Moderate deviations for the Durbin–Watson statistic related to the first-order autoregressive process

Penda, S. Valère Bitseki; Djellout, Hacène; Proïa, Frédéric

doi:10.1051/ps/2013038

Cited by 12 publications

(16 citation statements)

References 23 publications

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“…All these modeling analyses were performed in R version 3.5.2, and the R Package "car" ''MASS'' and ''relaimpo'' were used to run the GLMs (R Core Team, 2017). In addition, the Durbin-Watson statistic (DW value: 0-4) was introduced to check the autocorrelation between residuals of optimal models (Penda et al, 2012). A value near 2 indicates non-autocorrelation between residuals, whereas values below (above) 2 indicate positive (negative) autocorrelation between residuals.…”

Section: Discussionmentioning

confidence: 99%

Effects of the Water-Sediment Regulation Scheme on the Expansion of Spartina alterniflora at the Yellow River Estuary, China

Zheng

Gao

et al. 2021

Front. Environ. Sci.

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In recent decades, the invasion of saltmarsh plant Spartina alterniflora (S. alterniflora) over a large part of coastal wetlands in China, including the Yellow River Estuary (YRE) as a regional economic hub and global ecosystem services hotspot, has caused increasing concern because of its serious threats to native ecosystems. During the same period, local authorities have implemented a Water-Sediment Regulation Scheme (WSRS) in the Yellow River for flood mitigation and delta restoration purposes. The altered hydrological regime has resulted in unintended changes to estuarine ecosystem. However, the direct consequence of the WSRS on the expansion of S. alterniflora remains unclear. In this study, quantitative relationship between the inter- and intra-annual expansion patterns of S. alterniflora represented by relevant landscape metrics and indicators that quantify the concurrent variations of river and sediment discharges as the proxy of the WSRS impacts were analysed over the period of Year 2011–2018, and the analyses were performed on the YRE as a whole and on five different zones subdivided based on the invasion sequence. The results showed that there was no significant difference in the inter-annual area variation of S. alterniflora between the years with and without WSRS. Compared with the years without WSRS (2016–2017), the intra-annual (monthly) increment of the various landscape metrics [i.e., NP (number of patches), CA (class area), LPI (largest patch index) and AI (aggregation index] were found to be significantly higher in the initial stage of peak growing season (June-July) than in the mid- and late stages (July-September) in the years with WSRS (2011–2015, 2018) in the subregion located close to the south bank of YRE as the most prominent impact zone. In addition, F (mean flow), Ff (number of high flow pulses), Tf (Julian date of maximum flow) and D (duration of WSRS) were identified as the explanatory variables for the intra-annual vegetation landscape pattern changes, and their relative contributions to resultant changes were also assessed. Our results broaden the understanding of estuarine hydrological disturbance as a potential driver regulating the saltmarsh vegetation, and also have implications for S. alterniflora invasion control at estuaries under changing environment.

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Section: Discussionmentioning

confidence: 99%

Effects of the Water-Sediment Regulation Scheme on the Expansion of Spartina alterniflora at the Yellow River Estuary, China

Zheng

Gao

et al. 2021

Front. Environ. Sci.

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“…This work [4] had the ambition to bring the Durbin-Watson statistic back into light. It also inspired Bitseki Penda, Djellout and Proïa [5] who established moderate deviation principles on the least squares estimators and the Durbin-Watson statistic for the first-order autoregressive process where the driven noise is also given by a first-order autoregressive process.…”

Section: Introductionmentioning

confidence: 98%

Further results on theh- test of Durbin for stable autoregressive processes

Proïa

2013

Journal of Multivariate Analysis

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The purpose of this paper is to investigate the asymptotic behavior of the Durbin-Watson statistic for the stable p−order autoregressive process when the driven noise is given by a first-order autoregressive process. It is an extension of the previous work of Bercu and Proïa devoted to the particular case p = 1. We establish the almost sure convergence and the asymptotic normality for both the least squares estimator of the unknown vector parameter of the autoregressive process as well as for the serial correlation estimator associated with the driven noise. In addition, the almost sure rates of convergence of our estimates are also provided. Then, we prove the almost sure convergence and the asymptotic normality for the Durbin-Watson statistic and we derive a two-sided statistical procedure for testing the presence of a significant first-order residual autocorrelation that appears to clarify and to improve the well-known h-test suggested by Durbin. Finally, we briefly summarize our observations on simulated samples.

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“…Assume that E[V 4 1 ] < ∞. Then, we have the joint asymptotic normality [Bitseki Penda-Djellout-Proïa [5]]. Assume that the hypothesis (H1), (H2) are satisfied.…”

Section: Moderate Deviations For ρ Nmentioning

confidence: 99%

“…Theorem 3.13. [Bitseki Penda-Djellout-Proïa [5]]. Assume that the hypothesis (H1), (H2) are satisfied.…”

Section: Moderate Deviations For ρ Nmentioning

confidence: 99%