Estimation Of Conditional Quantiles Research Articles

Multivariate copula-based conditional quantiles: analytic higher-order moments and ratio estimation approaches

ABSTRACT In this paper, we aim to modify multivariate copula-based conditional quantiles for a targeted random variable, given multiple random variables attaining their respective quantiles. Specifically, we propose two modifications through the Cornish–Fisher expansion, one of which involves its analytic higher-order unconditional moments. The second one accounts for its higher-order conditional moments estimated using a ratio estimation method. By considering multivariate elliptical and Archimedean copulas with Johnson's SU margins, our simulation study shows that this method provides more accurate conditional moment estimators compared to the naive method. They result in expanded conditional quantile estimators, whose efficiency is relatively better than their unexpanded versions, particularly at lower and higher quantile levels under a stronger (tail) dependence assumption. A much higher efficiency is gained when the first modification is performed. These findings are validated using an empirical study based on cryptocurrency return data and a comparative analysis against the existing estimation approaches.

Modelling an Improved Swarm Optimizer and Boosted Quantile Estimator For Malicious Flow Monitoring And Prediction In Network

For a long time, malware has posed a significant risk to computer system security. The effectiveness of conventional detection techniques based on static and dynamic analysis is restricted due to the quick advancement of anti-detection technologies. In recent years, AI-based malware detection has increasingly been employed to combat malware due to its improved predictive ability. Unfortunately, because malware may be so diverse, it can be challenging to extract features from it, which makes using AI for malware detection ineffective. A malware classifier based on an Improved Salp Swarm optimization for feature selection and a Boosted tree with Conditional Quantile Estimation (ISSO-BCQE) is developed to adapt different malware properties to solve the problem. Specifically, the malware code is extracted, and the feature sequence is generated into a boosting tree where the feature map of the node is extracted using BCQE, where a boosting network is used to design a classifier and the method's performance is finally analyzed and compared. The results show that our model works better than other approaches regarding FPR and accuracy. It also shows that the method beats current methods with the highest accuracy of 99.6% in most detecting circumstances. It is also stable in handling malware growth and evolution.

A simple nonparametric conditional quantile estimator for time series with thin tails

In this study, we consider a simple conditional quantile estimator in a nonparametric framework with time series data. We prove the consistency and asymptotic normality of our simple estimator for absolutely regular processes (β-mixing). This simple estimator can get better finite sample performances at thin tails than the check-function-based estimator. Finite sample simulation results show that our simple estimators have better finite sample performances at thin tails of time series data.

Incidence anddeterminants ofout-of-pocket health expenditure inEthiopia 2012-16.

This study assesses the incidence of catastrophic health expenditure (CHE) and identifies the significant factors that expose households to higher levels of out-of-pocket (OOP) health expenditure. Data from the fifth and the sixth Ethiopian National Health Accounts household surveys, which were conducted in 2012-13 and 2015-16, respectively, are used. The incidence of CHE is estimated using both the capacity-to-pay and the budget share approaches. To ensure the robustness of our findings, both unconditional and conditional quantile estimators are adopted as multivariate regression techniques to estimate the impact of socio-economic variables on the distribution of households' OOP expenditure. Our findings show that the incidence of CHE in Ethiopia ranges from 1.7% to 4.7% depending on the approach and the threshold adopted. Larger families, the unemployed, the extremely poor, those who seek care at private-owned providers and families with members affected by chronic illness face higher OOP expenditure. Hence, policy should target those with these identified socio-economic characteristics in the provision of financial risk protection such as fee waiver systems and subsidies.

Neural networks for quantile claim amount estimation: a quantile regression approach

AbstractIn this paper, we discuss the estimation of conditional quantiles of aggregate claim amounts for non-life insurance embedding the problem in a quantile regression framework using the neural network approach. As the first step, we consider the quantile regression neural networks (QRNN) procedure to compute quantiles for the insurance ratemaking framework. As the second step, we propose a new quantile regression combined actuarial neural network (Quantile-CANN) combining the traditional quantile regression approach with a QRNN. In both cases, we adopt a two-part model scheme where we fit a logistic regression to estimate the probability of positive claims and the QRNN model or the Quantile-CANN for the positive outcomes. Through a case study based on a health insurance dataset, we highlight the overall better performances of the proposed models with respect to the classical quantile regression one. We then use the estimated quantiles to calculate a loaded premium following the quantile premium principle, showing that the proposed models provide a better risk differentiation.

The effects of ICT, electricity consumption, innovation and renewable power generation on economic growth: An income level analysis for the emerging economies

Information and Communication Technology (ICT), especially internet-use and technological innovation are argued to have brought significant structural changes that drive economic growth. The current study verifies this argument using data for 16 emerging economies from 2000 to 2018. In this analysis, we have investigated the effects of ICT, innovation, electricity-consumption and renewable power generation, on the economic growth of the emerging economies. Using Instrumental-Variable GMM and fixed-effects regression with Driscoll-Kraay standard-errors, it is found that, ICT not only increases economic growth monotonically, but also increases the effectiveness of financial development on growth. However, ICT is also found to accentuate the negative effects of trade on economic growth. In order to account for the heterogeneities among these economies, both conditional and unconditional panel quantile estimators have been used for an income-level analysis. This shows that internet-use increases growth significantly in the lower and middle-income quantiles; innovation is found to have significant negative effects on growth, except for the highest income-quantile, while the positive growth-effects of electricity-consumption are confirmed across all quantiles. These findings suggest that the emerging economies should increase internet-connectivity to induce network-effect and to improve their capital markets, while also augmenting renewable electricity generation for environmentally-sustainable economic growth.

Extremal quantile autoregression for heavy-tailed time series

The conventional quantile estimator of the extreme conditional quantiles under quantile autoregression models is relatively unstable due to data sparsity in the tails. Extreme value theory provides a mathematical foundation of extrapolation to estimate extreme quantiles. However, the asymptotic distributions of existing estimators are often complicated making it inconvenient to apply for statistical inference. We develop a new adaptive estimation procedure based on a generalized Hill estimator of the extreme value index to estimate extreme conditional quantiles in autoregression models. We establish the asymptotic normality of the proposed estimators under some regularity conditions by applying the martingale central limit theorem. The asymptotic variances have closed expressions and can be directly estimated. Based on these results, we propose a procedure to construct confidence intervals for the extreme conditional quantiles. We also provide a diagnostic tool to check the heavy-tailedness of the distribution. Simulation studies and a real data analysis are carried out to demonstrate the advantages of the proposed methods over existing approaches.

Multiple Imputation Based on Conditional Quantile Estimation

Multiple imputation is a simulation-based approach for the analysis of data with missing observations. It is widely utilized in many set- tings and preeminent among general approaches when the analytical method does not involve a likelihood function or this is too complex. We consider a multiple imputation method based on the estimation of conditional quantiles of missing observations given the observed data. The method does not require modeling a likelihood and has desirable features that may be useful in some practical settings. It can also be applied to impute dependent, bounded, censored and count data. In a simulation study it shows some advantage over the alternative meth- ods considered in terms of mean squared error across all scenarios except when the data arise from a normal distribution where all meth- ods considered perform equally well. We present an application to the estimation of percentiles of body mass index conditional on physical activity assessed by accelerometers.

Nonparametric C- and D-vine-based quantile regression

AbstractQuantile regression is a field with steadily growing importance in statistical modeling. It is a complementary method to linear regression, since computing a range of conditional quantile functions provides more accurate modeling of the stochastic relationship among variables, especially in the tails. We introduce a nonrestrictive and highly flexible nonparametric quantile regression approach based on C- and D-vine copulas. Vine copulas allow for separate modeling of marginal distributions and the dependence structure in the data and can be expressed through a graphical structure consisting of a sequence of linked trees. This way, we obtain a quantile regression model that overcomes typical issues of quantile regression such as quantile crossings or collinearity, the need for transformations and interactions of variables. Our approach incorporates a two-step ahead ordering of variables, by maximizing the conditional log-likelihood of the tree sequence, while taking into account the next two tree levels. We show that the nonparametric conditional quantile estimator is consistent. The performance of the proposed methods is evaluated in both low- and high-dimensional settings using simulated and real-world data. The results support the superior prediction ability of the proposed models.

Random forest estimation of conditional distribution functions and conditional quantiles

We propose a theoretical study of two realistic estimators of conditional distribution functions using random forests. The estimation process uses the bootstrap samples generated from the original dataset when constructing the forest. Bootstrap samples are reused to define the first estimator, while the second uses the original sample, once the forest has been built. We prove that both proposed estimators of the conditional distribution functions are consistent uniformly a.s. To the best of our knowledge, it is the first proof of a.s. consistency (previous consistency results are in L2 norm or in probability) and including the bootstrap part. The consistency result holds for a large class of functions, including additive models and products. The consistency of conditional quantiles estimators follows that of distribution functions estimators using standard arguments.

Asymptotic Results of a Nonparametric Conditional Quantile Estimator in the Single Functional Index Modeling under Random Censorship

Abstract The main objective of this paper is to estimate non-parametrically the quantiles of a conditional distribution based on the single-index model in the censorship model when the sample is considered as an independent and identically distributed (i.i.d.) random variables. First of all, a kernel type estimator for the conditional cumulative distribution function (cond-cdf) is introduced. Afterwards, we give an estimation of the quantiles by inverting this estimated cond-cdf, the asymptotic properties are stated when the observations are linked with a single-index structure. Simulation study is also presented to illustrate the validity and finite sample performance of the considered estimator. Finally, the estimation of the functional index via the pseudo-maximum likelihood method is discussed, but not tackled.

Conditional quantile analysis for realized GARCH models

This article introduces a novel quantile approach to harness the high‐frequency information and improve the daily conditional quantile estimation. Specifically, we model the conditional standard deviation as a realized generalized autoregressive conditional heteroskedasticity (GARCH) model and employ conditional standard deviation, realized volatility, realized quantile, and absolute overnight return as innovations in the proposed dynamic quantile models. We devise a two‐step estimation procedure to estimate the conditional quantile parameters. The first step applies a quasi‐maximum likelihood estimation procedure, with the realized volatility as a proxy for the volatility proxy, to estimate the conditional standard deviation parameters. The second step utilizes a quantile regression estimation procedure with the estimated conditional standard deviation in the first step. Asymptotic theory is established for the proposed estimation methods, and a simulation study is conducted to check their finite‐sample performance. Finally, we apply the proposed methodology to calculate the value at risk of 20 individual assets and compare its performance with existing competitors.

Bayesian nonparametric quantile process regression and estimation of marginal quantile effects.

Flexible estimation of multiple conditional quantiles is of interest in numerous applications, such as studying the effect of pregnancy-related factors on low and high birth weight. We propose a Bayesian nonparametric method to simultaneously estimate noncrossing, nonlinear quantile curves. We expand the conditional distribution function of the response in I-spline basis functions where the covariate-dependent coefficients are modeled using neural networks. By leveraging the approximation power of splines and neural networks, our model can approximate any continuous quantile function. Compared to existing models, our model estimates all rather than a finite subset of quantiles, scales well to high dimensions, and accounts for estimation uncertainty. While the model is arbitrarily flexible, interpretable marginal quantile effects are estimated using accumulative local effect plots and variable importance measures. A simulation study shows that our model can better recover quantiles of the response distribution when the data are sparse, and an analysis of birth weight data ispresented.

Applying interval PCA and clustering to quantile estimates: empirical distributions of fertilizer cost estimates for yearly crops in European Countries

The decision to adopt one or another of the sustainable land management alternatives should not be based solely on their respective benefits in terms of climate change mitigation but also based on the performances of the productive systems used by farm holdings, assessing their environmental impacts through the cost of fertilizer resources used. This communication uses the symbolic clustering tools in order to analyze the conditional quantile estimates of the fertilizer costs of yearly crop productions in agriculture, as a replacement proxy for internal soil erosion costs. After recalling the conceptual framework of the estimation of agricultural production costs, we present the empirical data model, the quantile regression approach and the interval principal component analysis clustering tools used to obtain typologies of European countries on the basis of the conditional quantile distributions of fertilizer cost empirical estimates. The comparative analysis of econometric results for yearly crops between European countries illustrates the relevance of the typologies obtained for international comparisons to assess land management alternatives based on their impact on agricultural carbon sequestration in soils.

Extreme quantile estimation for partial functional linear regression models with heavy-tailed distributions.

In this article, we propose a novel estimator of extreme conditional quantiles in partial functional linear regression models with heavy-tailed distributions. The conventional quantile regression estimators are often unstable at the extreme tails due to data sparsity, especially for heavy-tailed distributions. We first estimate the slope function and the partially linear coefficient using a functional quantile regression based on functional principal component analysis, which is a robust alternative to the ordinary least squares regression. The extreme conditional quantiles are then estimated by using a new extrapolation technique from extreme value theory. We establish the asymptotic normality of the proposed estimator and illustrate its finite sample performance by simulation studies and an empirical analysis of diffusion tensor imaging data from a cognitive disorder study.

CLT for single functional index quantile regression under dependence structure

Abstract In this paper, we investigate the asymptotic properties of a nonparametric conditional quantile estimation in the single functional index model for dependent functional data and censored at random responses are observed. First of all, we establish asymptotic properties for a conditional distribution estimator from which we derive an central limit theorem (CLT) of the conditional quantile estimator. Simulation study is also presented to illustrate the validity and finite sample performance of the considered estimator. Finally, the estimation of the functional index via the pseudo-maximum likelihood method is discussed, but not tackled.

Extreme quantile regression for tail single-index varying-coefficient models

This paper studies the estimation of extreme conditional quantile for single-index varying-coefficient models (SIVCM). Our contribution is a three-step extreme quantile regression procedure for SIVCM. In the first step, we estimate the intermediate conditional quantile in a quantile regression framework. In the second step, we estimate the extreme value index (EVI) based on the estimated intermediate quantile. In the third step, we extrapolate the intermediate conditional quantile to the extreme tails by adapting the extreme value theory (EVT). We obtain the asymptotation of tail single-index varying-coefficient estimators and demonstrate through simulation study and real data example that the proposed methods enjoy higher accuracy than the conventional quantile regression estimates.

Measuring the effects of tourists’ relative willingness to spend and third-degree price discrimination on inbound tourism expenditure differentials

Tourism expenditures are determined by a set of antecedents that reflect tourists’ willingness and ability to spend, and de facto incremental monetary outlays at which willingness and ability is transformed into total expenditures. Based on the neoclassical theoretical argument of utility-constrained expenditure minimization, we extend the current literature by applying a sustainability-based segmentation criterion, namely, the Legatum Prosperity IndexTM to the decomposition of a total expenditure differential into tourists’ relative willingness to spend and an upper bound of third-degree price discrimination, using mean-level and conditional quantile estimates. Our results indicate that understanding the price–quantity composition of international inbound tourism expenditure differentials assists agents in the tourism industry in their quest for profit maximization.

QUANTILE DOUBLE AUTOREGRESSION

Many financial time series have varying structures at different quantile levels, and also exhibit the phenomenon of conditional heteroskedasticity at the same time. However, there is presently no time series model that accommodates both of these features. This paper fills the gap by proposing a novel conditional heteroskedastic model called “quantile double autoregression”. The strict stationarity of the new model is derived, and self-weighted conditional quantile estimation is suggested. Two promising properties of the original double autoregressive model are shown to be preserved. Based on the quantile autocorrelation function and self-weighting concept, three portmanteau tests are constructed to check the adequacy of the fitted conditional quantiles. The finite sample performance of the proposed inferential tools is examined by simulation studies, and the need for use of the new model is further demonstrated by analyzing the S&P500 Index.

Learning Multiple Quantiles With Neural Networks

We present a neural network model for estimation of multiple conditional quantiles that satisfies the noncrossing property. Motivated by linear noncrossing quantile regression, we propose a noncrossing quantile neural network model with inequality constraints. In particular, to use the first-order optimization method, we develop a new algorithm for fitting the proposed model. This algorithm gives a nearly optimal solution without the projected gradient step that requires polynomial computation time. We compare the performance of our proposed model with that of existing neural network models on simulated and real precipitation data. Supplementary materials for this article are available online.