Robust bent line regression.

@article{Zhang2017RobustBL,
  title={Robust bent line regression.},
  author={Feipeng Zhang and Qunhua Li},
  journal={Journal of statistical planning and inference},
  year={2017},
  volume={185},
  pages={
          41-55
        }
}

Figures and Tables from this paper

Bent line quantile regression via a smoothing technique

A bent line quantile regression model can describe the conditional quantile function of the response variable with two different straight lines, which intersect at an unknown change point. This paper

Robust continuous piecewise linear regression model with multiple change points

TLDR
This paper uses the LARS algorithm via generalized BIC to refine the candidate threshold estimates and obtain the ultimate estimators, which are less sensitive to outliers and heavy-tailed data, and therefore achieves robustness.

Real-time detection of a change-point in a linear expectile model

In the present paper we address the real-time detection problem of a change-point in the coefficients of a linear model with the possibility that the model errors are asymmetrical and that the

Robust Algorithms for Change-Point Regressions Using the t-Distribution

TLDR
A modified version of the proposed EMT and FCT, which fits the t change-point regression model to the data after moderately pruning high leverage points, is introduced, and the preference of the t-based approach over normal-based methods for better robustness and computational efficiency is demonstrated.

A continuous threshold expectile model

Estimation and inference for multikink expectile regression with longitudinal data

TLDR
In this article, parameter estimation, kink points testing and statistical inference for a longitudinal multikink expectile regression model is investigated and the number selection consistency of kinks points and the asymptotic normality of all estimators are demonstrated.

SUGGESTING MULTIPHASE REGRESSION MODEL ESTIMATION WITH SOME THRESHOLD POINT

  • O. Ali
  • Mathematics, Computer Science
    JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES
  • 2020
TLDR
The main goal of this paper is to suggest a new hybrid estimator obtained by an ad-hoc algorithm which relies on data driven strategy that overcomes outliers and introduces a new employment of an unweighted estimation method named "winsorization" which is a good method to get robustness in regression estimation via special technique to reduce the effect of the outliers.

NEW ROBUST ESTIMATOR OF CHANGE POINT IN SEGMENTED REGRESSION MODEL FOR BED-LOAD OF RIVERS

  • O. Ali
  • Mathematics
    JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES
  • 2019
Segmentation has vital employment in regression analysis where data have some change point. Traditional estimation methods such as Hudson, D.J.;(1966) and Muggeo, V. M., (2003)have been reviewed .

References

SHOWING 1-10 OF 41 REFERENCES

A Lack-of-Fit Test for Quantile Regression

We propose an omnibus lack-of-fit test for linear or nonlinear quantile regression based on a cusum process of the gradient vector. The test does not involve nonparametric smoothing but is consistent

Testing for Threshold Effects in Regression Models

In this article, we develop a general method for testing threshold effects in regression models, using sup-likelihood-ratio (LR)-type statistics. Although the sup-LR-type test statistic has been

FURTHER DETAILS ON INFERENCE UNDER RIGHT CENSORING FOR TRANSFORMATION MODELS WITH A CHANGE-POINT BASED ON A COVARIATE THRESHOLD

We consider linear transformation models applied to right censored survival data with a change-point based on a covariate threshold. We establish consistency and weak convergence of the nonparametric

SELECTING THE NUMBER OF CHANGE-POINTS IN SEGMENTED LINE REGRESSION.

TLDR
It is shown that, under some conditions, the number of change-points selected by the permutation procedure is consistent and compared with such information-based criterior as the Bayesian Information Criteria, the Akaike Information Criterion, and Generalized Cross Validation.

Model selection by LASSO methods in a change-point model

TLDR
A linear regression model with multiple change-points occurring at unknown times and the LASSO technique, which allows simultaneously the parametric estimation, including the change- points estimation, and the automatic variable selection is considered.

Testing for change points due to a covariate threshold in quantile regression

We develop a new procedure for testing change points due to a covariate threshold in regression quantiles. The proposed test is based on the CUSUM of the subgradient of the quantile objective

The Estimation of the Parameters of a Linear Regression System Obeying Two Separate Regimes

Abstract In attempting to estimate the parameters of a linear regression system obeying two separate regimes, it is necessary first to estimate the position of the point in time at which the switch

Fitting bent lines to data, with applications to allometry.

  • R. Chappell
  • Mathematics
    Journal of theoretical biology
  • 1989

Estimating regression models with unknown break‐points

  • V. Muggeo
  • Mathematics
    Statistics in medicine
  • 2003
This paper deals with fitting piecewise terms in regression models where one or more break‐points are true parameters of the model. For estimation, a simple linearization technique is called for,

Testing for Structural Change in Regression Quantiles

Most studies in the structural change literature focus solely on the conditional mean, while under various circumstances, structural change in the conditional distribution or in conditional quantiles