Parametric Modeling of Quantile Regression Coefficient Functions With Longitudinal Data

Frumento, Paolo; Bottai, Matteo; Fernández‐Val, Iván

doi:10.1080/01621459.2021.1892702

Cited by 9 publications

(7 citation statements)

References 50 publications

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“…The QRCM paradigm has been applied to censored and truncated data (Frumento and Bottai 2017 ) and to longitudinal data (Frumento et al. 2021 ). The idea of Frumento and Salvati ( 2021 ) is to apply QRCM also to a discrete response such as a count, thus avoiding jittering.…”

Section: Methodsmentioning

confidence: 99%

Quantile regression for count data: jittering versus regression coefficients modelling in the analysis of credits earned by university students after remote teaching

Carcaiso

Grilli

2022

Stat Methods Appl

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The extension of quantile regression to count data raises several issues. We compare the traditional approach, based on transforming the count variable using jittering, with a recently proposed approach in which the coefficients of quantile regression are modelled by parametric functions. We exploit both methods to analyse university students’ data to evaluate the effect of emergency remote teaching due to COVID-19 on the number of credits earned by the students. The coefficients modelling approach performs a smoothing that is especially convenient in the tails of the distribution, preventing abrupt changes in the point estimates and increasing precision. Nonetheless, model selection is challenging because of the wide range of options and the limited availability of diagnostic tools. Thus the jittering approach remains fundamental to guide the choice of the parametric functions.

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Section: Methodsmentioning

confidence: 99%

Quantile regression for count data: jittering versus regression coefficients modelling in the analysis of credits earned by university students after remote teaching

Carcaiso

Grilli

2022

Stat Methods Appl

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“…As mentioned in Frumento and Bottai (2016); Yang et al (2017);Frumento et al (2021), valid choices of b (τ ) are, for example, functions of the form τ α , log(τ ), log(1 − τ ), α τ , the quantile function of any distribution with finite moments, splines, or a combination of the above. In general, the selected basis set b (τ ) should satisfy two conditions.…”

Section: Model and Estimationmentioning

confidence: 99%

“…Most economists take care of the high quantiles of oil prices, because oil price fluctuations have considerable effects on economic activity. In the past decades, traditional parametric and semiparametric modelling strategies for quantile regression have been well developed, including Kim (2007); Belloni and Chernozhukov (2011); Kai et al (2011); Wang et al (2012); Feng and Zhu (2016); Frumento and Bottai (2016); Ma and He (2016); Frumento et al (2021) and among others.…”

Section: Introductionmentioning

confidence: 99%

Jackknife Partially Linear Model Averaging for the Conditional Quantile Prediction

Lv¹,

Guo²,

Wu³

2022

Preprint

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Estimating the conditional quantile of the interested variable with respect to changes in the covariates is frequent in many economical applications as it can offer a comprehensive insight. In this paper, we propose a novel semiparametric model averaging to predict the conditional quantile even if all models under consideration are potentially misspecified. Specifically, we first build a series of non-nested partially linear sub-models, each with different nonlinear component. Then a leaveone-out cross-validation criterion is applied to choose the model weights. Under some regularity conditions, we have proved that the resulting model averaging estimator is asymptotically optimal in terms of minimizing the out-of-sample average quantile prediction error. Our modelling strategy not only effectively avoids the problem of specifying which a covariate should be nonlinear when one fits a partially linear model, but also results in a more accurate prediction than traditional model-based procedures because of the optimality of the selected weights by the cross-validation criterion. Simulation experiments and an illustrative application show that our proposed model averaging method is superior to other commonly used alternatives.

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“…For instance,

Q_{ε_{t}} (τ) = θ_{0} + θ_{1} τ

under

b (τ) = {(1, τ)}^{⊤}

. However, it is difficult to parameterize the quantile regression coefficients accurately, and their method cannot guarantee obtain the non‐crossing of different quantile estimators (Frumento et al ., 2021). Population conditional quantile functions cannot cross each other for different quantile orders; however, the estimated regression curves often violate this (Jiang and Yu, 2023).…”

Section: Introductionmentioning

confidence: 99%

Non‐crossing quantile double‐autoregression for the analysis of streaming time series data

Jiang,

Kai Choy,

2023

Journal Time Series Analysis

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Many financial time series not only have varying structures at different quantile levels and exhibit the phenomenon of conditional heteroscedasticity at the same time but also arrive in the stream. Quantile double‐autoregression is very useful for time series analysis but faces challenges with model fitting of streaming data sets when estimating other quantiles in subsequent batches. This article proposes a renewable estimation method for quantile double‐autoregression analysis of streaming time series data due to its ability to break with storage barrier and computational barrier. Moreover, the proposed flexible parametric structure of the quantile function enables us to predict any interested quantile value without quantile curve crossing problem or keeping the desirable monotone property of the conditional quantile function. The proposed methods are illustrated using current data and the summary statistics of historical data. Theoretically, the proposed statistic is shown to have the same asymptotic distribution as the standard version computed on an entire data stream with the data batches pooled into one data set, without additional condition. Simulation studies and an empirical example are presented to illustrate the finite sample performance of the proposed methods.

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Parametric Modeling of Quantile Regression Coefficient Functions With Longitudinal Data

Cited by 9 publications

References 50 publications

Quantile regression for count data: jittering versus regression coefficients modelling in the analysis of credits earned by university students after remote teaching

Quantile regression for count data: jittering versus regression coefficients modelling in the analysis of credits earned by university students after remote teaching

Jackknife Partially Linear Model Averaging for the Conditional Quantile Prediction

Non‐crossing quantile double‐autoregression for the analysis of streaming time series data

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