Based on the nonlinear system theory, we introduce previously undescribed dependence measures for stationary causal processes. Our physical and predictive quantify degree of outputs inputs in systems. The proposed provide a natural framework limit theory In particular, under conditions with quite simple forms, present theorems partial sums, empirical processes, kernel density estimates. are mild easily verifiable because they directly related to data-generating mechanisms.

Journal Article Nonparametric estimation of large covariance matrices longitudinal data Get access Wei Biao Wu, Wu Search for other works by this author on: Oxford Academic Google Scholar Mohsen Pourahmadi Biometrika, Volume 90, Issue 4, December 2003, Pages 831–844, https://doi.org/10.1093/biomet/90.4.831 Published: 01 2003

We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear some nonlinear are discussed. Strong laws large numbers the iterated logarithm also obtained under easily verifiable conditions.

We study geometric moment contracting properties of nonlinear time series that are expressed in terms iterated random functions. Under a Dini-continuity condition, central limit theorem for additive functionals such systems is established. The empirical processes sample paths shown to converge Gaussian the Skorokhod space. An exponential inequality present bound joint cumulants, which ensures applicability several asymptotic results spectral analysis series. Our provide vehicle statistical...

Summary We consider statistical inference of trends in mean non-stationary models. A test statistic is proposed for the existence structural breaks trends. On basis a strong invariance principle stationary processes, we construct simultaneous confidence bands with asymptotically correct nominal coverage probabilities. The results are applied to global warming temperature data and Nile river flow data. Our band trend series supports claim that increasing over last 150 years.

We consider the problem of approximating sums high dimensional stationary time series by Gaussian vectors, using framework functional dependence measure. The validity approximation depends on sample size $n$, dimension $p$, moment condition and underlying processes. also an estimator for long-run covariance matrices study its convergence properties. Our results allow constructing simultaneous confidence intervals mean vectors high-dimensional with asymptotically correct coverage...

We consider estimation of covariance matrices and their inverses (a.k.a. precision matrices) for high-dimensional stationary locally time series. In the latter case evolve smoothly in time, thus forming a matrix function. Using functional dependence measure Wu [Proc. Natl. Acad. Sci. USA 102 (2005) 14150-14154 (electronic)], we obtain rate convergence thresholded estimate illustrate how affects convergence. Asymptotic properties are also obtained which is based on graphical Lasso principle....

We present a systematic asymptotic theory for statistics of stationary time series.In particular, we consider properties sample means, covariance functions, matrix estimates, periodograms, spectral density U -statistics, kernel and regression estimates linear nonlinear processes.The is built upon physical predictive dependence measures, new measure which based on system theory.Our measures are particularly useful dealing with complicated series such as eigenvalues matrices maximum deviations...

We consider estimation of quantile curves for a general class nonstationary processes. Consistency and central limit results are obtained local linear estimates under mild short-range dependence condition. Our applied to environmental data sets. In particular, our can be used address the problem whether climate variability has changed, an important raised by IPCC (Intergovernmental Panel on Climate Change) in 2001.

Approximations to sums of stationary and ergodic sequences by martingales are investigated. Necessary sufficient conditions for such be asymptotically normal conditionally given the past up time 0 obtained. It is first shown that a martingale approximation necessary normality then if only approximating satisfy Lindeberg–Feller condition. Using explicit construction martingales, central limit theorem derived sample means linear processes. The not functional version theorem. This an example,...

We establish the Bahadur representation of sample quantiles for linear and some widely used nonlinear processes. Local fluctuations empirical processes are discussed. Applications to trimmed Winsorized means given. Our results extend previous ones by establishing sharper bounds under milder conditions thus provide new insight into theory dependent random variables.

We consider asymptotic problems in spectral analysis of stationary causal processes. Limiting distributions periodograms and smoothed periodogram density estimates are obtained applications to the domain bootstrap given. Instead commonly used strong mixing conditions, our theory we impose conditions only involving (conditional) moments, which easily verifiable for a variety nonlinear time series.

Summary The paper considers construction of simultaneous confidence tubes for time varying regression coefficients in functional linear models. Using a Gaussian approximation result non-stationary multiple series, we show that the constructed have asymptotically correct nominal coverage probabilities. Our results are applied to problem testing whether certain parametric forms, which is fundamental inference As an application, analyse environmental data set and study association between...

We consider nonparametric estimation of spectral densities stationary processes, a fundamental problem in analysis time series. Under natural and easily verifiable conditions, we obtain consistency asymptotic normality density estimates. Asymptotic distribution maximum deviations the estimates is also derived. The latter result sheds new light on classical tests white noises.

We obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes. A precise order magnitude is derived spectral radius sample matrices. also consider thresholded estimator that can better characterize sparsity if the true sparse. As our main tool, we implement Toeplitz [Math. Ann. 70 (1911) 351–376] idea and relate eigenvalues matrices to densities or Fourier transforms covariances. develop large deviation result quadratic forms processes using m-dependence...

The celebrated results of Koml\'os, Major and Tusn\'ady [Z. Wahrsch. Verw. Gebiete 32 (1975) 111-131; Z. 34 (1976) 33-58] give optimal Wiener approximation for the partial sums i.i.d. random variables provide a powerful tool in probability statistics. In this paper we extend KMT large class dependent stationary processes, solving long standing open problem theory. Under framework causal processes functional dependence measures Wu [Proc. Natl. Acad. Sci. USA 102 (2005) 14150-14154], show...

In this paper, some general theory is presented for locally stationary processes based on the approximation and derivative. Laws of large numbers, central limit theorems as well deterministic stochastic bias expansions are proved obeying an expansion in terms addition it shown that applies to nonlinear non-stationary Markov-models. results applied derive asymptotic properties maximum likelihood estimates parameter curves such models.

Knowledge graph completion (KGC) has become a focus of attention across deep learning community owing to its excellent contribution numerous downstream tasks. Although recently have witnessed surge work on KGC, they are still insufficient accurately capture complex relations, since adopt the single and static representations. In this work, we propose novel Disentangled Graph Attention Network (DisenKGAT) for which leverages both micro-disentanglement macro-disentanglement exploit...

Abstract To study the roles of translational accuracy, efficiency, and Hill-Robertson effect in codon usage bias, we studied intragenic spatial distribution synonymous bias four prokaryotic (Escherichia coli, Bacillus subtilis, Sulfolobus tokodaii, Thermotoga maritima) two eukaryotic (Saccharomyces cerevisiae Drosophila melanogaster) genomes. We generated supersequences at each position across genes a genome computed overall position. By quantitatively evaluating trend patterns using...

In this paper we provide a detailed characterization of the asymptotic behavior kernel density estimators for one-sided linear processes. The conjecture that normality estimator holds under short-range dependence is proved minimal assumptions on bandwidths. We also depict dichotomous and trichotomous phenomena various choices bandwidths when process long-range dependent.

We study asymptotic properties of $M$-estimates regression parameters in linear models which errors are dependent. Weak and strong Bahadur representations the derived a central limit theorem is established. The results applied to with being short-range dependent processes, heavy-tailed processes some widely used nonlinear time series.

We consider asymptotic behavior of Fourier transforms stationary ergodic sequences with finite second moments. establish a central limit theorem (CLT) for almost all frequencies and also an annealed CLT. The theorems hold regular sequences. Our results shed new light on the foundation spectral analysis distribution periodogram, it provides nice blend harmonic analysis, theory processes martingales.