Asymptotics of the signed-rank estimator under dependent observations

We consider a nonlinear regression model when the index variable is multidimensional. Such models are useful in signal processing, texture modelling, and spatio-temporal data analysis. A generalised form of the signed-rank estimator of the nonlinear regression coefficients is proposed. This general form of the signed-rank (SR) estimator includes L p estimators and hybrid variants. Sufficient conditions for strong consistency and asymptotic normality of the estimator are given. It is shown that the rate of convergence to normality can be different from √ n. The sufficient conditions are weak in the sense that they are satisfied by harmonic-type functions for which results in the current literature may not apply. A simulation study shows that certain generalised SR estimators (e.g. signed rank) perform better in recovering signals than others (e.g. least squares) when the error distribution is contaminated or is heavy-tailed.

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“…The proof follows a similar approach as the ones given in Bindele and Abebe (2012) and Bindele (2014). It is sketched in Appendix 3.…”

Section: Asymptotic Normalitymentioning

confidence: 97%

“…Thus, the GSR estimator appears to be a good candidate for dealing with nonlinear models with multidimensional indices, especially those of the harmonic variety. We should note that asymptotic normality of the signed-rank (SR) estimator for the classic nonlinear models with dependent errors was recently established in Bindele (2014).…”

Section: Introductionmentioning

confidence: 99%

Generalised signed-rank estimation for nonlinear models with multidimensional indices

Nguelifack

Kwessi

Abebe

2015

Journal of Nonparametric Statistics

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“…Another important approach using such rank scores in estimating the true nonlinear regression parameter is developed in [6] for i.i.d. Under the violation of the independence assumption, if {ε t } satisfies either the φ-mixing or α-mixing conditions as discussed in [8], the asymptotic properties of the SR estimator are given in [9]. When {ε t } is assumed to be a sequence of independent and identically distributed random variables, conditions needed for the consistency and the √ T-asymptotic normality ofβ T are established in [1].…”

Section: Introductionmentioning

confidence: 99%

“…By considering the negative gradient function S T (β) = −∇D T (β), it is shown under mild conditions in [1,9] that S T (β 0 ) is asymptotically normal N(0, T ), where 0 is a vector of zeros and T some positive-definite matrix. Inferences about β 0 for finite samples require the estimation of the asymptotic variance ofβ T which is not a simple task due to the complexity of the objective function considered.…”

Section: Introductionmentioning

confidence: 99%

Signed-rank regression inference via empirical likelihood

Bindele

Zhao

2015

Journal of Statistical Computation and Simulation

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For the general stochastic regression analysis of complete data, Bindele and Abebe [Bounded influence nonlinear signed-rank regression. Can J Stat. 2012;40(1):172-189. Available from: http://dx.doi.org/10.1002/cjs.10134 ] proposed the signed-rank (SR) estimator. However, there exists an over-coverage problem for the confidence intervals of the regression parameters when the sample size is small. In this paper, we investigate an empirical likelihood (EL) approach to construct confidence intervals for the regression parameters based on the SR estimating equation. The limiting distribution of log-empirical likelihood ratio is χ 2 distribution. We carry out extensive simulation studies to compare the proposed method with the normal approximation-based method. The simulation results show that the proposed method outperforms the existing method in terms of the coverage probability and average length of confidence intervals. We illustrate the EL method using a real data example.

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“…Note that nonlinear signed-rank methods with i.i.d errors have been studied by , and with dependent errors by Bindele (2014). The interested reader can refer to Murkherjee (1999) for an extensive review of different estimation techniques including M-estimation, R-estimation and L-estimation.…”

mentioning

confidence: 99%

Signed-rank analysis of a partial linear model with B-splines estimated monotone non parametric function

Kwessi

Nguelifack

2016

Communications in Statistics - Theory and Methods

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For a partially linear regression model, we propose a signed-rank estimation method. The proposed estimator for the linear unknown parameter vector is shown to have √ n-consistency while monotone B-splines are used to estimate the unknown monotone nonparametric function. Finite samples simulations are carried out to evaluate the performance of the proposed estimation method and a practical application on the study of Air Pollution data is given.

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Asymptotics of the signed-rank estimator under dependent observations

Cited by 6 publications

References 26 publications

Generalised signed-rank estimation for nonlinear models with multidimensional indices

Generalised signed-rank estimation for nonlinear models with multidimensional indices

Signed-rank regression inference via empirical likelihood

Signed-rank analysis of a partial linear model with B-splines estimated monotone non parametric function

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