Related papers: A specification test for nonlinear nonstationary m…
This paper provides a new theoretical lens for understanding the finite-sample performance of kernel-based specification tests, such as the Kernel Conditional Moment (KCM) test. Rather than introducing a fundamentally new test, we isolate…
Understanding statistical inference under possibly non-sparse high-dimensional models has gained much interest recently. For a given component of the regression coefficient, we show that the difficulty of the problem depends on the sparsity…
We investigate the behavior of Fourier transforms for a wide class of nonstationary nonlinear processes. Asymptotic central and noncentral limit theorems are established for a class of nondegenerate and degenerate weighted $V$-statistics…
Considering a regression model, we address the question of testing the nullity of the regression function. The testing procedure is available when the variance of the observations is unknown and does not depend on any prior information on…
The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…
Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…
Data-driven methods for modeling dynamic systems have received considerable attention as they provide a mechanism for control synthesis directly from the observed time-series data. In the absence of prior assumptions on how the time-series…
This article introduces a novel nonparametric methodology for Generalized Linear Models which combines the strengths of the binary regression and latent variable formulations for categorical data, while overcoming their disadvantages.…
A simple test is proposed for examining the correctness of a given completely specified response function against unspecified general alternatives in the context of univariate regression. The usual diagnostic tools based on residuals plots…
Researchers faced with a sequence of candidate model specifications must often choose the best specification that does not violate a testable identification assumption. One option in this scenario is sequential specification tests:…
Let $\{X_n, n \ge 1\}$ be a sequence of stationary associated random variables. We discuss another set of conditions under which a central limit theorem for U-statistics based on $\{X_n, n \ge 1\}$ holds. We look at U-statistics based on…
One reason why standard formulations of the central limit theorems are not applicable in high-dimensional and non-stationary regimes is the lack of a suitable limit object. Instead, suitable distributional approximations can be used, where…
Structure discovery in graphical models is the determination of the topology of a graph that encodes conditional independence properties of the joint distribution of all variables in the model. For some class of probability distributions,…
This paper develops a unified finite-time theory for the ordinary least squares estimation of possibly unstable and even slightly explosive vector autoregressive models under linear restrictions, with the applicable region $\rho(A)\leq…
We study goodness-of-fit testing for non-causal autoregressive time series with non-Gaussian stable noise. To model time series exhibiting sharp spikes or occasional bursts of outlying observations, the exponent of the non-Gaussian stable…
We consider functional linear regression models where functional outcomes are associated with scalar predictors by coefficient functions with shape constraints, such as monotonicity and convexity, that apply to sub-domains of interest. To…
In spatial statistics, kriging models are often designed using a stationary covariance structure; this translation-invariance produces models which have numerous favorable properties. This assumption can be limiting, though, in…
A time-varying empirical spectral process indexed by classes of functions is defined for locally stationary time series. We derive weak convergence in a function space, and prove a maximal exponential inequality and a…
This paper considers a general class of nonparametric time series regression models where the regression function can be time-dependent. We establish an asymptotic theory for estimates of the time-varying regression functions. For this…
This paper investigates the relationship between various measure-theoretic properties of U-statistics with fixed sample size $N$ and the same properties of their kernels. Specifically, the random variables are replaced with elements in some…