Corpus ID: 218613675

Nonparametric regression for locally stationary random fields under stochastic sampling design

@article{Kurisu2020NonparametricRF,
  title={Nonparametric regression for locally stationary random fields under stochastic sampling design},
  author={Daisuke Kurisu},
  journal={arXiv: Statistics Theory},
  year={2020}
}
In this study, we develop an asymptotic theory of nonparametric regression for locally stationary random fields (LSRFs) $\{{\bf X}_{{\bf s}, A_{n}}: {\bf s} \in R_{n} \}$ in $\mathbb{R}^{p}$ observed at irregularly spaced locations in $R_{n} =[0,A_{n}]^{d} \subset \mathbb{R}^{d}$. We first derive the uniform convergence rate of general kernel estimators, followed by the asymptotic normality of an estimator for the mean function of the model. Moreover, we consider additive models to avoid the… Expand
3 Citations
ESTIMATION OF TIME-VARYING CHARACTERISTICS OF LOCALLY STATIONARY FUNCTIONAL TIME SERIES
This paper develops an asymptotic theory for estimating the time-varying characteristics of locally stationary functional time series. We introduce a kernel-based method to estimate the time-varyingExpand
Nonparametric regression for locally stationary functional time series
In this study, we develop an asymptotic theory of nonparametric regression for a locally stationary functional time series. First, we introduce the notion of a locally stationary functional timeExpand
On the estimation of locally stationary functional time series
This study develops an asymptotic theory for estimating the time-varying characteristics of locally stationary functional time series. We introduce a kernel-based method to estimate the time-varyingExpand

References

SHOWING 1-10 OF 105 REFERENCES
The Frequency Domain
uirliioso of fhe freqriericy clrmoiri attd true hero to the eigineering profession.
The existence and asymptotic properties
  • mixing random fields. J. Multivaraite Anal
  • 1999
Nonparametric regression for locally stationary time series
In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time seriesExpand
Central limit theorems for weighted sum of a spatial process under a class of stochastic and fixed design
  • Sankhya Ser. A
  • 2003
A Likelihood Approximation for Locally Stationary Processes
A new approximation to the Gaussian likelihood of a multivariate locally stationary process is introduced. It is based on an approximation of the inverse of the covariance matrix of such processes.Expand
Inference on Causal and Structural Parameters using Many Moment Inequalities
This article considers the problem of testing many moment inequalities where the number of moment inequalities, denoted by $p$, is possibly much larger than the sample size $n$. There is a variety ofExpand
Additive processes and stochastic integrals
Stochastic integrals of nonrandom $(l\times d)$-matrix-valued functions or nonrandom real-valued functions with respect to an additive process $X$ on $\mathbb{R}^d$ are studied. Here an additiveExpand
Continuous-time ARMA processes
Continuous-time autoregressive (CAR) processes have been of interest to physicists and engineers for many years (see e.g., Fowler, 1936 ). Early papers dealing with the properties and statisticalExpand
Continuous-time ARMA processes, Handbook of Statistics: Stochastic
  • 2000
Fitting time series models to nonstationary processes
A general minimum distance estimation procedure is presented for nonstationary time series models that have an evolutionary spectral representation. The asymptotic properties of the estimate areExpand
...
1
2
3
4
5
...