Quantile Information Research Articles

Transfer learning with high dimensional composite quantile regression

Transfer learning has gained wide popularity due to its ability to enhance the performance of target tasks by utilizing external information sources. Despite this, current transfer learning methods often struggle to consistently and effectively handle heterogeneous and/or heavy tail data. To address this issue, we propose a robust transfer learning method based on the composite quantile regression model that can adapt to a variety of data types and integrate multiple quantile information. Additionally, this method can handle situations where the error term variance is infinite. A challenging scenario in transfer learning is that the transferable data set is unknown, so we design two detection algorithms to correctly identify valid transferable data sets. Through numerical simulations and empirical analysis, we verify the good performance of the above algorithms based on the high-dimensional composite quantile regression model.

A novel time series probabilistic prediction approach based on the monotone quantile regression neural network

Quantile regression is widely applied in various fields such as economy, energy, meteorological prediction research in recent years since it does not require distribution assumptions, has relatively loose conditions, and can effectively estimate the uncertainty of time series forecasting. In this paper, a monotone quantile regression neural network (MQRNN) framework is constructed for time series quantile forecasting. The proposed approach takes the monotonicity of quantile into consideration and handles the quantile crossing problem by adding the quantile information into the input structure and using the gradient based point-wise loss function. Aiming at the complex characteristics of time series, such as time-varying and asymmetric heavy-tailed features, a new quantile function is utilized to describe the complete conditional distribution information of data. Under this model framework, non-crossing multiple quantiles can be predicted simultaneously. The proposed approach is implemented based on artificial neural networks, and the constructed model is applied to actual data in different fields. The experimental results demonstrate that the proposed method combined with long short-term memory (LSTM) can provide accurate and reliable multi-quantile prediction, and alleviate the problem of quantile crossing.

Quantile-guided multi-strategy algorithm for dynamic multiobjective optimization

Dynamic multiobjective optimization problems (DMOPs) require that the algorithm is capable of tracking the position of Pareto-optimal solution (PS) in a rapidly changing environment. Prediction-based and memory-based methods currently gain much attention for their good tracking ability. However, an elaborate predictor may not be suitable for different problems and the improper reuse of the memory may lower the quality of solution. To overcome these limitations, a quantile-guided multi-strategy algorithm (QMA) for dynamic multiobjective optimization is proposed in this paper. Quantile is always employed to represent characteristics of data because of its robustness to the outliers. In QMA, historical quantile information of decision space is used to find the new position of quantile. Then, the solution set is expanded based on the new quantile. Moreover, historical search information is used to assist in the evolution of population, which is achieved through selecting the mapping matrix as a judgment of retrieval. Meanwhile, the quantile-guided environmental change degree detector is employed to determine the number of retained and the randomly generated individuals when there is no similarity. Experimental results carried out on various DMOPs demonstrate that QMA is highly competitive compared with some state-of-the-art algorithms.

Efficient Estimation for the Derivative of Nonparametric Function by Optimally Combining Quantile Information

In this article, we focus on the efficient estimators of the derivative of the nonparametric function in the nonparametric quantile regression model. We develop two ways of combining quantile regression information to derive the estimators. One is the weighted composite quantile regression estimator based on the quantile weighted loss function; the other is the weighted quantile average estimator based on the weighted average of quantile regression estimators at a single quantile. Furthermore, by minimizing the asymptotic variance, the optimal weight vector is computed, and consequently, the optimal estimator is obtained. Furthermore, we conduct some simulations to evaluate the performance of our proposed estimators under different symmetric error distributions. Simulation studies further illustrate that both estimators work better than the local linear least square estimator for all the symmetric errors considered except the normal error, and the weighted quantile average estimator performs better than the weighted composite quantile regression estimator in most situations.

A novel quantile-guided dual prediction strategies for dynamic multi-objective optimization

Dynamic multi-objective optimization problems (DMOPs) require evolutionary algorithms (EAs) to accurately track the Pareto-optimal Front (PF) and generate the solutions along the PF in the constantly changing environment. In order to solve the DMOPs, a novel quantile-guided dual prediction strategies evolutionary algorithm (NQDPEA) is proposed in this paper. Quantiles are often employed to characterize data in statistics. In NQDPEA, the evolution of the population is guided by the quantile, which is to predict the position of the quantile in a new environment through historical quantile information. Then, a new solution set is expanded according to the location of the new quantile. Moreover, its prediction strategies not only predict Pareto-optimal set (PS) by quantile in the decision space but also predict the PF by quantile in objective space and then mapping back to decision space. Through the adaptive combination strategy, the proportion of the new solutions produced by each prediction strategy changes adaptively. To prove the performance of NQDPEA, it is compared with four powerful EAs on 13 test instances. Experimental results show that NQDPEA can effectively generate high quality solutions uniformly along PF.

Quantile information share under Markov regime‐switching

AbstractThis paper introduces a new quantile information share (QIS) method by extending the conventional QIS to Markov regime‐switching models. For most commodities in the full sample, our results show that the relationship among the spot QIS, the spot return quantile, and the futures return quantile is displayed by a saddle surface or a half saddle surface. The information share (IS) of the futures markets is saddle shaped in the low‐ and high‐volatility states. Moreover, the spot market has a larger IS in the low‐volatility state than that in the high‐volatility state for most commodities.

Selection of Scots pine seedling growth stimulants in extreme conditions of the Northern Kazakhstan steppe zone

The aim of this research is to determine optimal methods of using stimulants in a pre-sowing treatment of common pine seeds to increase their germination and obtain high-quality planting material. A study has been performed in forest nurseries of the State Forest Natural Reserve (SFNR) “Ertis Ormany” (Pavlodar region) and the Arykbalyk Branch of the State National Natural Park (SNNP) “Kokshetau” (Akmola region). The research is done with one-and two-year-old seedlings of ordinary pine sowing of 2017. A presowing seed preparation is carried out according to six options by using various types of stimulants. A method of mathematical processing of the thus obtained measurements of the seedlings with an insufficient number of measured plants is proposed by using a bootstrap analysis with and without quantile information. It allows one to estimate the influence of stimulants on the average growth of one-and two-year-old seedlings at a reliable level. As a result of these studies, it has been revealed that the pre-sowing treatment of pine seeds with ordinary stimulants increases the average height of annual seedlings. However, the results obtained in this experiment depend on the region of nursery location, but the use of soil irrigation with an “EridGrow” activator has increased the average height in both nurseries: by 13.9% in the “Kokshetau” SNNP for one-year-old seedlings, by 37.2% for two-year-old seedlings compared with the average height of the control seedlings. For pine seedlings in the “Ertis Ormany” SFNR nursery the influence of the stimulants is insignificant, but the positive effect on the average growth with the “EridGrow” soil irrigation is a 7.3% increase in the first year and a 24.7% one in the second year.

The economic order quantity taking into account additional information about the known quantile of the cumulative distribution function of the product’s sales volume

In modern logistics and supply chain management, the task of inventory management is paramount. The total costs of the enterprise and consequently, its profit, directly depend on the accuracy of calculating the volumes and terms of orders. In this work, the problem of increasing the accuracy of calculating the economic order quantity for a product was solved by involving additional information about the known quantile of a given level of the distribution function of the volume of product’s demand. The quantile information was used to recalculate the annual demand for the product, based on a modified estimator of the sales expectation for the period. The modified estimator is asymptotically unbiased, normal, and more accurate than the traditional sample mean in the sense of mean squared error. New formulas for calculating the economic order quantity and its confidence interval were presented and tested on real data on the monthly sales volumes of goods of a large retail store network over two years. It is shown that the classic way of mean calculation led to an underestimation of the volume of the economic order quantity, which in turn increased the risk of a shortage, and hence a drop in the quality of logistics services. The new calculation method also showed that the period between orders should be one day shorter. The work is practically significant; according to its results, recommendations are given to the enterprise.

Maximum entropy distributions with quantile information

Quantiles are available in various problems for developing probability distributions. In some problems quantiles are elicited from experts and used for fitting parametric models, which induce non-elicited information. In some other problems comparisons are made with a quantile of an assumed model which is noncommittal to the quantile information. The maximum entropy (ME) principle provides models that avoid these issues. However, the information theory literature has been mainly concerned about models based on moment information. This paper explores the ME models that are the minimum elaborations of the uniform and moment-based ME models by quantiles. This property provides diagnostics for the utility of elaboration in terms of the information value of each type of information over the other. The ME model with quantiles and moments is represented as the mixture of truncated distributions on consecutive intervals whose shapes and existence are determined by the moments. Elaborations of several ME distributions by quantiles are presented. The ME model based only on quantiles elicited by the fixed interval method possesses a useful property for pooling information elicited from multiple experts. The elaboration of Laplace distribution is an extension of the information theory connection with minimum risk under symmetric loss functions to the asymmetric linear loss. This extension produces a new Asymmetric Laplace distribution. Application examples compare ME priors with a parametric model fitted to elicited quantiles, illustrate measuring uncertainty and disagreement of economic forecasters based on elicited probabilities, and adjust ME models for a fundamental quantile in an inventory management problem.

Quantile information share

This paper presents a new method to estimate Hasbrouck‐type market information share in price discovery. The prevailing market information share is calculated on the basis of conditional mean. We propose a conditional quantile regression approach to obtain a new market information share measure, quantile information share, which varies across the combinations of different price quantiles. The method is illustrated with two data sets, one on the spot and futures markets in pricing S&P 500 equity index, and the other on price discovery for a cross‐listed stock.

A quantile approach of Tsallis entropy for order statistics

The quantile-based entropy measures possess some unique properties than its distribution function approach. In this article, the concept of quantile based Tsallis entropy is extended for order statistics. We prove that the generalized quantile information between ith order statistics and parent random variable is distribution free. Also the quantile version of Tsallis entropy for residual lifetime has been derived and its monotonicity property is studied. Further some characterization results based on the Tsallis quantile entropy for residual and inactivity time for the series and parallel system have been studied.

Explaining and Forecasting Euro Area Inflation: The Role of Domestic and Global Factors

In this paper, we study the fit and the predictive performance of the Phillips curve for euro area inflation with regard to different inflation series, time periods and predictor variables, notably different global factors. We compare the relative performance of a large set of alternative global factors in the Phillips curve, such as commodity prices, import prices, global consumer inflation, global economic slack and foreign demand. We find that traditional global indicators such as oil prices and import prices provide more accurate information for euro area headline inflation than global slack measures. In what regards the forecast ability of the Phillips curve for headline inflation, we show that it is unstable and depends strongly on the time period. Global factors provide only limited additional information for forecasting. In addition, we explore whether domestic demand and global factors are useful for analysing the entire conditional distribution of euro area inflation. We find that their impact varies across inflation quantiles (low vs. high inflation) and that inflation is more persistent at the low end of the distribution. We provide evidence that quantile information can lead to more accurate forecasts in periods of persistently low inflation.

Estimation and inference of combining quantile and least-square regressions with missing data

In this paper, we consider how to incorporate quantile information to improve estimator efficiency for regression model with missing covariates. We combine the quantile information with least-squares normal equations and construct an unbiased estimating equations (EEs). The lack of smoothness of the objective EEs is overcome by replacing them with smooth approximations. The maximum smoothed empirical likelihood (MSEL) estimators are established based on inverse probability weighted (IPW) smoothed EEs and their asymptotic properties are studied under some regular conditions. Moreover, we develop two novel testing procedures for the underlying model. The finite-sample performance of the proposed methodology is examined by simulation studies. A real example is used to illustrate our methods.

Bayesian composite Tobit quantile regression

ABSTRACTComposite quantile regression models have been shown to be effective techniques in improving the prediction accuracy [H. Zou and M. Yuan, Composite quantile regression and the oracle model selection theory, Ann. Statist. 36 (2008), pp. 1108–1126; J. Bradic, J. Fan, and W. Wang, Penalized composite quasi-likelihood for ultrahighdimensional variable selection, J. R. Stat. Soc. Ser. B 73 (2011), pp. 325–349; Z. Zhao and Z. Xiao, Efficient regressions via optimally combining quantile information, Econometric Theory 30(06) (2014), pp. 1272–1314]. This paper studies composite Tobit quantile regression (TQReg) from a Bayesian perspective. A simple and efficient MCMC-based computation method is derived for posterior inference using a mixture of an exponential and a scaled normal distribution of the skewed Laplace distribution. The approach is illustrated via simulation studies and a real data set. Results show that combine information across different quantiles can provide a useful method in efficient statistical estimation. This is the first work to discuss composite TQReg from a Bayesian perspective.

Accelerated failure time model with quantile information

The censored linear regression model, also referred to as the accelerated failure time model, is a useful alternative to the popular Cox model in the analysis of censored survival data. In this paper, we combine the quantile information with censored least-squares normal equations to get estimators with smaller estimated standard error for regression parameters. An inverse probability-weighted method is proposed to construct unbiased estimating equations with censored data and the lack of smoothness of the objective equations is overcome by replacing them with smooth approximations. The proposed estimators are established based on the empirical likelihood method and generalized method of moments, respectively, and their asymptotic properties are studied under some regular conditions. We also conduct some simulation experiments to investigate the finite-sample properties of the proposed estimators. The Stanford Heart Transplant data are used to illustrate the proposed estimating method.

A quantile regression forecasting model for ICT development

Purpose – Because quantile regression gets more popular and provides more comprehensive interpretations, it is important to advance quantile regression for forecasting. By extending the convention quantile regression, the purpose of this paper is to propose a quantile regression-forecasting model to forecast information and communication technology (ICT) development. Design/methodology/approach – This paper proposes an approach to forecasting based on quantile regression method. Findings – Via quantile information criterion, the proposed approach can identify whether the independent variables are predictable. For those which are predictable, the proposed approach can be used to forecast these variables. Practical implications – The proposed approach is used to forecast ICT development. It can also be used to forecast other problem domains. Originality/value – Based on the empirical results, the proposed approach advances the application of quantile regression model to forecast. The applicability of quantile regression model is greatly enhanced.

A new quantile regression forecasting model

Quantile regression is popular because it provides more information as well as comprehensive interpretations. To improve forecasting performance, this study proposes a new quantile information criterion (NQIC), on the basis of the coefficient of variation, and expects the NQIC to reflect whether a variable is predictable. The health care expenditure data determine the thresholds for the NQICs. The thresholds assist in forecasting the development of information and communication technology. From the empirical analyses, the NQICs and thresholds greatly improve the forecasting performance.

Quantile tomography: using quantiles with multivariate data

The use of quantiles to obtain insights about multivariate data is addressed. It is argued that incisive insights can be obtained by considering directional quantiles, the quantiles of projections. Directional quantile envelopes are proposed as a way to condense this kind of information; it is demonstrated that they are essentially halfspace (Tukey) depth levels sets, coinciding for elliptic distributions (in particular multivariate normal) with density contours. Relevant questions concerning their indexing, the possibility of the reverse retrieval of directional quantile information, invariance with respect to affine transformations, and approximation/asymptotic properties are studied. It is argued that the analysis in terms of directional quantiles and their envelopes offers a straightforward probabilistic interpretation and thus conveys a concrete quantitative meaning; the directional definition can be adapted to elaborate frameworks, like estimation of extreme quantiles and directional quantile regression, the regression of depth contours on covariates. The latter facilitates the construction of multivariate growth charts---the question that motivated all the development.

Bayesian Meta-Analysis of Social Network Data via Conditional Uniform Graph Quantiles

Many basic questions in the social network literature center on the distribution of aggregate structural properties within and across populations of networks. Such questions are of increasing relevance given the growing availability of network data suitable for meta-analytic studies, as well as the rise of study designs that involve the collection of data on multiple networks drawn from a larger population. Despite this, little work has been done on model-based inference for the properties of graph populations, or on methods for comparing such populations. Here, we attempt to rectify this gap by introducing a family of techniques that combines an existing approach to the identification of structural biases in network data (the use of conditional uniform graph quantiles) with strategies drawn from nonparametric Bayesian analysis. Conditional uniform graph quantiles are the quantiles of an observed structural property in the reference distribution produced by evaluating that property over all graphs with certain fixed characteristics (e.g., size or density). These quantiles have long been used to measure the extent to which a property of interest on a single network deviates from what would be expected given that network's other characteristics. The methods introduced here employ such quantile information to allow for principled inference regarding the distribution of structural biases within (and comparison across) populations of networks, given data sampled at the network level. The data requirements of these methods are minimal, thus making them well-suited to meta-analytic applications for which complete network data (as opposed to summary statistics) are often unavailable. The structural biases inferred using these methods can be expressed in terms of posterior predictives for familiar and easily communicated quantities, such as p-values. In addition to the methods themselves, we present algorithms for posterior simulation from this model class, illustrating their use with applications to the analysis of social structure within urban communes and radio communications among emergency personnel. We also discuss how this approach may applied to quantiles arising from other reference distributions, such as those obtained using general exponential-family random graph models.

Characterizing the Distribution of Safety Occurrences in Aviation

The demand for air travel continues to grow rapidly, and by 2010, air traffic in Europe is expected to be twice the 1990 level. This increase in air traffic may adversely affect safety if appropriate measures are not taken. Regulators and Air Navigation Service Providers (ANSPs) analyze incidents to identify ways to prevent them from happening again. Incidents are rare events in airspace, and this poses problems with robust statistical testing and trend analysis. Aviation safety analysis uses the Poisson distribution where possible, but doubts remain as to its appropriateness. Incident data from ANSP were analyzed over 17 years in a logical quantitative manner using extreme value theory (EVT), a method that uses the limited amount of information available on incidents and defines a distribution that can be used to make statistical inferences. EVT has had considerable use in other fields but little in aviation. A statistical analysis and validation framework is outlined and used to test the data using Poisson, negative binomial, and EVT. The goodness-of-fit tests, as well as other statistical tests, indicate that by far the best fit of the data is achieved using EVT. Further analysis using EVT shows its efficacy as a tool for monitoring and predicting incidents, based on statistical hypothesis and the use of quantile information.