Estimating the parametric component of nonlinear partial spline model

Huang, Tzee‐Ming; Chen, Hung

doi:10.1016/j.jmva.2008.01.007

Cited by 13 publications

(5 citation statements)

References 22 publications

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“…Assumptions (C1)-(C4) and (C6) are also assumed in Huang and Chen (2008). The smoothness assumption of the nonparametric functions is greatly relaxed in our paper and we believe that our assumption (C2) is close to being minimal.…”

Section: Proof Of Main Resultsmentioning

confidence: 89%

“…Li and Nie (2008) proposed an estimation procedure for β and α(·) by using a profile nonlinear least squares and local linear technique. Huang and Chen (2008) considered the spline profile least squares estimator of a parameter β when α(·) was approximated by some graduating function. The consistency and asymptotic normality of the resulting estimate are established.…”

Section: Introductionmentioning

confidence: 99%

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Testing serial correlation for partially nonlinear models

Zhou

Qian

2010

Journal of the Korean Statistical Society

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a b s t r a c tPartially nonlinear models, as extensions of partially linear models are extensively used in statistical modeling. This paper considers the spline empirical log-likelihood ratio for testing serial correlation in partially nonlinear models. It is shown that the proposed empirical log-likelihood ratio converges to the standard chi-square distribution under the null hypothesis of no serial correlation. Some simulations are conducted to estimate the rejection probabilities under the null hypothesis and serial correlation. An example of application is also illustrated.

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Section: Proof Of Main Resultsmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Testing serial correlation for partially nonlinear models

Zhou

Qian

2010

Journal of the Korean Statistical Society

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“…The above regularity conditions are common in the literature of nonlinear regression with random design (see for example Huang & Chen, 2008;Wang & Leblanc, 2008). Assumption (H5) is necessary to find the asymptotic distribution of the LS estimator, while assumption (H2) is needed to control the rest in Taylor's expansion of h. Assumption (H3) corresponds to the assumption of finite fourth moments of X i in the linear case.…”

Section: Assumptions and Modelmentioning

confidence: 99%

Asymptotic behaviour of the LS estimator in a nonlinear model with long memory

Ciuperca

2011

Journal of the Korean Statistical Society

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International audienceThe behaviour of the LS estimator in a nonlinear regression model is investigated, when both the regressors and the errors are long memory processes. The convergence rate, the asymptotic distribution of the LS estimator depend on long memory parameters, Hermite ranks and on expectation of the partial derivative with respect to the parameter of the regression function. We show that the asymptotic distribution of this estimator can be non-normal. An application of these results is presented for testing a structural change in a model with change-point. Numerical simulations confirm the theoretical results

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“…Li and Nie (2008) introduced the profile nonlinear least squares approach and the linear approximation method. Huang and Chen (2008) developed the spline profile least square estimator when the nonparametric function was approximated by some graduating functions. Song et al (2010) proposed a sieve least squares method.…”

Section: Introductionmentioning

confidence: 99%

A robust and efficient estimation method for partially nonlinear models via a new MM algorithm

Jiang

Tian

2017

Stat Papers

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When the observed data set contains outliers, it is well known that the classical least squares method is not robust. To overcome this difficulty, Wang et al. (J Am Stat Assoc 108(502): 632-643, 2013) proposed a robust variable selection method by using the exponential squared loss (ESL) function with a tuning parameter. Although many important statistical models are investigated, to date, in the presence of outliers there is no paper to study the partially nonlinear model by using the ESL function. To fill in this gap, in this paper, we propose a robust and efficient estimation method for the partially nonlinear model based on the ESL function. Under certain conditions, we have shown that the proposed estimators can achieve the best convergence rates. Next, the asymptotic normality of the proposed estimators is established. In addition, we develop a new minorization-maximization algorithm to calculate the estimates for both non-parametric and parametric parts and present a procedure for deriving initial values. Finally, we provide a data-driven approach to select the tuning parameters. Numerical simulations and a real data analysis are used to illustrate that when there are outliers, the proposed ESL method is more robust and efficient for partially nonlinear models than the existing linear approximation method and the composite quantile regression method.

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Estimating the parametric component of nonlinear partial spline model

Cited by 13 publications

References 22 publications

Testing serial correlation for partially nonlinear models

Testing serial correlation for partially nonlinear models

Asymptotic behaviour of the LS estimator in a nonlinear model with long memory

A robust and efficient estimation method for partially nonlinear models via a new MM algorithm

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