Linear Quantile Research Articles

PARTIALLY FUNCTIONAL LINEAR QUANTILE REGRESSION WITH MEASUREMENT ERRORS.

Ignoring measurement errors in conventional regression analyses can lead to biased estimation and inference results. Reducing such bias is challenging when the error-prone covariate is a functional curve. In this paper, we propose a new corrected loss function for a partially functional linear quantile model with function-valued measurement errors. We establish the asymptotic properties of both the functional coefficient and the parametric coefficient estimators. We also demonstrate the finite-sample performance of the proposed method using simulation studies, and illustrate its advantages by applying it to data from a children obesity study.

Neural Networks for Partially Linear Quantile Regression

Deep learning has enjoyed tremendous success in a variety of applications but its application to quantile regression remains scarce. A major advantage of the deep learning approach is its flexibility to model complex data in a more parsimonious way than nonparametric smoothing methods. However, while deep learning brought breakthroughs in prediction, it is not well suited for statistical inference due to its black box nature. In this article, we leverage the advantages of deep learning and apply it to quantile regression where the goal is to produce interpretable results and perform statistical inference. We achieve this by adopting a semiparametric approach based on the partially linear quantile regression model, where covariates of primary interest for statistical inference are modeled linearly and all other covariates are modeled nonparametrically by means of a deep neural network. In addition to the new methodology, we provide theoretical justification for the proposed model by establishing the root-n consistency and asymptotically normality of the parametric coefficient estimator and the minimax optimal convergence rate of the neural nonparametric function estimator. Across several simulated and real data examples, the proposed model empirically produces superior estimates and more accurate predictions than various alternative approaches.

Probabilistic State of Health and Remaining Useful Life Prediction for Li-Ion Batteries

Lithium-ion batteries are widely used in electric vehicles due to their high specific energy value. The continuous charge/discharge cycles pf batteries, determining a change of their State of Health (SoH) and a reduction of their Remaining Useful Life (RUL). The relevant literature describes a variety of methods for the prognostic of battery degradation and RUL estimation, based on electrochemical models or on statistical and artificial intelligence techniques. However, the capacity degradation of lithium-ion batteries depends on many uncertain parameters that are suitable to be estimated and modeled within a probabilistic framework. Therefore, the development of new probabilistic methodologies for the prognostic of lithium-ion batteries can be useful and effective. In this paper, probabilistic models based on time series (AutoRegressive Integrated Moving Average model with eXogenous predictors, (ARIMAX)) and regression approaches (Linear Quantile Regression (LQR), Bootstrap Multiple Linear Regression (B-MLR) and Bayesian Bootstrap Multiple Linear Regression (BB-MLR)) are developed and compared for this purpose. All the considered models are specifically suited up to exploit data coming from Accelerated Degradation Tests (ADTs), and developed under two different approaches (i.e., non-differentiation and differentiation of the target time series) to predict SoH and RUL. Moreover, a dedicated procedure to extract a single, point value from the probabilistic predictions is presented to let the models work also in deterministic scenarios. The performance and the comparison between the proposals and several benchmarks taken from the literature are carried out using data from publicly available databases, confirming the validity and the accuracy of the proposed solutions.

Crown width model for planted Korean pine in eastern Liaoning mountains based on mixed effect linear quantile

Crown width is a critical variable in reflecting the individual tree growth status and in developing forest growth and yield models. With the crown width base model as reference, we developed the crown width quantile regression models for different quantiles (0.50, 0.90, 0.93, 0.95, 0.96, 0.99) based on the data of 2763 Korean pines in 66 permanent plots from the 10-55 years old plantations in Dabiangou forest farm, mountainous areas of eastern Liaoning Province. We used the reparameterization method by introducing the single tree competition index (Rd) and used the dummy variable method by introducing stand density and forest layer variables. We then selected optimal quantile of maximum crown width in the stand by comparing our model developed routine to the traditional methods. The final crown width linear mixed effect quantile regression model was developed based on the optimal quantile at the plot level. The influence of each variable on crown width was analyzed to reflect the difference of crown width among individual trees in the stand. The models with different stand densities and forest layers had significant difference based on F statistical test: the Ra2 of the model increased by 0.0104, the root mean square error decreased by 0.0115 and the mean square error reduction was 7.4%, after the variables of forest layer, forest density, and competition being incorporated into the basic model. The developed quantile regression model performed better than that of the ordinary least square method in simulating the maximum crown width of a single tree in the forest stand. The selected best quantile of the quantile regression model for the upper forest layer and lower forest layer was 0.96 and 0.93, respectively. The linear quantile regression model with the mixed effect was superior to the traditional quantile regression model in Akaike, Bayesion and HQ information criterion and other evaluation para-meters, the standard error for the parameters of estimates was significantly reduced, and the introduced mixed effect well explained differences among different plots. For the upper forest layer and lower forest layer, the maximum crown width decreased with increasing stand density, increased with increasing relative diameters. The influence of stand density on the crown width of the lower forest layer was greater than that of the upper forest layer. The crown width would increase first and then decrease with the increases of DBH when the stand density was large enough. The mixed effect of the quantile regression model developed here could significantly improve the fitting stability of the model. The sustainable development of Korean pine plantation in the mountainous area of eastern Liaoning Pro-vince should be realized by adjusting stand density and moderate tending and thinning in the future.

Prediction of Travel Time Reliability on Interstates Using Linear Quantile Mixed Models

Under the Moving Ahead for Progress in the 21st Century Act (MAP-21), state Departments of Transportation (DOTs) are responsible for reporting travel time reliability and also setting targets and showing progress toward those targets. To know how to improve travel time reliability and what to expect from investments in transportation infrastructure, state DOTs need a better understanding of the factors that affect travel time reliability and methods to predict future travel time reliability. This paper proposes linear quantile mixed models (LQMMs) to quantify travel time reliability impact factors and predict selected reliability measures (level of travel time reliability [LOTTR] and the 90th percentile) to address these needs. The method was demonstrated using probe vehicle data from interstate segments in Virginia that had been partitioned into approximately homogeneous clusters based on the similarity of their cumulative distribution functions (CDFs) of travel times. Using clustered data meant that LQMMs were only necessary for a limited number of clusters rather than for hundreds of individual segments, thus making the process more efficient and manageable. The LQMMs showed that frequencies of non-recurrent events, such as incidents and weather, were correlated with higher travel time percentiles. The prediction performance of LQMMs was compared with trend line predictions, a common method used in practice. The results showed that LQMMs significantly improved prediction accuracy.

Plasma Protein Levels Analysis in Multiple Sclerosis Sardinian Families Identified C9 and CYP24A1 as Candidate Biomarkers.

Here we investigate protein levels in 69 multiple sclerosis (MS) cases and 143 healthy controls (HC) from twenty Sardinian families to search for promising biomarkers in plasma. Using antibody suspension bead array technology, the plasma levels of 56 MS-related proteins were obtained. Differences between MS cases and HC were estimated using Linear Mixed Models or Linear Quantile Mixed Models. The proportion of proteins level variability, explained by a set of 119 MS-risk SNPs as to the literature, was also quantified. Higher plasma C9 and CYP24A1 levels were found in MS cases compared to HC (p < 0.05 after Holm multiple testing correction), with protein level differences estimated as, respectively, 0.53 (95% CI: 0.25, 0.81) and 0.42 (95% CI: 0.19, 0.65) times plasma level standard deviation measured in HC. Furthermore, C9 resulted in both statistically significantly higher relapsing-remitting MS (RRMS) and secondary-progressive MS (SPMS) compared to HC, with SPMS showing the highest differences. Instead, CYP24A1 was statistically significantly higher only in RRMS as compared to HC. Respectively, 26% (95% CI: 10%, 44%) and 16% (95% CI: 9%, 39%) of CYP24A1 and C9 plasma level variability was explained by known MS-risk SNPs. Our results highlight C9 and CYP24A1 as potential biomarkers in plasma for MS and allow us to gain insight into molecular disease mechanisms.

Predicting crown width for Larix gmelinii based on linear quantiles groups

Predicting crown width for Larix gmelinii based on linear quantiles groups

Stock Returns and Cash Flows: A New Asset Pricing Approach

On this purpose, this work is focused on a non-conventional profitability measure, at least in terms of assets pricing models, where dividends or profits are widely used. The attention is focused on a proxy measure of Operating Cash Flows: the “Ebitda after Capex”. The relationship returns – cash flows’ volatility has been examined through an empirical analysis conducted on the stocks of the SP the simple Ordinary Least Squares regressions (OLS), the linear Quantile (LQR) regression and the Multiple regression model (MLR), all performed at different levels in terms of stocks (QoQ and YoY) and sectors (MoM, QoQ, YoY). The cross-sectional and time-series results support the effects of cash flow’ volatility on the stocks’ performance and highlighted its sensitivity respect not only the different short-term and long-term horizons, but also in terms of sector’ exposure.

An Individual Risk Model for Premium Calculation Based on Quantile: A Comparison between Generalized Linear Models and Quantile Regression

This article deals with the use of quantile regression and generalized linear models for a premium calculation based on quantiles. A premium principle is a functional that assigns a usually loaded premium to any distribution of claims. The loaded premium is generally greater than the expected value of the loss and the difference is considered to be a risk margin or a safety loading. The failure of a right charge of individual risk rate exposes the insurer to adverse selection and, consequently, to deteriorating financial results. The article aim is to define the individual pure premium rates and the corresponding risk margin in balance with some profit or solvency constraints. We develop a ratemaking process based on a two-part model using quantile regression and a gamma generalized linear model, respectively, in order to estimate the claim’s severity quantiles. Generalized linear models focus on the estimation of the mean of the conditional loss distribution but have some drawbacks in assessing distribution moments other than the mean and are very sensitive to outliers. On the contrary, quantile regression exceeds these limits leading to the estimate of conditional quantiles and is more accurate for a better measurement of the variability of a risk class. The proposed methodology for premium calculation allows us to find further limits of the generalized linear model as the solution we found, under specific assumptions for a generalized linear model, is equivalent to the application of the expected value premium principle. Finally, the methodology we suggest for the two-part quantile regression allows reducing the practical issue of overmodeling and over-parameterization with respect to other proposals on the same topic.

Improving precipitation forecasts using extreme quantile regression

Aiming to estimate extreme precipitation forecast quantiles, we propose a nonparametric regression model that features a constant extreme value index. Using local linear quantile regression and an extrapolation technique from extreme value theory, we develop an estimator for conditional quantiles corresponding to extreme high probability levels. We establish uniform consistency and asymptotic normality of the estimators. In a simulation study, we examine the performance of our estimator on finite samples in comparison with a method assuming linear quantiles. On a precipitation data set in the Netherlands, these estimators have greater predictive skill compared to the upper member of ensemble forecasts provided by a numerical weather prediction model.

APPLICATION OF WAVELET REGRESSION WITH LOCAL LINEAR QUANTILE REGRESSION IN FINANCIAL TIME SERIES FORECASTING.

21Jun 2017 APPLICATION OF WAVELET REGRESSION WITH LOCAL LINEAR QUANTILE REGRESSION IN FINANCIAL TIME SERIES FORECASTING. M. A. Ghazal , W. Alabeid and Gh. Alshreef. Department of Mathematics, Faculty of Science, Damietta University, Damietta, Egypt.

Penalized Empirical Likelihood based Variable Selection for Partially Linear Quantile Regression Models with Missing Responses

In this paper, we consider variable selection for partially linear quantile regression models with missing response at random. We first propose a role penalized empirical likelihood based variable selection method, and show that such variable selection method is consistent and satisfi es sparsity. Further more, to avoid the influence of nonparametric estimator on the variable selection for the parametric components, we also propose a double penalized empirical likelihood variable selection method. Some simulation studies and a real data application are under taken to assess the finite sample performance of the proposed variable selection methods, and simulation results indicate that the proposed variable selection methods are workable.

Partially adaptive quantile estimators

ABSTRACTThis paper contrasts two approaches to estimating quantile regression models: traditional semi-parametric methods and partially adaptive estimators using flexible probability density functions (pdfs). While more general pdfs could have been used, the skewed Laplace was selected for pedagogical purposes. Monte Carlo simulations are used to compare the behavior of the semi-parametric and partially adaptive quantile estimators in the presence of possibly skewed and heteroskedastic data. Both approaches accommodate skewness and heteroskedasticity which are consistent with linear quantiles; however, the partially adaptive estimator considered allows for non linear quantiles and also provides simple tests for symmetry and heteroskedasticity. The methods are applied to the problem of estimating conditional quantile functions for wages corresponding to different levels of education.

Best linear unbiased and invariant estimation in location-scale families based on double-ranked set sampling

In this article, we propose the best linear unbiased estimators (BLUEs) and best linear invariant estimators (BLIEs) for the unknown parameters of location-scale family of distributions based on double-ranked set sampling (DRSS) using perfect and imperfect rankings. These estimators are then compared with the BLUEs and BLIEs based on ranked set sampling (RSS). It is shown that under perfect ranking, the proposed estimators are uniformly better than the BLUEs and BLIEs obtained via RSS. We also propose the best linear unbiased quantile (BLUQ) and the best linear invariant quantile (BLIQ) estimators for normal distribution under DRSS. It is observed that the proposed quantile estimators are more efficient than the BLUQ and BLIQ estimators based on RSS for both perfect and imperfect orderings.

Bahadur Representation of Linear Kernel Quantile Estimator for Stationary Processes

In this article, we discuss the method of linear kernel quantile estimator proposed by Parzen (1979). We establish a Bahadur representation in sense of almost surely convergence with the rate log− αn under the case of S-mixing random variable sequence which was proposed by Berkes (2009). We also obtain the strong consistence of this estimator and its convergence rate.

Application of empirical mode decomposition with local linear quantile regression in financial time series forecasting.

This paper mainly forecasts the daily closing price of stock markets. We propose a two-stage technique that combines the empirical mode decomposition (EMD) with nonparametric methods of local linear quantile (LLQ). We use the proposed technique, EMD-LLQ, to forecast two stock index time series. Detailed experiments are implemented for the proposed method, in which EMD-LPQ, EMD, and Holt-Winter methods are compared. The proposed EMD-LPQ model is determined to be superior to the EMD and Holt-Winter methods in predicting the stock closing prices.

Evaluating forecast performances of the quantile autoregression models in the present global crisis in international equity markets

In this research, we compare the one-step-ahead out-of-sample forecast performances of the linear Quantile Autoregression (QAR) model as well as the latest sophisticated nonlinear copula-based QAR models for four daily equity index returns during the current financial tumultuous period. In addition, two Conditional Autoregressive Value-at-Risk (CAViaR) models proposed by Engle and Manganelli (2004) are also considered. In order to obtain the robust evaluation results, we estimate the time-varying parameters via two forecasting schemes (recursive and rolling) and examine the accuracy of the Value-at-Risk (VaR) forecast by three different test procedures. Our main findings are that the CAViaR models provide good forecast performance in most cases and they are superior to both linear and nonlinear copula-based QAR models.