Related papers: Methods of Retrieving Large-Variable Exponents
In the present paper we consider the varying coefficient model which represents a useful tool for exploring dynamic patterns in many applications. Existing methods typically provide asymptotic evaluation of precision of estimation…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
Identifying causal effects in the presence of unmeasured variables is a fundamental challenge in causal inference, for which proxy variable methods have emerged as a powerful solution. We contrast two major approaches in this framework: (1)…
We present a new method for approximating real-valued functions on ${\mathbb R}^+$ by linear combinations of exponential functions with complex coefficients. The approach is based on a multi-point Pad\'e approximation of the Laplace…
Several methods to extract an asymmetry parameter in an event distribution function are discussed and compared in terms of statistical precision and applicability. These methods are: simple counting rate asymmetries, event weighting…
As technology advanced, collecting data via automatic collection devices become popular, thus we commonly face data sets with lengthy variables, especially when these data sets are collected without specific research goals beforehand. It…
High-dimensional complex systems can be studied through multivariate analysis, as Principal Component Analysis, however large samples of observations frequently are needed for it. Here it is examined a method for small samples based on…
Singularly-perturbed ordinary differential equations often exhibit Stokes' phenomenon, which describes the appearance and disappearance of oscillating exponentially small terms across curves in the complex plane known as Stokes curves.…
We obtain asymptotic for the quantity $\int_0^1 \bigg|\sum_{n\le X}\tau_k(n)e(n\alpha)\bigg|d\alpha$ where $\tau_k(n) = \sum_{d_1\dots d_k = n} 1$. This follows from a quick application of the circle method. Along the way, we find minor arc…
Composition methodologies in the current literature are mainly to promote estimation efficiency via direct composition, either, of initial estimators or of objective functions. In this paper, composite estimation is investigated for both…
In the context of a linear model with a sparse coefficient vector, exponential weights methods have been shown to be achieve oracle inequalities for prediction. We show that such methods also succeed at variable selection and estimation…
This paper studies optimal estimation of large-dimensional nonlinear factor models. The key challenge is that the observed variables are possibly nonlinear functions of some latent variables where the functional forms are left unspecified.…
We derive asymptotic expansions for the prices of a variety of European and barrier-style claims in a general local-stochastic volatility setting. Our method combines Taylor series expansions of the diffusion coefficients with an expansion…
We develop a model-based empirical Bayes approach to variable selection problems in which the number of predictors is very large, possibly much larger than the number of responses (the so-called 'large p, small n' problem). We consider the…
We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence…
We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…
We consider the estimation of densities in multiple subpopulations, where the available sample size in each subpopulation greatly varies. This problem occurs in epidemiology, for example, where different diseases may share similar…
We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms, focussing on the case of multiple, non-commensurate frequencies. We derive an asymptotic expansion in inverse powers of the…
We apply symmetry and invariance methods to analyse systems of difference equations. Non trivial symmetries are derived and their exact solutions obtained.
For a second-order linear differential equation with two irregular singular points of rank three, multiple Laplace-type contour integral solutions are considered. An explicit formula in terms of the Stokes multipliers is derived for the…