Related papers: Asymptotic theory for regression models with fract…
When predicting scalar responses in the situation where the explanatory variables are functions, it is sometimes the case that some functional variables are related to responses linearly while other variables have more complicated…
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…
We propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data, where both the predictor and response are functions of a covariate such as time. Predictor and response processes have smooth…
Classical mathematical statistics deals with models that are parametrized by a Euclidean, i.e. finite dimensional, parameter. Quite often such models have been and still are chosen in practical situations for their mathematical simplicity…
A general asymptotic theory is given for the panel data AR(1) model with time series independent in different cross sections. The theory covers the cases of stationary process, nearly non-stationary process, unit root process, mildly…
We revisit classical asymptotics when testing for a structural break in linear regression models by obtaining the limit theory of residual-based and Wald-type processes. First, we establish the Brownian bridge limiting distribution of these…
We consider the statistical experiment of functional linear regression (FLR). Furthermore, we introduce a white noise model where one observes an Ito process, which contains the covariance operator of the corresponding FLR model in its…
We study asymptotic behaviour of stochastic approximation procedures with three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function.…
This paper discusses the asymptotic behavior of regression models under general conditions. First, we give a general inequality for the difference of the sum of square errors (SSE) of the estimated regression model and the SSE of the…
The question whether a time series behaves as a random walk or as a station- ary process is an important and delicate problem, particularly arising in financial statistics, econometrics, and engineering. This paper studies the problem to…
We consider parameter estimation, hypothesis testing and variable selection for partially time-varying coefficient models. Our asymptotic theory has the useful feature that it can allow dependent, nonstationary error and covariate…
Non-standard distributional approximations have received considerable attention in recent years. They often provide more accurate approximations in small samples, and theoretical improvements in some cases. This paper shows that the…
This paper develops a general asymptotic theory for nonparametric kernel regression in the presence of cluster dependence. We examine nonparametric density estimation, Nadaraya-Watson kernel regression, and local linear estimation. Our…
In a growth-fragmentation system, cells grow in size slowly and split apart at random. Typically, the number of cells in the system grows exponentially and the distribution of the sizes of cells settles into an equilibrium 'asymptotic…
Some problems in the theory and applications of stochastic processes can be reduced to solving integral equations. While explicit solutions for these equations are often elusive, valuable insights can be gained through their asymptotic…
Consider estimation of the regression function based on a model with equidistant design and measurement errors generated from a fractional Gaussian noise process. In previous literature, this model has been heuristically linked to an…
We examine the time-dependent behavior of a nonlinear system driven by a two-frequency forcing. By using a non-perturbative approach, we are able to derive an asymptotic expression, valid in the long-time limit, for the time average of the…
We investigate asymptotic properties of least-absolute-deviation or median quantile estimates of the location and scale functions in nonparametric regression models with dependent data from multiple subjects. Under a general dependence…
The paper presents a systematic theory for asymptotic inference of autocovariances of stationary processes. We consider nonparametric tests for serial correlations based on the maximum (or ${\cal L}^\infty$) and the quadratic (or ${\cal…
We establish central and non-central limit theorems for sequences of functionals of the Gaussian output of an infinitely-wide random neural network on the d-dimensional sphere . We show that the asymptotic behaviour of these functionals as…