Composite change point estimation for bent line quantile regression

Abstract

The bent line quantile regression describes the situation where the conditional quantile function of the response is piecewise linear but still continuous in covariates. In some applications, the change points at which the quantile functions are bent tend to be the same across quantile levels or for quantile levels lying in a certain region. To capture such commonality, we propose a composite estimation procedure to estimate model parameters and the common change point by combining information across quantiles. We establish the asymptotic properties of the proposed estimator, and demonstrate the efficiency gain of the composite change point estimator over that obtained at a single quantile level through numerical studies. In addition, three different inference procedures are proposed and compared for hypothesis testing and the construction of confidence intervals. The finite sample performance of the proposed procedures is assessed through a simulation study and the analysis of a real data.

Gaussian copula based composite quantile regression in semivarying models with longitudinal data

“…Assumption (A6) is an important condition in deriving the limiting behavior of rank score statistic and Assumption (A7) requires that the matrix Ψ n is strictly positive definite. Both the two conditions can also be found in Zhang et al (2017).…”

“…The minimization problem in (2.3) becomes a standard linear quantile regression, which can be readily implemented by some existing convex optimization packages. However, just as pointed by Zhang et al (2017), for multiple quantiles estimation, there may exist such situation that the estimates at upper quantile levels are smaller than that at lower quantile levels, i.e. the crossing of quantile curves.…”

“…Zhang et al (2014) formally demonstrated the existence of quantile threshold effect of BMI on systolic BP by using quantile score test statistic. Moreover, Zhang et al (2017) Table ??. From the table, we observe that all the P-values approach zeros, suggesting significant kink effects at all quantiles.…”

Change-point multivariable quantile regression to explore effect of weather variables on building energy consumption and estimate base temperature range

“…Both asymptotic and bootstrapping methods provide robust results for standard errors and confidence limits for regression coefficient estimates [40]. We used the bootstrap technique for deriving confidence intervals (CIs) of the derivative of a QR model as more practical [41]. The triplets of variables ( , and ) with replacement from { |} were resampled, 1 , 1 , , )| = 1, ⋯, and these bootstrap samples were then used to re-estimate , and .…”

Robust continuous piecewise linear regression model with multiple change points

“…Zhang et al [3] developed a sup-score-type statistic to test for change points due to a covariate threshold. Zhang et al [4] proposed a composite change point estimation for bent line quantile regression and derived the estimators' consistency and asymptotic properties. Zhang and Li [5] proposed a continuous threshold expectile model, which is also a bent line model under expectile regression.…”