Moment Conditions Research Articles

Modeling to COVID-19 and cancer data: Using the generalized Burr-Hatke model

This paper describes an extended version of the Burr–Hatke distribution via generalizing its survival function. This model is called as the generalized Burr-Hatke distribution. The suggested model's hazard rate function can be non-increasing (decreasing) form. Related statistical characteristics of the proposed model are identified. We provide closed-form expressions for the density function, hazard rate function, moments and their related metrics. In addition, some of the proposed model's reliability attributes, such as mean residual life and mean inactivity time, are determined both empirically and visually. The characterization of GBH model based on hazard rate, truncated and conditional moments is also provided. The maximum likelihood technique is employed for estimating the unknown model parameters. To explore the behavior of the estimates, Monte Carlo Simulation can be used. Finally, the new model's performance is verified using two sets of real data.

Estimation and hypothesis test for varying coefficient single-index multiplicative models

ABSTRACT Estimation and hypothesis test for varying coefficient single-index multiplicative models are considered in this paper. To estimate an unknown single-index parameter, a profile product relative error estimation is proposed for the single-index parameter with a leave-one-component-out estimation method. A Wald-type test statistic is proposed to test a linear hypothesis test of the single-index. We employ the smoothly clipped absolute deviation penalty to simultaneously select variables and estimate regression coefficients. To study the model checking problem, we propose a variant of the integrated conditional moment test statistic by using a linear projection weighting function, and we also suggest a bootstrap procedure for calculating critical values. Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analysed for illustration.

Asymptotic Efficiency of Joint Estimator Relative to Two-Stage Estimator Under Misspecified Likelihoods

Abstract The two-stage estimator is often more tractable when there are nuisance parameters that can be separately estimated and plugged into an objective function. The joint estimator tends to bear the higher computational cost since it estimates all parameters in one stage by optimizing the sum of objective functions used in the two stages. It is well-known that the joint estimator is asymptotically more efficient than the two-stage estimator if the objective function is the true log-likelihood. When the objective function is not the true log-likelihood, I show that the relative asymptotic efficiency of the joint estimator still holds under a finite number of testable moment conditions. The implications of the main result on models based on quasi-limited information likelihoods are discussed.

On duration effects in non-life insurance pricing

The paper discusses duration effects on the consistency of mean parameter and dispersion parameter estimators in exponential dispersion families (EDFs) that are the standard models used for non-life insurance pricing. Focus is on the standard generalised linear model assumptions where both the mean and variance, conditional on duration, are linear functions in terms of duration. We derive simple convergence results that highlight consequences when the linear conditional moment assumptions are not satisfied. These results illustrate that: (i) the resulting mean estimators always have a relevant asymptotic interpretation in terms of the duration adjusted actuarially fair premium—a premium that only agrees with the standard actuarial premium using a duration equal to one, given that the expected value is linear in the duration; (ii) deviance based estimators of the dispersion parameter in an EDF should be avoided in favour of Pearson estimators; (iii) unless the linear moment assumptions are satisfied, consistency of dispersion and plug-in variance estimators can not be guaranteed and may result in spurious over-dispersion. The results provide explicit conditions on the underlying data generating process that will lead to spurious over-dispersion that can be used for model checking. This is illustrated based on real insurance data, where it is concluded that the linear moment assumptions are violated, which results in non-negligible spurious over-dispersion.

Goodness-of-fit tests for the one-sided Lévy distribution based on quantile conditional moments

In this paper we introduce a novel statistical framework based on the first two quantile conditional moments that facilitates effective goodness-of-fit testing for one-sided Lévy distributions. The scale-ratio framework introduced in this paper extends our previous results in which we have shown how to extract unique distribution features using conditional variance ratio for the generic class of α-stable distributions. We show that the conditional moment-based goodness-of-fit statistics are a good alternative to other methods introduced in the literature tailored to the one-sided Lévy distributions. The usefulness of our approach is verified using an empirical test power study. For completeness, we also derive the asymptotic distributions of the test statistics and show how to apply our framework to real data.

Measure-valued affine and polynomial diffusions

We introduce a class of measure-valued processes, which – in analogy to their finite dimensional counterparts – will be called measure-valued polynomial diffusions. We show the so-called moment formula, i.e. a representation of the conditional marginal moments via a system of finite dimensional linear PDEs. Furthermore, we characterize the corresponding infinitesimal generators obtaining a representation analogous to polynomial diffusions on R+m, in cases where their domain is large enough. In general the infinite dimensional setting allows for richer specifications strictly beyond this representation. As a special case, we recover measure-valued affine diffusions, sometimes also called Dawson–Watanabe superprocesses. From a mathematical finance point of view, the polynomial framework is especially attractive since it allows to transfer many famous finite dimensional models and their tractability properties to an infinite dimensional measure-valued setting.

HETEROSKEDASTICITY ROBUST SPECIFICATION TESTING IN SPATIAL AUTOREGRESSION

Spatial autoregressive (SAR) and related models offer flexible yet parsimonious ways to model spatial and network interactions. SAR specifications typically rely on a particular parametric functional form and an exogenous choice of the so-called spatial weight matrix with only limited guidance from theory in making these specifications. Also, the choice of a SAR model over other alternatives, such as spatial Durbin (SD) or spatial lagged X (SLX) models, is often arbitrary, raising issues of potential specification error. To address such issues, this paper develops a new specification test within the SAR framework that can detect general forms of misspecification including that of the spatial weight matrix, the functional form and the model itself. The test is robust to the presence of heteroskedasticity of unknown form in the disturbances and the approach relates to the conditional moment test framework of Bierens ([1982, Journal of Econometrics 20, 105–134], [1990, Econometrica 58, 1443–1458]). The Bierens test is shown to be inconsistent in general against spatial alternatives and the new test introduces modifications to achieve test consistency in the spatial setting. A central element is the infinite-dimensional endogeneity induced by spatial linkages. This complexity is addressed by introducing a new component to the omnibus test that captures the effects of potential spatial matrix misspecification. With this modification, the approach leads to a simple pivotal test procedure with standard critical values that is the first test in the literature to have power against misspecifications in the spatial linkages. We derive the asymptotic distribution of the test under the null hypothesis of correct SAR specification and prove consistency. A Monte Carlo study is conducted to study its finite sample performance. An empirical illustration on the performance of the test in modeling tax competition in Finland is included.

Evolution and statement of the rural studies in Latin America

The structure and evolutionary dynamic of the rural world of Latin America has always been a privileged topic in research and scientific reflection, not only at the level of the continent, but also at the international level. Scientific production has always reflected the problems of this vast rural world, but always under the influence of the social, political, and economic conditions of each historical moment. In this paper, we analyze the current scientific production on the rural world with a historical perspective, to understand the evolution of scientific thought and production. We appeal to a very simple bibliometric method based on the analysis of the most prestigious journals about the rural reality of the continent. The analysis allows us to observe a clear trend towards new topics, linked to the problems of the rural world, such as the new relationship between the countryside and the city, environmental problems, the emergence of new ways of producing, among others.

Alpha–beta-power family of distributions with applications to exponential distribution

This article proposes a new way to increase the flexibility of a family of statistical distributions by adding two additional parameters. The newly proposed family is called the alpha–beta power transformation family of distributions. A specific model, the alpha–beta power exponential distribution, was thoroughly investigated. The hazard rates of the proposed distribution can be decreasing, bathtub-shaped, and unimodal. The derived structural features of the proposed model include explicit formulations for the quantiles, the moments, the moment-generating function, and the incomplete and conditional moments. In addition, estimates of maximum likelihood, least squares, weighted least squares, and minimum distance of Cramér von Mises, von Anderson–Darling, and right-tail Anderson–Darling are obtained for the unknown parameters. Two real data sets were examined to demonstrate the usefulness of the proposed approach.

Markovian analysis of U.S. Treasury volatility: Asymmetric responses to macroeconomic announcements

Extensive is the literature supporting the announcement effect of the release of pre-scheduled macroeconomic news on U.S. Treasuries conditional moments; nevertheless, none of them considered possible asymmetric responses to these news arrival depending on the latent regimes characterizing the U.S. economy. Owing to the peculiar U.S. interest rate environment over the last 23 years, not allowing for stochastic-switching states even in the GARCH-class models may miss important volatility pattern. Hence, the therein model proposes the first partitioning of Treasuries excess returns in different regimes (normal, crash and low-rate) through hidden Markov chains to, only in a subsequent moment, apply a conditional volatility GARCH-class model augmented by dummy variables accounting for macroeconomic release days. The same model is then re-run to assess the explanatory power of U.S. Treasury auctions within volatility modeling. Results point to a statistically significant and asymmetric effects imparted by both prescheduled macroeconomic releases and new issuances on U.S. Treasury excess returns depending on both the regime and the securities’ maturities, while evidencing the very different characteristics of GARCH and ARCH coefficients depending on the regime.

Randomized limit theorems for stationary ergodic random processes and fields

Using the randomization approach, introduced by A. Tempelman in Randomized multivariate central limit theorems for ergodic homogeneous random fields, Stochastic Processes and their Applications. 143 (2022), 89–105, we prove: (a) a randomized version of the invariance principle (the functional CLT); (b) a version the Glivenko–Cantelli theorem; (c) a randomized theorem about convergence of empirical processes to the Brownian bridge. We also weaken the moment condition in the randomized CLTs, proved in the mentioned article. The main point of our work is that most of our theorems are valid for all ergodic homogeneous random fields on Zm and Rm,m≥1.

On the Bivariate Extension of the Extended Standard U-quadratic Distribution

This paper derives the bivariate version of the extended standard U-quadratic (eSU) distribution using the method of compounding or pseudo family of distributions. The joint probability and cumulative distribution functions of the derived distribution are obtained and it is observed that the said distribution can generate bivariate shape with the following properties: $(i)$ $X$ and $Y$ have bathtub shapes; $(ii)$ $X$ has constant and $Y$ has bathtub shapes; and $(iii)$ $X$ has inverted bathtub and $Y$ has bathtub shapes. Moreover, some properties of the derived distribution such as the marginal distribution, conditional distributions, conditional moments, product and ratio moments are derived. Further, the maximum likelihood estimation is performed to estimate the parameters of the derived distribution. Also, a simulation study is carried out to evaluate the behavior of the estimates of the parameters. Moreover, we derive a new bivariate Kumaraswamy distribution and use it to simulate bivariate data with $X$ and $Y$ having bathtub shapes. Furthermore, A new bivariate version of the Cubic Transmuted Uniform (CTU) distribution is also derived. Finally, the proposed Bivariate eSU distribution is applied to simulated data and compared with the said Bivarite Cubic Transmuted Uniform distribution. The result shows that the proposed Bivariate eSU distribution provides a better fit for the said simulated dataset as compared with the Bivariate CTU distribution.

On the convergence of gradient descent for robust functional linear regression

Functional data analysis offers a set of statistical methods concerned with extracting insights from intrinsically infinite-dimensional data and has attracted considerable amount of attentions in the past few decades. In this paper, we study robust functional linear regression model with a scalar response and a functional predictor in the framework of reproducing kernel Hilbert spaces. A gradient descent algorithm with early stopping is introduced to solve the corresponding empirical risk minimization problem associated with robust loss functions. By appropriately selecting the early stopping rule and the scaling parameter of the robust losses, the convergence of the proposed algorithm is established when the response variable is bounded or satisfies a moment condition. Explicit learning rates with respect to both estimation and prediction error are provided in terms of regularity of the regression function and eigenvalue decay rate of the integral operator induced by the reproducing kernel and covariance function.

An approximated exponentially tilted empirical likelihood estimator of moment condition models

. This study proposes an approximated estimator for moment condition models. Our estimator approximates the exponentially tilted empirical likelihood (ETEL) estimator in Schennach (2007) by using a second-order approximation of implied probabilities (IPs) for the exponential tilting (ET). The resulting approximated ETEL estimator generates positive IPs. As the nested optimization of ETEL and EL is avoided, it is computationally simple. It is second-order asymptotically equivalent to the EL estimator. In particular, it has the same O(n −1) bias as EL. It also has the same O(n −2) variance as EL. Like ET and ETEL estimators, it is n convergent under model misspecification, while the EL estimator may not be.

A simple method to construct multivariate dual framelets with high-order vanishing moments

When constructing multivariate framelets, it is often unavoidable to work with matrices of multivariate trigonometric polynomials and complicated matrix decomposition problems. These problems become even harder when good properties such as high-order vanishing moments are required on the framelets. In this paper, we establish a new method for constructing multivariate dual framelets with high-order vanishing moments. The underlying scheme of our algorithm is the famous Mixed Extension Principle that allows us to derive the high-pass filters (or framelet generators) from a given pair of refinable filters with high-order linear-phase moments. Our method only involves two steps: (1) directly constructing the first few pairs of high-pass filters by using the linear-phase moment conditions of the refinement filters; (2) solving a system of linear equations to obtain the rest of the high-pass filters. Both are easy to implement for scientific computation, regardless of what dimension or dilation matrix we work with. Apart from high-order vanishing moments, we will see that if the refinement filters take coefficients from some subfield [Formula: see text] of [Formula: see text] that is closed under complex conjugation, so do the high-pass filters. Furthermore, our algorithm gives the upper bounds for the number of high-pass filters in arbitrary dimensions. At the end of the paper, we will give several illustrative examples, from which we can also see that the support sizes of the high-pass filters are comparable with those of the refinement filters.

VIX option pricing through nonaffine GARCH dynamics and semianalytical formula

AbstractThis paper develops analytical approximations for volatility index (VIX) option pricing under nonaffine generalized autoregressive conditional heteroskedasticity (GARCH) models as advocated by Christoffersen et al. We obtain the approximation formulae for pricing VIX options and then evaluate their performance with three expansions under four empirically well‐tested models. Our numerical experiments find that the weighted expansion generated by the fat‐tailed weighting kernel can significantly reduce approximation error over the Gram‐Charlier expansion; the Taylor expansion of conditional moments can lead to divergence for parameters with certain high persistence in the affine GARCH, nonlinear asymmetric GARCH, and Glosten‐Jagannathan‐Runkle GARCH models, while surviving during high persistence in the exponential GARCH.

A tri-variate moment projection method for multi-dimensional particle population balance dynamics

This study develops a tri-variate moment projection method (TVMPM) for solving particle dynamics problems governed by the population balance equations involving any three internal coordinates of particles, such as volume, surface area, component mass, etc. By leveraging the concept of conditional moments, the multi-dimensional moments are expressed as the product of marginal moments and several conditional moments, facilitating the solution of high-dimensional moments. To obtain abscissas and conditional weights in different dimensions for reconstructing moments, a three-dimensional (3-D) adaptive Blumstein-Wheeler algorithm is proposed and implemented, which can also improve the stability in the third dimension, where ill-conditioning issues are more likely to arise. More importantly, by fixing the smallest particle abscissas, TVMPM can directly track the weight of the smallest particles, thereby closing the shrinkage and fragmentation terms. An analysis of the sources of errors arising from this approach is also presented. To mitigate potential interference from external factors, constant kernels for inception, growth, coagulation, shrinkage and fragmentation are employed to validate the effectiveness of TVMPM. The resulting moments from TVMPM are computed for both individual and combined processes, and subsequently compared with the moments derived from the direct simulation algorithm (DSA). The results demonstrate that TVMPM maintains a high level of accuracy across various numbers of quadrature nodes for particle dynamics with 3-D internal coordinates, while significantly reducing computational efforts compared to DSA. This study reveals that the developed algorithms and framework are promising for further extending MPM to higher dimensions. Moreover, owing to its accuracy and efficiency, TVMPM shows great potential for implementation in computational fluid dynamics (CFD) for particle dynamics in realistic systems.

The Mechanics of Elastomeric Sheet Reinforced With Bidirectional Fiber Mesh Subjected to Flexure on Boundaries

Abstract We investigate the concurrent three-dimensional deformations of fiber-reinforced composite sheets subjected to out-of-plane bending moments via a continuum model, where we invoke the neo-Hookean strain energy model for the matrix material of fiber-reinforced composite, and assimilate the strain energy of fiber reinforcements into the matrix material model by accounting for stretching, bending, and twisting kinematics of the fibers through the computations of the first-order and second-order gradient of deformation. Emphasis is placed on deriving the Euler equation and boundary conditions of bending moment within the framework of the variational principle and configuring composite surfaces using differential geometry. Significant attention has been given to illustrating the concurrent three-dimensional deformation of fiber composite, meshwork deformation, and fiber kinematics. The simulation results reveal that for a square fiber composite subjected to the out-of-plane bending moment, the maximum in-plane deformation of matrix material occurs along the diagonal direction of the domain while the center of the domain experiences weak in-plane deformation. Notably, the matrix material performs isotropic/anisotropic properties depending on the domain size/shape. In addition, the simulated unit fiber deformations reasonably validate the overall deformation of the network, underscoring that the deformations of the embedded fiber units govern the overall mechanical performance of the fiber meshwork. More importantly, the continuum model qualitatively provides reasonable predictions on the damage patterns of construction materials by demonstrating the kinematics of matrix material and meshwork deformation.

Multiplier subsample bootstrap for statistics of time series

Block-based bootstrap, block-based subsampling and multiplier bootstrap are three common nonparametric tools for statistical inference under dependent observations. Combining the ideas of those three, a novel resampling approach, the multiplier subsample bootstrap (MSB), is proposed. Instead of generating a resample from the observations, the MSB imitates the statistic by weighting the block-based subsample statistics with independent standard Gaussian random variables. Given the asymptotic normality of the statistic, the bootstrap validity is established under some mild moment conditions. Involving the idea of MSB, the other resampling approach, the hybrid multiplier subsampling periodogram bootstrap (HMP), is developed for mimicking frequency-domain spectral mean statistics in the paper. A simulation study demonstrates that both the MSB and HMP achieve good performance.

Effectiveness of public health spending in Sub-Saharan Africa: The moderating role of health system efficiency

ABSTRACT Public health spending (PHS) has been extensively investigated concerning population health outcomes (PHO), but its effectiveness has been less analysed. To this end, this study examines the association between domestic general government health expenditure (DGGHE) and PHO in terms of disability-adjusted life year (DALY) while testing the role of health system efficiency (HSE) in its effects. The under-five mortality(U5MR) is also used in the analysis to assess the effectiveness of services. The study uses publicly available data from 2008 to 2018 across forty-three countries in SSA and applies the GMM estimator based on linear and nonlinear moment conditions. The findings indicate that an increase in DGGHE was significantly associated with a decrease in DALY and U5MR, with the lowest decrease in countries with the lowest HSE scores. Therefore, the study urges governments in SSA countries to consider mechanisms that enhance health system efficiency while planning interventions based on increased spending on health.