Fixed-design regression for linear time series

Tran, Lanh Tat; Roussas, George G.; Yakowitz, S.; Van, B. Truong

doi:10.1214/aos/1032526952

Cited by 125 publications

(43 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where {h n } is a sequence of positive constants tending to 0 and nh n → ∞, and the design points satisfy 0 = x n,0 ≤ x n,1 ≤ · · · ≤ x n,n = 1, this weight also was used by Tran et al [26]. Assume that (iii) there exist positive constants c 1 and c 2 such that c 1 n…”

Section: Corollary 22 Suppose That (A1) Is Satisfied and That Specmentioning

confidence: 99%

“…Roussas et al [22] established asymptotic normality of g n (x) assuming that the errors are from a strictly stationary stochastic process and satisfy the strong mixing condition. Tran et al [26] discussed again asymptotic normality of g n (x) assuming that the errors form a linear time series, more precisely, a weakly stationary linear process based on a martingale difference sequence.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Berry-Esseen Type Bound of Regression Estimator Based on Linear Process Errors

Liang¹,

Li²

2008

Journal of the Korean Mathematical Society

View full text Add to dashboard Cite

Abstract. Consider the nonparametric regression modelis an unknown regression function, x ni are known fixed design points, and the correlated errors {ϵ ni , 1 ≤ i ≤ n} have the same distribution as {V i , 1 ≤ i ≤ n}, here Vt = P ∞ j=−∞ ψ j e t−j with P ∞ j=−∞ |ψ j | < ∞ and {et} are negatively associated random variables. Under appropriate conditions, we derive a Berry-Esseen type bound for the estimator of g(·). As corollary, by choice of the weights, the BerryEsseen type bound can attain O(n −1/4 (log n) 3/4 ).

show abstract

Section: Corollary 22 Suppose That (A1) Is Satisfied and That Specmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Berry-Esseen Type Bound of Regression Estimator Based on Linear Process Errors

Liang¹,

Li²

2008

Journal of the Korean Mathematical Society

View full text Add to dashboard Cite

show abstract

“…Roussas, Tran and Ioannides (1992), Tran, Roussas, Yakowitz and Truong Van (1996)). The rate of convergence of kernel estimates is una¤ected by this level of serial correlation, though the asymptotic variance di¤ers from that in the iid case (unlike in the stochastic-design model in which the argument of g in (1) is instead a weakly dependent stationary stochastic sequence).…”

Section: Introductionmentioning

confidence: 99%

Inference on Non-Stationary Time Series with Moving Mean

Gao

Robinson

2013

SSRN Journal

View full text Add to dashboard Cite

A semiparametric model is proposed in which a parametric …ltering of a nonstationary time series, incorporating fractionally di¤erencing with short memory correction, removes correlation but leaves a nonparametric deterministic trend. Estimates of the memory parameter and other dependence parameters are proposed, and shown to be consistent and asymptotically normally distributed with parametric rate. Tests with standard asymptotics for I(1) and other hypotheses are thereby justi…ed. Estimation of the trend function is also considered. We include a Monte Carlo study of …nite-sample performance.

show abstract

“…Tran et al [8] obtained the asymptotic normality of g n (x) assuming that the errors form a linear time series, more precisely, a weakly stationary linear process based on a martingale difference sequence. Hu et al [9] generalized the main results of Tran et al [8]. Liang and Jing [10] established the consistency, uniform consistency, and asymptotic normality of g n (x) under negatively associated (NA) samples.…”

Section: Introductionmentioning

confidence: 99%

The consistency for estimator of nonparametric regression model based on NOD errors

Yang

Wang

et al. 2012

J Inequal Appl

View full text Add to dashboard Cite

By using some inequalities for NOD random variables, we give its application to investigate the nonparametric regression model based on these errors. Some consistency results for the estimator of g(x) are presented, including the mean convergence, uniform convergence, almost sure convergence and convergence rate. We generalize some related results and as an example of designed assumptions for weight functions, we give the nearest neighbor weights.

show abstract

Fixed-design regression for linear time series

Cited by 125 publications

References 27 publications

A Berry-Esseen Type Bound of Regression Estimator Based on Linear Process Errors

A Berry-Esseen Type Bound of Regression Estimator Based on Linear Process Errors

Inference on Non-Stationary Time Series with Moving Mean

The consistency for estimator of nonparametric regression model based on NOD errors

Contact Info

Product

Resources

About