence, azimuth, polarization and wavelength, to achieve higher measurement accuracy. This analysis not only requires an effective optimization strategy but is also time-consuming. In this work, we propose a general MCO method that incorporates error propagation theory and condition-number-based error estimation technique, by which the MCO problem can be formulated as an optimization problem for the condition number of the coefficient matrix in the linear estimation of parameter deviations. The method is demonstrated on a multi-wavelength Mueller matrix scatterometry measuring a Si grating. With the help of the neural-network-based surrogate model, the feasibility of the method is verified by making a comparison with Latin hypercube sampling. Fitting results of the measured and calculated Mueller matrix spectra obtained at the selected optimal measurement configuration show a good agreement. The proposed method is promising to provide an alternate solution to globally evaluate the MCO problem in optical scatterometry and other measurement scenarios.

Darcy Forchhemier Prandtl-Eyring nanofluid flow with variable heat transfer and entropy generation using Cattaneo-Christov heat flux model: Statistical approach

In the current investigation, we studied the Prandtl-Eyring nanofluid with base fluid engine oil is flowing through a heated stretching surface with entropy production of and variable transfer analysis. Titanium dioxide (TiO2) nanoparticles (NPs) are mixes with engine oil to produce the nanofluid. By exposing the flow of the nanofluid over the heated, slippery surface, we are able to analyze the thermal transmission and flow mechanism. The effects of Darcy-Forchhemier, heat absorption/generation, Cattaneo-Cristov heat flux model and radiative flux are also taken into account in this study. Highly nonlinear partial differential equations that describe the nanofluids flow are converted into a set of ordinary differential equations via similarity transformation. The numerical technique named “shooting technique” is applied to obtain solution of the resulting system of ODEs. Error estimation, regression, and correlation statistical analysis techniques are used. Statistical approach is also applied on the model. In order to evaluate the constancy of the association features, the probable error is determined. Tables and figures are used to present the results. It has been noted that including nanoparticles into engine oil decreases skin friction while accelerating the transfer of energy. Deceleration is caused by the velocity field being greatly impacted by elements including porosity, the Darcy effect, and the nanoparticles volume fraction. Additionally, as the Brinkman number rises, entropy generation rises and the Bejan number falls.

A Feedrate Planning Method in CNC System Based on Servo Response Error Model

Reducing servo response error and further making reduction on contour error is crucial for high-precision computer numerical control (CNC) machine tools. For a permanent magnet synchronous motor (PMSM) servo system, there is always a response lag in feedrate tracking, which would introduce response error into the machining trajectory. Therefore, it is necessary to improve the performance of feedrate planning and interpolation for trajectory path. In this paper, a novel contour error compensation strategy is proposed. Compared with the mainstream methods, the proposed method offers a simplified alternative to existing contour error estimation techniques. Through a three-closed-loop control structure of a PMSM servo system, a response error model is founded. Afterwards, an improved S-model feedrate planning method is introduced according to the servo response error compensation. This predicted error is subsequently compensated in each interpolation cycle, resulting in a reduction of contour error. Finally, simulations and experiments are performed to demonstrate that the contour error can be reduced in both the ‘∞’-shaped Non-Uniform Rational B-Spline (NURBS) curve path and the butterfly-shaped NURBS curve path using the proposed method.

Efficient Error Estimation for High-Level Design Space Exploration of Approximate Computing Systems

This article presents an error estimation technique for a data-flow graph (DFG) representation of an approximate computing (AC) circuit. The technique, which may be used during the high-level design of digital circuits, estimates error metrics for the outputs of the approximate circuit. The proposed technique receives as an input, output error characterizations of arithmetic modules in a high-level library. The error modeling of a library module is accomplished by dividing the input (operand) ranges into intervals and then characterizing the output error for different combinations of these input intervals. Subsequently, the error for each combination is stored in a lookup table (LUT). The module error models are integrated into a design space exploration (DSE) framework to evaluate different combinations of exact and approximate realizations of various operations in the DFG. The DSE, which performs error calculation and propagation from inputs to outputs of the target DFG, may be used to explore trade-offs between the output error and other design metrics of the approximate circuit, e.g., energy efficiency. The efficacy of the proposed method is assessed for three image processing benchmarks. Results for these benchmarks demonstrate that the framework can efficiently generate the Pareto frontier (PF) in the trade-off space of accuracy versus energy efficiency for the targeted benchmarks. Compared to a purely simulation-based exploration, the proposed technique provides an average of 92 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times$</tex-math> </inline-formula> speed improvement.

Response of Indonesian mineral supply to global renewable energy generation: Analysis based on gravity model approach

The captivating surge of energy transitions in the major industrialized nations has elevated the global demand for critical minerals. The demand pattern has enabled mineral-abundant emerging economies like Indonesia to enter the international market by exporting mineral goods. Accordingly, we investigate the Indonesian mineral export supply's response to the renewable energy production of the 18 clean energy-generating countries, considering crude oil and mineral prices, exchange rates, and economic growth of the resource and importer countries from 1990 to 2020. In doing so, we apply the Poisson Pseudo-maximum Likelihood (PPML) approach to measuring the panel gravity model for mineral exports in Indonesia. As a result, we observe a significant response of Indonesia's mineral export supply to the renewable energy generation of the 18 mineral importing countries. Besides, mineral and crude oil prices are insignificant, whereas the importer countries' exchange rates and income growth positively influence Indonesia's mineral export growth. However, Indonesia's income factor negatively affects its mineral export supply. Finally, we validate our results using an alternative estimator, the Driscoll-Kraay robust standard error estimation technique. Therefore, our findings suggest implementing Indonesia's existing mineral policy to produce finished mineral goods to materialize the worldwide vision of energy transitions toward a crossroad of net-zero emissions by the middle of the current century.

Application of the error estimation technique in the method of fundamental solutions for solving incident wave problem with multiple cylinders

This article attempts to solve the problem of oblique incident wave with multiple cylinders using the method of fundamental solutions (MFS) combined with a proposed error estimation technique. In real engineering, many problems only have an empirical result without an exact solution. There are three advantages to the proposed error estimation technique. First, the error estimation technique can provide a reliable solution to approximate the analytical solution. Second, the optimal number of points for the source and collocation points can be determined. Third, a scheme refinement of adaptive distribution of source points can be developed employing the error estimation technique. The theory of single-layer and double-layer potential formulas in the MFS method is considered in this paper. The numerical examples include water wave passing through one, two, and four circular cylinders, respectively. The results show the resultant forces on the cylinder and free surface elevation around the cylinder, respectively. The results are then presented.

Conformable finite element method for conformable fractional partial differential equations

&lt;abstract&gt;&lt;p&gt;The finite element (FE) method is a widely used numerical technique for approximating solutions to various problems in different fields such as thermal diffusion, mechanics of continuous media, electromagnetism and multi-physics problems. Recently, there has been growing interest among researchers in the application of fractional derivatives. In this paper, we present a generalization of the FE method known as the conformable finite element method, which is specifically designed to solve conformable fractional partial differential equations (CF-PDE). We introduce the basis functions that are used to approximate the solution of CF-PDE and provide error estimation techniques. Furthermore, we provide an illustrative example to demonstrate the effectiveness of the proposed method. This work serves as a starting point for tackling more complex problems involving fractional derivatives.&lt;/p&gt;&lt;/abstract&gt;

Performance of Inexpensive Local Error Estimation Techniques for Integral Equation Numerical Solutions

The performance of several inexpensive local error estimation techniques is evaluated in connection with the Rao-Wilton-Glisson method of moments numerical solutions of the electric field integral equation. Results for 18 perfectly conducting test targets are used to evaluate the performance of the estimators. Two of the estimators produce error maps that consistently exhibit high correlations with reference solutions. These estimators are also suitable for “goal-oriented” estimation of secondary quantities, such as identifying cells that contribute the most error to the radar cross section of the target.

Optimal Fractional Pilot Duration for a Correlated Receive Diversity Reliable PLC System With Imperfect CSI in Nakagami-m Noise Environment

The paper presents a single-input-multiple-output-based power line communication (PLC) system employing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${M}$ </tex-math></inline-formula> -ary phase-shift keying signaling for data transmission, with the channels subjected to correlated Rayleigh multipath channels and corrupted by Nakagami- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${m}$ </tex-math></inline-formula> noise environment. The channel state information for the PLC system is obtained prior to data transmission using the minimum mean square error estimation technique, utilizing which a maximum likelihood-based sub-optimal receiver is proposed. The closed-form expression for the symbol error probability (SEP) is derived, for the cases of the channels following exponential and uniform correlations, using a characteristic function approach. Furthermore, the optimal pilot symbol duration is obtained to maximize the normalized error-free data rate of the system, which simultaneously saves on the energy of the pilot symbols and reduces the SEP of the data symbols. The numerical results demonstrate the effect of variation of different system parameters such as signal-to-noise ratio, channel diversity, pilot symbol quality, correlation factor, and the noise shape parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${m}$ </tex-math></inline-formula> of the background noise on the maximum normalized error-free data rate and thereby providing various insights into the system design for a reliable and energy-efficient PLC system with imperfect knowledge of the channels at the receiver.