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This paper presents a class of Two-Step General Linear Methods for the numerical solution of Retarded Functional Differential Equations. Explicit methods up to order five are constructed. To avoid order reduction for mildly stiff problems…
Stability and error estimate for the Oseen equations in a projection based variational setup has been derived in this paper. The use of Geometric Conservation Law (GCL) provides unconditional stability whereas without using GCL we have a…
This paper develops a methodology for approximating the posterior first two moments of the posterior distribution in Bayesian inference. Partially specified probability models, which are defined only by specifying means and variances, are…
We consider the problem of estimating the common time of a change in the mean parameters of panel data when dependence is allowed between the panels in the form of a common factor. A CUSUM type estimator is proposed, and we establish first…
Differential equations are commonly used to model dynamical deterministic systems in applications. When statistical parameter estimation is required to calibrate theoretical models to data, classical statistical estimators are often…
We consider the class of all stationary Gaussian process with explicit parametric spectral density. Under some conditions on the autocovariance function, we defined a GMM estimator that satisfies consistency and asymptotic normality, using…
In recent years, orthogonal chirp division modulation (OCDM) has gained attention as a robust communication waveform due to its strong resistance to both time-domain and frequency-domain interference. However, similar to orthogonal…
Using backpropagation to compute gradients of objective functions for optimization has remained a mainstay of machine learning. Backpropagation, or reverse-mode differentiation, is a special case within the general family of automatic…
Variational inference has become an increasingly attractive fast alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, a major obstacle to the widespread use of variational methods is the lack of…
Adaptive gradient optimization methods, such as Adam, are prevalent in training deep neural networks across diverse machine learning tasks due to their ability to achieve faster convergence. However, these methods often suffer from…
This paper develops efficient GMM estimation when the moment conditions are misspecified. We observe that the influence function of the standard GMM estimator under misspecification depends on both the original moment conditions and their…
Stochastic gradient descent with momentum (SGDM) methods have become fundamental optimization tools in machine learning, combining the computational efficiency of stochastic gradients with the acceleration benefits of momentum. Despite…
Piecewise growth mixture models (PGMM) are a flexible and useful class of methods for analyzing segmented trends in individual growth trajectory over time, where the individuals come from a mixture of two or more latent classes. These…
Momentum methods have been shown to accelerate the convergence of the standard gradient descent algorithm in practice and theory. In particular, the minibatch-based gradient descent methods with momentum (MGDM) are widely used to solve…
Differentiable simulators promise faster computation time for reinforcement learning by replacing zeroth-order gradient estimates of a stochastic objective with an estimate based on first-order gradients. However, it is yet unclear what…
In this note we derive the backward (automatic) differentiation (adjoint [automatic] differentiation) for an algorithm containing a conditional expectation operator. As an example we consider the backward algorithm as it is used in Bermudan…
Generalized empirical likelihood and generalized method of moments are well spread methods of resolution of inverse problems in econometrics. Each method defines a specific semiparametric model for which it is possible to calculate…
Form factors of a simple system have been calculated in various forms of relativistic quantum mechanics, using a single-particle current. Their comparison has shown large discrepancies. The comparison is extended here to instant- and…
In this article, we propose a new method for calculating the mixed correlation coefficient (Pearson, polyserial and polychoric) matrix and its covariance matrix based on the GMM framework. We build moment equations for each coefficient and…
We study two procedures (reverse-mode and forward-mode) for computing the gradient of the validation error with respect to the hyperparameters of any iterative learning algorithm such as stochastic gradient descent. These procedures mirror…