This work is concerned with the homogenization problem for singularly perturbed stochastic wave equations. Under the assumption that the coefficients are only Hölder continuous, we prove the weak convergence of the original system to a limit equation with an extra Gaussian term by using the technique of Poisson equation in Hilbert space. The optimal convergence rate is also obtained.
We establish a Cramér type moderate deviation for random walks conditioned to stay positive, which gives the relative error for the central limit theorem proved by Iglehart (1974). Unlike the traditional technique of conjugate distributions, our approach is based on the strong approximation between random walks and Brownian motion in the same vein as Grama and Xiao (2021).
In research fields such as financial market analysis and social network research, understanding variable grouping relationships is fundamental to effective data analysis. This study describes the concept of the covariance tensor and emphasizes its significant role in analyzing matrix variable groupings through block structures. We propose a novel tensor decomposition-based method to exploit these structures for group identification. In addition, we explore the asymptotic properties of our estimators, focusing on the precision of the estimation of the number of groups and the asymptotic convergence of classification error rates to zero. We validate the effectiveness of the method through extensive numerical simulations across diverse data volumes and complexities, affirming its capability in variable grouping.
Our goal is to estimate the characteristic exponent of the input to a Lévy-driven storage system from a sample of equispaced workload observations. The estimator relies on an approximate moment equation associated with the Laplace-Stieltjes transform of the workload at exponentially distributed sampling times. The estimator is pointwise consistent for any observation grid. Moreover, a high frequency sampling scheme yields asymptotically normal estimation errors for a class of input processes. A resampling scheme that uses the available information in a more efficient manner is suggested and assessed via simulation experiments.
We propose new joint tests of the semiparametric conditional independence assumption and provide their asymptotic properties. To overcome the problem caused by the parameter estimation effect, we employ a convenient multiplier bootstrap to approximate the limiting distributions of the test statistics.
This paper considers a risk model driven by a spectrally negative Lévy process, where any surplus above () is deducted away as dividends and any deficit is covered by injected capitals/raised money. For such a risk model, we define a variant of Parisian ruin time as the first time that the surplus process stays continuously below () for a time interval with length larger than some pre-specified exponential random variable that is marked on this time interval. A recursive formula for the moments of the Net Present Value (NPV) of dividends paid until Parisian ruin is provided. The expected NPV of capitals injected until the Parisian ruin time is also characterized compactly in terms of the scale functions of the underlying process.
A number of absolute moment-based upper bounds for Gini’s mean difference are extended to general L-moments. Improvement of some bounds by alternative choice of centre for the absolute moments is explored. Different bounds are compared numerically. The distribution for which upper bounds for Gini’s mean difference are attained is given. Extension is made to trimmed L-moments and hence to probability weighted moments.
This work deals with the problem of nonparametric estimation of a regression function when the response variable may be missing according to a not-missing-at-random (NMAR) setup. To assess the theoretical performance of our estimators, we study their strong convergence properties in norms where we also look into their rates of convergence. We also study applications of our results to the problem of statistical classification in semi-supervised learning.
We propose specification tests for parametric quantile regression models versus semiparametric alternatives over a continuum of quantile levels. The test statistics are constructed as continuous functionals of a quantile-marked residual process. We show that using an orthogonal projection on the tangent space of nuisance parameters at each quantile index delivers unified asymptotic properties for tests based on different estimators. Consistency of the tests and asymptotic power under a sequence of local alternatives converging to the null at a parametric rate are also discussed. We propose a simple multiplier bootstrap procedure to carry out the tests, whose nominal levels are well approximated in our simulation study for modest sample sizes.
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