Approximate Estimation Research Articles

Semiparametric approach to estimation of marginal mean effects and marginal quantile effects

We consider a semiparametric generalized linear model and study estimation of both marginal mean effects and marginal quantile effects in this model. We propose an approximate maximum likelihood estimator, and rigorously establish the consistency, the asymptotic normality, and the semiparametric efficiency of our method in both the marginal mean effect and the marginal quantile effect estimation. Simulation studies are conducted to illustrate the finite sample performance, and we apply the new tool to analyze a Swiss non-labor income data and discover a new interesting predictor.

On a generalization of the extended best polynomial approximation operator in Orlicz–Lorentz spaces

AbstractIn this paper, we consider the best polynomial approximation operator defined on an Orlicz–Lorentz space , and its extension to , where w is a non‐negative continuous weight function and is the derivative of ϕ, which is not required to be an Orlicz function. Our work generalizes a recent result in this field on an Orlicz–Lorentz space generated by an Orlicz function. In addition, we establish some properties and estimates for any extended best polynomial approximation.

Choice of degree of Bernstein polynomial model

Methods based on moments and modes for choosing Bernstein polynomial model degree are proposed. Simulation showed that the mean integrated square errors of the maximum approximate Bernstein likelihood estimates of density using degrees selected by the proposed methods and the change-point method are smaller than that of the kernel density but either closer to or smaller than that of the parametric maximum likelihood estimator.

Effective estimation of nonlinear errors-in-variables models

Model variables are inevitably affected and interfered by measurement errors in statistical models inference. In this paper, we investigate the effective estimators of unknown operators in the nonlinear errors-in-variables models. By combining the maximum quasi-likelihood approach and the nonparametric local estimation method, a modified approximate maximum quasi-likelihood estimators are applied to evaluate the unknown parameters of the models. Under some mild assumptions, the consistency and asymptotic normality of the corresponding estimators are established. In order to further illustrate the advantages of the modified approach, we utilize simulation examples and actual data of monozygotic twins for analysis. The results visually show the robustness of the modified estimator as well as higher precision and accuracy.

Physics-guided identification of Euler–Bernoulli beam PDE model from full-field displacement response with SimultaNeous basis function Approximation and Parameter Estimation (SNAPE)

Full-field measurements of the continuous spatiotemporal response of the physical processes such as structural vibration or fluid flow generate large datasets. In many scientific fields, such continuous spatiotemporal dynamic models are represented by partial differential equations (PDEs). In the past, attempts have been made to identify the PDE models from the measured response by inferring its parameters by the use of either regression or deep learning-based techniques. But the previously presented regression-based methods fail to estimate the parameters of the higher-order PDE models in the presence of moderate noise. Likewise, the deep learning-based methods lack the much-needed property of repeatability and robustness in the identification of PDE models from the measured response. The authors introduced the method of SimultaNeous Basis Function Approximation and Parameter Estimation (SNAPE) in a recent paper which addresses such drawbacks by fitting basis functions to the measured response and simultaneously infer the parameters of the PDE model. In this paper the theory and formulation of SNAPE is presented to perform physics-guided identification of the Euler–Bernoulli beam PDE model which is widely applied in the modeling of large scale infrastructures to nanoscale structures.The domain knowledge of the physics is used as a constraint in the formulation of the optimization framework. The alternating direction method of multipliers (ADMM) algorithm is used to simultaneously optimize the loss function over the parameter space of the PDE model and coefficient space of the basis functions. The proposed method not only infers the parameters but also estimates a continuous function that approximates the solution to the PDE model. The efficacy of the method is both numerically and experimentally validated on noise corrupted full-field vibration response. The method neither requires the knowledge of the initial or boundary conditions of the beam nor comprises of model discretization error as in the case of finite element model updating. SNAPE demonstrates its applicability on various homogeneous and time-varying nonhomogeneous boundary conditions.

A novel geometric AR(1) model and its estimation

This paper proposes a first-order geometric autoregressive model based on a new thinning operator. The parameters of the model are estimated by the method of Two-Stage Conditional Least Squares and Saddlepoint Approximation. Simulation studies demonstrate that the saddlepoint approximation estimator performs well, even in the case of small sample sizes. To illustrate the significance of the model, a real data analysis of the number of downloads of a TeX editor is presented.

Higher-order time domain boundary elements for elastodynamics: graded meshes and hp versions

The solution to the elastodynamic equation in the exterior of a polyhedral domain or a screen exhibits singular behavior from the corners and edges. The detailed expansion of the singularities implies quasi-optimal estimates for piecewise polynomial approximations of the Dirichlet trace of the solution and the traction. The results are applied to hp and graded versions of the time domain boundary element method for the weakly singular and the hypersingular integral equations. Numerical examples confirm the theoretical results for the Dirichlet and Neumann problems for screens and for polygonal domains in 2d. They exhibit the expected quasi-optimal convergence rates and the singular behavior of the solutions.

Jacobian spectral collocation method for spatio-temporal coupled Fokker-Planck equation with variable-order fractional derivative

Fractional Fokker–Planck equation plays an important role in describing anomalous dynamics. In this paper, we consider a spectral method for the spatio-temporal coupled fractional Fokker-Planck equation with variable-order fractional derivative. After introducing a suitable intermediate variable, the original equation can be split into two parts and decoupled. Then a spectral collocation method is employed to the resulting equation. Specifically, the points collocated both in temporal and spatial domains are related to fractional Jacobi functions, and the so-called fractional interpolation functions are used as basis functions for temporal semi-discretization. A recurrence relation is derived for fast generation of the fractional differentiation matrix. Regularity analysis for the solution as well as the convergence estimates for the spectral approximation are established for the constant-order case. Several numerical tests demonstrate the efficiency of the method and support the theoretical results.

Algorithms and Software for Numerical Estimation of Posinomial Regression Models Using the Least Squares Method

The article is devoted to the construction of posinomial regression models with several monomes for each input variable. Such models generalize well-known polynomial regressions. Investigated by a posin with one variable and two monomes. The algorithm «A» of approximate estimation of posinomial regressions using the least squares method is proposed. The main disadvantage of the algorithm «A» is that due to the inter-monomic multicollinearity, the estimated posinomial regression may not be consistent with the meaningful meaning of the factors included in it. Therefore, algorithm «B» was developed, which guarantees not only the preservation of the meaningful meaning of the factors, but also the significance of all posinomial regression coefficients according to the Student's t-criterion. Algorithm «B» was implemented in the form of the POSITON-1 software package. The work of the software package is demonstrated by the example of solving a specific applied problem.

Modelling of ship resistance and power consumption for the global fleet: The MariTEAM model

A system that can reliably estimate power consumption based on operational profiles and weather conditions is needed to evaluate global shipping emissions and alternative reduction scenarios. Due to a lack of detailed ship information, uncertainties in collected data, and computing complexity, many prior bottom-up investigations used simplified calculations and empirical equations. Some methodologies offered only approximate estimates that were not enough to capture power consumption trends based on the global fleet’s geographical, seasonal, and operational features. This work intends to develop and implement a power prediction method that can be applied in a bottom-up approach based on fleet composition and trading patterns. We present a comprehensive approach for powering prediction, encompassing data pre-processing, ship resistance estimation, and propulsion efficiency, based on the Maritime Transport Environmental Assessment Model. The model’s predictions match well with full-scale measurements of three operating ships and 2018 EU-MRV (European Union-Monitoring, Reporting, and Verification) data on annual fuel consumption and emissions for ships. The average error with the MRV data on annual CO2 emissions is below the median of 3% and the semi-interquartile range of 14%. Thus, the proposed model can be used to simulate the power performance and energy consumption of worldwide shipping.

Sharp error estimates for spatial-temporal finite difference approximations to fractional sub-diffusion equation without regularity assumption on the exact solution

Finite difference method as a popular numerical method has been widely used to solve fractional diffusion equations. In the general spatial error analyses, an assumption $$u\in C^{4}({\bar{\varOmega }})$$ is needed to preserve $${\mathcal {O}}(h^{2})$$ convergence when using central finite difference scheme to solve fractional sub-diffusion equation with Laplace operator, but this assumption is somewhat strong, where u is the exact solution and h is the mesh size. In this paper, a novel analysis technique is proposed to show that the spatial convergence rate can reach $${\mathcal {O}}(h^{\min (\sigma +\frac{1}{2}-\epsilon ,2)})$$ in both $$l^{2}$$ -norm and $$l^{\infty }$$ -norm in one-dimensional domain when the initial value and source term are both in $${\dot{H}}^{\sigma }(\varOmega )$$ but without any regularity assumption on the exact solution, where $$\sigma \ge 0$$ and $$\epsilon >0$$ being arbitrarily small. After making slight modifications on the scheme, acting on the initial value and source term, the spatial convergence rate can be improved to $${\mathcal {O}}(h^{2})$$ in $$l^{2}$$ -norm and $${\mathcal {O}}(h^{\min (\sigma +\frac{3}{2}-\epsilon ,2)})$$ in $$l^{\infty }$$ -norm. It is worth mentioning that our spatial error analysis is applicable to high dimensional cube domain by using the properties of tensor product. Moreover, two kinds of averaged schemes are provided to approximate the Riemann–Liouville fractional derivative, and $${\mathcal {O}}(\tau ^{2})$$ convergence is obtained for all $$\alpha \in (0,1)$$ . Finally, some numerical experiments verify the effectiveness of the built theory.

Whole-Body Composition Features by Computed Tomography in Ovarian Cancer: Pilot Data on Survival Correlations.

The primary objective of this study was to assess the associations of computed tomography (CT)-based whole-body composition values with overall survival (OS) and progression-free survival (PFS) in epithelial ovarian cancer (EOC) patients. The secondary objective was the association of body composition with chemotherapy-related toxicity. Thirty-four patients (median age 64.9 years; interquartile range 55.4-75.4) with EOC and thorax and abdomen CT scans were included. Clinical data recorded: age; weight; height; stage; chemotherapy-related toxicity; and date of last contact, progression and death. Automatic extraction of body composition values was performed by dedicated software. Sarcopenia was defined according to predefined cutoffs. Statistical analysis included univariate tests to investigate associations of sarcopenia and body composition with chemotoxicity. Association of body composition parameters and OS/PFS was evaluated by log-rank test and Cox proportional hazard model. Multivariate models were adjusted for FIGO stage and/or age at diagnosis. We found significant associations of skeletal muscle volume with OS (p = 0.04) and PFS (p = 0.04); intramuscular fat volume with PFS (p = 0.03); and visceral adipose tissue, epicardial and paracardial fat with PFS (p = 0.04, 0.01 and 0.02, respectively). We found no significant associations between body composition parameters and chemotherapy-related toxicity. In this exploratory study, we found significant associations of whole-body composition parameters with OS and PFS. These results open a window to the possibility to perform body composition profiling without approximate estimations.

A finite element approximation to a viscoelastic Euler–Bernoulli beam with internal damping

We analyze a finite element approximation to a viscoelastic Euler–Bernoulli beam with internal damping that undergoes vibrations under external excitation. We prove the wellposedness of the problem and regularity estimates of the exact solution to the model. We then utilize these results to prove an optimal-order error estimate of the numerical approximation assuming only the regularity of the data of the model but not that of the exact solution. Because the model exhibits its salient features that are different from those of conventional elastic Euler–Bernoulli beams, a new estimate technique is used in the analysis. We finally carry out numerical experiments to substantiate the error estimate and to investigate the dynamic response of the viscoelastic Euler–Bernoulli beam, in comparison with the conventional Euler–Bernoulli beam.

Method of Particular Solutions for Second-Order Differential Equation with Variable Coefficients via Orthogonal Polynomials

In this paper, with classic Legendre polynomials, a method of particular solutions (MPS, for short) is proposed to solve a kind of second-order differential equations with a variable coefficient on a unit interval. The particular solutions, satisfying the natural Dirichlet boundary conditions, are constructed with orthogonal Legendre polynomials for the variable coefficient case. Meanwhile, we investigate the a-priori error estimates of the MPS approximations. Two a-priori error estimations in H 1 - and L ∞ -norms are shown to depict the convergence order of numerical approximations, respectively. Some numerical examples and convergence rates are provided to validate the merits of our proposed meshless method.

Regression analysis of mixed panel count data with dependent observation processes

Event history data commonly occur in many areas and a great deal of literature on their analysis has been established. However, most of the existing methods apply only to a single type of event history data. Recently, several authors have discussed the analysis of mixed types of event history data and the existence of dependent observation processes is another issue that one often has to deal with in the analysis of event history data. This paper discusses regression analysis of mixed panel count data with dependent observation processes, which has not been addressed in the literature, and for the problem, an approximate likelihood estimation approach is proposed. For the implementation, an EM algorithm is developed and the proposed estimators are shown to be consistent and asymptotically normal. An extensive simulation study is performed to assess the performance of the proposed approach and indicates that it works well in practical situations. An application to a set of real data is provided.

АНАЛІЗ ТА ОЦІНКА ОБСЯГІВ ФІНАНСУВАННЯ ВІДНОВЛЕННЯ ТРАНСПОРТНОЇ ТА ЦИВІЛЬНОЇ ІНФРАСТРУКТУРИ УКРАЇНИ

Introduction. Critical infrastructure, including transport and civilian infrastructure, is one of the determining factors for the stable and efficient functioning of the economy and development of the state. In this regard, in order to organize the restoration and modernization of Ukrainian infrastructure damaged as a result of Russian aggression, it is extremely important to determine the necessary amount of funding for these works, which will provide more favorable conditions for determining the sources of funding, timing and appropriate resources for their implementation. Problem Statement. A wide range of damage and destruction has been sustained by a fairly large number of transport and civilian infrastructure facilities, making it impossible to determine their exact extent. At present, generalized statistics on the scale of such losses are mostly known. Therefore, the development of methodological approaches to building approximation estimates of the required amount of funding for the restoration and modernization of Ukrainian transport and civil infrastructure is quite relevant from both a scientific and practical point of view. Purpose. To develop a mathematical model and an appropriate algorithm for calculating an approximation of the required amount of funding for the restoration and modernization of transport and civil infrastructure. To analyze the data on the extent of their destruction and damage caused by the Russian aggression. Materials and Methods. Statistical data and generalized estimates of the extent of damage and destruction of Ukraine's transport and civilian infrastructure. Expert estimates of the costs of restoring infrastructure. Methods of mathematical modeling, systematic and statistical analysis of losses to the country's economy. Results. The data on the volume of destruction and damage to the main objects of transport and civil infrastructure of Ukraine were analyzed. On the basis of the proposed approach, approximations of the amount of funding required for their restoration are calculated. Conclusion. The results of the study show that direct costs for the restoration of transport and civil infrastructure will amount to more than $ 252.2 billion, and, accordingly, indirect costs, taking into account the coefficient of 1.2 – $ 302.6 billion. Thus, in the coming years, it is necessary to ensure the implementation of modernization and restoration of Ukrainian infrastructure totaling more than $ 554.8 billion.

Consistency results for the dual-wind discontinuous Galerkin method

This paper further analyzes the dual-wind discontinuous Galerkin (DWDG) method for approximating Poisson’s problem by directly examining the relationship between the Laplacian and the underlying discrete Laplacian. DWDG methods are derived from the DG differential calculus framework that defines discrete differential operators to replace continuous differential operators. We establish a priori error estimates for the DWDG approximation of Δ. Since the DWDG method does not satisfy a Galerkin orthogonality condition, we also explore the relationship between the DWDG approximation and the Ritz projection defined to satisfy an exact Galerkin orthogonality condition linked to the DWDG method. Numerical experiments are provided to validate the theoretical results.

Approximate maximum likelihood time-delay estimation for two closely spaced sources

The study of ground reflections of Global Navigation Satellite System (GNSS) signals, as in GNSS Reflectometry (GNSS-R) can lead to the receiver height estimation. The latter is estimated by comparing the time of arrival difference between the direct and reflected signals, also called path separation. In ground-based scenarios, this path separation can be very small, inducing important interference between paths, which makes it difficult to correctly obtain altimetry products. The path separation estimation can be obtained by a brute force dual source maximum likelihood estimator (2S-MLE), but this solution has a large computational cost. On the other hand, the path separation is so small that a number of approximations can be done. In this study, a third order Taylor approximation of the dual source likelihood criterion is proposed to reduce its complexity. The proposed algorithm performance is compared to the non approximated 2S-MLE for the estimation of the path separation, and to a standard single source processing for the estimation of the direct signal time-delay. These results, along with the corresponding lower bounds, prove that the proposed approach may be of interest for two applications: ground-based GNSS-R altimetry (or radar with low elevation targets) and GNSS multipath mitigation.

Unsupervised mixture estimation via approximate maximum likelihood based on the Cramér - von Mises distance

Mixture distributions with dynamic weights are an efficient way of modeling loss data characterized by heavy tails. However, maximum likelihood estimation of this family of models is difficult, mostly because of the need to evaluate numerically an intractable normalizing constant. In such a setup, simulation-based estimation methods are an appealing alternative. The approximate maximum likelihood estimation (AMLE) approach is employed. It is a general method that can be applied to mixtures with any component densities, as long as simulation is feasible. The focus is on the dynamic lognormal-generalized Pareto distribution, and the Cramér - von Mises distance is used to measure the discrepancy between observed and simulated samples. After deriving the theoretical properties of the estimators, a hybrid procedure is developed, where standard maximum likelihood is first employed to determine the bounds of the uniform priors required as input for AMLE. Simulation experiments and two real-data applications suggest that this approach yields a major improvement with respect to standard maximum likelihood estimation.

Automating NISQ Application Design with Meta Quantum Circuits with Constraints (MQCC)

Near-term intermediate scale quantum (NISQ) computers are likely to have very restricted hardware resources, where precisely controllable qubits are expensive, error-prone, and scarce. Programmers of such computers must therefore balance trade-offs among a large number of (potentially heterogeneous) factors specific to the targeted application and quantum hardware. To assist them, we propose Meta Quantum Circuits with Constraints (MQCC) , a meta-programming framework for quantum programs. Programmers express their application as a succinct collection of normal quantum circuits stitched together by a set of (manually or automatically) added meta-level choice variables, whose values are constrained according to a programmable set of quantitative optimization criteria. MQCC’s compiler generates the appropriate constraints and solves them via an SMT solver, producing an optimized, runnable program. We showcase a few MQCC’s applications for its generality including an automatic generation of efficient error syndrome extraction schemes for fault-tolerant quantum error correction with heterogeneous qubits and an approach to writing approximate quantum Fourier transformation and quantum phase estimation that smoothly trades off accuracy and resource use. We also illustrate that MQCC can easily encode prior one-off NISQ application designs- –multi-programming (MP) , crosstalk mitigation (CM) —as well as a combination of their optimization goals (i.e., a combined MP-CM).