Using Extreme Value Theory Approaches to Estimate High Quantiles for Stroke Data

This paper aims to explore the application of Extreme Value Theory (EVT) in estimating the conditional extreme quantile for time-to-event outcomes by examining the functional relationship between ambulatory blood pressure trajectories and clinical outcomes in stroke patients. The study utilizes EVT to analyze the functional connection between ambulatory blood pressure trajectories and clinical outcomes in a sample of 297 stroke patients. The 24-hour ambulatory blood pressure measurement curves for every 15 minutes are considered, acknowledging a censored rate of 40%. The findings reveal that the sample mean excess function exhibits a positive gradient above a specific threshold, confirming the heavy-tailed distribution of data in stroke patients with a positive extreme value index. Consequently, the estimated conditional extreme quantile indicates that stroke patients with higher blood pressure measurements face an elevated risk of recurrent stroke occurrence at an early stage. This research contributes to the understanding of the relationship between ambulatory blood pressure and recurrent stroke, providing valuable insights for clinical considerations and potential interventions in stroke management.

Tests for Two-Sample Location Problem Based on Subsample Quantiles

This paper presents a new class of test procedures for two-sample location problem based on subsample quantiles. The class includes Mann-Whitney test as a special case. The asymptotic normality of the class of tests proposed is established. The asymptotic relative performance of the proposed class of test with respect to the optimal member of Xie and Priebe (2000) is studied in terms of Pitman efficiency for various underlying distributions.

Stochastic frontiers or regression quantiles for estimating the self-thinning surface in higher dimensions?

Stochastic frontier analysis and quantile regression are the two econometric approaches that have been commonly adopted in the determination of the self-thinning boundary line or surface in two and higher dimensions since their introduction to the field some 20 years ago.However,the rational for using one method over the other has,in most cases,not been clearly explained perhaps due to a lack of adequate appreciation of differences between the two approaches for delineating the self-thinning surface.Without an adequate understanding of such differences,the most informative analysis may become a missed opportunity,leading to an inefficient use of data,weak statistical inferences and a failure to gain greater insight into the dynamics of plant populations and forest stands that would otherwise be obtained.Using data from 170 plot measurements in even-aged Larix olgensis(A.Henry) plantations across a wide range of site qualities and with different abundances of woody weeds,i.e.naturally regenerated non-crop species,in northeast China,this study compared the two methods in determining the self-thinning surface across eight sample sizes from 30 to 170 with an even interval of 20 observations and also over a range of quantiles through repeated random sampling and estimation.Across all sample sizes and over the quantile range of 0.90 ≤τ≤0.99,the normal-half normal stochastic frontier estimation proved to be superior to quantile regression in statistical efficiency.Its parameter estimates had lower degrees of variability and correspondingly narrower confidence intervals.This greater efficiency would naturally be conducive to making statistical inferences.The estimated self-thinning surface using all 170 observations enveloped about 96.5% of the data points,a degree of envelopment equivalent to a regression quantile estimation with aτ of 0.965.The stochastic frontier estimation was also more objective because it did not involve the subjective selection of a particular value of τ for the favoured self-thinning surface from several mutually intersecting surfaces as in quantile regression.However,quantile regression could still provide a valuable complement to stochastic frontier analysis in the estimation of the self-thinning surface as it allows the examination of the impact of variables other than stand density on different quantiles of stand biomass.

Estimation of scale parameters of logistic distribution by linear functions of sample quantiles

The large sample estimation of standard deviation of logistic distribution employs the asymptotically best linear unbiased estimators based on sample quantiles. The sample quantiles are established from a pair of single spacing. Finally, a table of the variances and efficiencies of the estimator for 5≤n≤65 is provided and comparison is made with other linear estimators.

Best Equivariant Estimator of Extreme Quantiles in the Multivariate Lomax Distribution

The minimum risk equivariant estimator of a quantile of the common marginal distribution in a multivariate Lomax distribution with unknown location and scale parameters under Linex loss function is considered.

Bias Correction Technique for Estimating Quantiles of Finite Populations under Simple Random Sampling without Replacement

In this paper, the problem of nonparametric estimation of finite population quantile function using multiplicative bias correction technique is considered. A robust estimator of the finite population quantile function based on multiplicative bias correction is derived with the aid of a super population model. Most studies have concentrated on kernel smoothers in the estimation of regression functions. This technique has also been applied to various methods of non-parametric estimation of the finite population quantile already under review. A major problem with the use of nonparametric kernel-based regression over a finite interval, such as the estimation of finite population quantities, is bias at boundary points. By correcting the boundary problems associated with previous model-based estimators, the multiplicative bias corrected estimator produced better results in estimating the finite population quantile function. Furthermore, the asymptotic behavior of the proposed estimators is presented. It is observed that the estimator is asymptotically unbiased and statistically consistent when certain conditions are satisfied. The simulation results show that the suggested estimator is quite well in terms of relative bias, mean squared error, and relative root mean error. As a result, the multiplicative bias corrected estimator is strongly suggested for survey sampling estimation of the finite population quantile function.

Calculation of Two-Tailed Exact Probability in the Wald-Wolfowitz One-Sample Runs Test

The objectives of this paper are to demonstrate the algorithms employed by three statistical software programs (R, Real Statistics using Excel, and SPSS) for calculating the exact two-tailed probability of the Wald-Wolfowitz one-sample runs test for randomness, to present a novel approach for computing this probability, and to compare the four procedures by generating samples of 10 and 11 data points, varying the parameters n0 (number of zeros) and n1 (number of ones), as well as the number of runs. Fifty-nine samples are created to replicate the behavior of the distribution of the number of runs with 10 and 11 data points. The exact two-tailed probabilities for the four procedures were compared using Friedman’s test. Given the significant difference in central tendency, post-hoc comparisons were conducted using Conover’s test with Benjamini-Yekutielli correction. It is concluded that the procedures of Real Statistics using Excel and R exhibit some inadequacies in the calculation of the exact two-tailed probability, whereas the new proposal and the SPSS procedure are deemed more suitable. The proposed robust algorithm has a more transparent rationale than the SPSS one, albeit being somewhat more conservative. We recommend its implementation for this test and its application to others, such as the binomial and sign test.

Exploring a New Lifetime Distribution for Modelling the Waiting Time of Bank Customers

The fitting of lifetime distribution in real-life data has been studied in various fields of research. With the theory of evolution still applicable, more complex data from real-world scenarios will continue to emerge. Despite this, many researchers have made commendable efforts to develop new lifetime distributions that can fit this complex data. In this paper, we utilized the KM-transformation technique to increase the flexibility of the power Lindley distribution, resulting in the Kavya-Manoharan Power Lindley (KMPL) distribution. We study the mathematical treatments of the KMPL distribution in detail and adapt the widely used method of maximum likelihood to estimate the unknown parameters of the KMPL distribution. We carry out a Monte Carlo simulation study to investigate the performance of the Maximum Likelihood Estimates (MLEs) of the parameters of the KMPL distribution. To demonstrate the effectiveness of the KMPL distribution for data fitting, we use a real dataset comprising the waiting time of 100 bank customers. We compare the KMPL distribution with other models that are extensions of the power Lindley distribution. Based on some statistical model selection criteria, the summary results of the analysis were in favor of the KMPL distribution. We further investigate the density fit and probability-probability (p-p) plots to validate the superiority of the KMPL distribution over the competing distributions for fitting the waiting time dataset.

Correlation between Combined Urinary Metal Exposure and Grip Strength under Three Statistical Models:A Cross-sectional Study in Rural Guangxi

Objective This study aimed to investigate the potential relationship between urinary metals copper(Cu),arsenic(As),strontium(Sr),barium(Ba),iron(Fe),lead(Pb)and manganese(Mn)and grip strength.Methods We used linear regression models,quantile g-computation and Bayesian kernel machine regression(BKMR)to assess the relationship between metals and grip strength.Results In the multimetal linear regression,Cu(β=−2.119),As(β=−1.318),Sr(β=−2.480),Ba(β=0.781),Fe(β=1.130)and Mn(β=−0.404)were significantly correlated with grip strength(P<0.05).The results of the quantile g-computation showed that the risk of occurrence of grip strength reduction was−1.007(95%confidence interval:−1.362,−0.652;P<0.001)when each quartile of the mixture of the seven metals was increased.Bayesian kernel function regression model analysis showed that mixtures of the seven metals had a negative overall effect on grip strength,with Cu,As and Sr being negatively associated with grip strength levels.In the total population,potential interactions were observed between As and Mn and between Cu and Mn(P_(interactions) of 0.003 and 0.018,respectively).Conclusion In summary,this study suggests that combined exposure to metal mixtures is negatively associated with grip strength.Cu,Sr and As were negatively correlated with grip strength levels,and there were potential interactions between As and Mn and between Cu and Mn.

The Short-Term Prediction ofWind Power Based on the Convolutional Graph Attention Deep Neural Network

The fluctuation of wind power affects the operating safety and power consumption of the electric power grid and restricts the grid connection of wind power on a large scale.Therefore,wind power forecasting plays a key role in improving the safety and economic benefits of the power grid.This paper proposes a wind power predicting method based on a convolutional graph attention deep neural network with multi-wind farm data.Based on the graph attention network and attention mechanism,the method extracts spatial-temporal characteristics from the data of multiple wind farms.Then,combined with a deep neural network,a convolutional graph attention deep neural network model is constructed.Finally,the model is trained with the quantile regression loss function to achieve the wind power deterministic and probabilistic prediction based on multi-wind farm spatial-temporal data.A wind power dataset in the U.S.is taken as an example to demonstrate the efficacy of the proposed model.Compared with the selected baseline methods,the proposed model achieves the best prediction performance.The point prediction errors(i.e.,root mean square error(RMSE)and normalized mean absolute percentage error(NMAPE))are 0.304 MW and 1.177%,respectively.And the comprehensive performance of probabilistic prediction(i.e.,con-tinuously ranked probability score(CRPS))is 0.580.Thus,the significance of multi-wind farm data and spatial-temporal feature extraction module is self-evident.

Optimal convergence rates of nonparametric conditional quantiles in dependent cases

The ordinary quantiles for univariate data were successfully generalized to linear modelsin Koenker and Bassett. Regression quantiles provide more specific and more global in-formation on the relationship of two variables through their distributions. Mosteller andTukey argued that the use of regression quantiles helps to provide a more complete pic-

The Bahadur Representation for Sample Quantiles Under Dependent Sequence

On the one hand,we investigate the Bahadur representation for sample quantiles underφ-mixing sequence withφ(n)=O(n^-3)and obtain a rate as O(n-3/4 log n),a.s.On the other hand,by relaxing the condition of mixing coefficients to∑∞n=1φ^1/2(n)<∞,a rate O(n^-1/2(log n)^1/2),a.s.,is also obtained.

Simultaneous Estimation of Multiple Conditional Regression Quantiles

In this article, we put forward a new approach to estimate multiple conditional regression quantiles simultaneously. Unlike the double summation method in most of the literatures, our proposed model allows continuous variety for the quantile level over(0,1). As a result, all the quantile curves can be obtained via a 2-dimensional surface simultaneously. Most importantly, the proposed minimizing criterion can be readily transformed to a linear programming problem. We use tensor product bi-linear quantile smoothing B-splines tofit it. The asymptotic property of the estimator is derived and a real data set is analyzed to demonstrate the proposed method.

Hierarchical linear regression models for conditional quantiles

The quantile regression has several useful features and therefore is gradually developing into a comprehensive approach to the statistical analysis of linear and nonlinear response models,but it cannot deal effectively with the data with a hierarchical structure.In practice,the existence of such data hierarchies is neither accidental nor ignorable,it is a common phenomenon.To ignore this hierarchical data structure risks overlooking the importance of group effects,and may also render many of the traditional statistical analysis techniques used for studying data relationships invalid.On the other hand,the hierarchical models take a hierarchical data structure into account and have also many applications in statistics,ranging from overdispersion to constructing min-max estimators.However,the hierarchical models are virtually the mean regression,therefore,they cannot be used to characterize the entire conditional distribution of a dependent variable given high-dimensional covariates.Furthermore,the estimated coefficient vector (marginal effects)is sensitive to an outlier observation on the dependent variable.In this article,a new approach,which is based on the Gauss-Seidel iteration and taking a full advantage of the quantile regression and hierarchical models,is developed.On the theoretical front,we also consider the asymptotic properties of the new method,obtaining the simple conditions for an n1/2-convergence and an asymptotic normality.We also illustrate the use of the technique with the real educational data which is hierarchical and how the results can be explained.

ON COMPLETE CONVERGENCE OF NONPARAMETRIC REGRESSION M-QUANTILES

Consider the nonparametric regression model Y_i=m(x_i)+ε_i,i=1,…,n,where m(?)is an unknown function,and the design points x_i are knownand nonrandom.The robust nonparametric estimators were introduced by H(?)rdleand Gasser in 1984.These estimators can be viewed as regression M-quantiles.We then establish complete convergence for such quantiles under only the finitemoment condition.

Small area prediction of quantiles for zero-inflated data and an informative sample design

The Conservation Effects Assessment Project(CEAP)is a survey intended to quantify soil and nutrient loss on cropland.Estimates of the quantiles of CEAP response variables are published.Previous work develops a procedure for predicting small area quantiles based on a mixed effects quantile regression model.The conditional density function of the response given covariates and area random effects is approximated with the linearly interpolated generalised Pareto distribution(LIGPD).Empirical Bayes is used for prediction and a parametric bootstrap procedure is developed for mean squared error estimation.In this work,we develop two extensions of the LIGPD-based small area quantile prediction procedure.One extension allows for zero-inflated data.The second extension accounts for an informative sample design.We apply the procedures to predict quantiles of the distribution of percolation(a CEAP response variable)in Kansas counties.

The Alpha Power Topp-Leone Distribution: Properties, Simulations and Applications

This paper presents an extended lifetime probability distribution based on the alpha power transformation. We refer to the proposed distribution as “the Alpha Power Topp-Leone (APTL) distribution”. Mathematical properties of the APTL distribution such as the density and cumulative distribution functions, survival and hazard rate functions, quantile function, median, moments and its relative measures, probability weighted moment, moment generating function, Renyi entropy, and the distribution of order statistics were derived. The method of maximum likelihood estimation was employed to estimate the unknown parameters of the APTL distribution. Finally, we used two real data sets obtained from the literature to illustrate the applicability of the APTL distribution in real-life data fitting.

Asymmetric nexus between commercial policies and consumption‑based carbon emissions:new evidence from Pakistan

The current study extends the previous literature by exploring the effects of a newly discovered driver,i.e.,import taxes(as a proxy for commercial policies),on the consumption-based carbon emissions(CCO2e)for 1990Q1-2017Q4.For empirical analysis,several tests and methods,including Augmented Dickey–Fuller unit root test,Zivot–Andrews unit root test,asymmetric cointegration bound testing approach,non-linear ARDL,Wald-test,Granger causality test and wavelet quantile correlation(WQC)method are utilized.Furthermore,NARDL technique estimates reveal that contractionary commercial policy enhances the environmental quality by disrupting the detrimental effects of CCO2e.However,expansionary commercial policy escalates the environmental pollution by boosting the carbon emissions.Also,the exports and the renewable energy improve the ecological quality;however,GDP deteriorates the atmospheric quality by increasing the CCO2e.Besides,WQC method and the trivariate Granger causality test are deployed to confirm the robustness of the results.Based on the findings,some crucial policies are also recommended for sustainable and green development in Pakistan.

Declined trends of chlorophyll a in the South China Sea over 2005–2019 from remote sensing reconstruction

Chlorophyll a concentration(CHL)is an important proxy of the marine ecological environment and phytoplankton production.Long-term trends in CHL of the South China Sea(SCS)reflect the changes in the ecosystem’s productivity and functionality in the regional carbon cycle.In this study,we applied a previously reconstructed 15-a(2005–2019)CHL product,which has a complete coverage at 4 km and daily resolutions,to analyze the long-term trends of CHL in the SCS.Quantile regression was used to elaborate on the long-term trends of high,median,and low CHL values,as an extended method of conventional linear regression.The results showed downward trends of the SCS CHL for the 75th,50th,and 25th quantile in the past 15 a,which were−0.0040 mg/(m^(3)·a)(−1.62%per year),−0.0023 mg/(m^(3)·a)(−1.10%per year),and−0.0019 mg/(m^(3)·a)(−1.01%per year).The negative trends in winter(November to March)were more prominent than those in summer(May to September).In terms of spatial distribution,the downward trend was more significant in regions with higher CHL.These led to a reduced standard deviation of CHL over time and space.We further explored the influence of various dynamic factors on CHL trends for the entire SCS and two typical systems(winter Luzon Strait(LZ)and summer Vietnam Upwelling System(SV))with single-variate linear regression and multivariate Random Forest analysis.The multivariate analysis suggested the CHL trend pattern can be best explained by the trends of wind speed and mixed-layer depth.The divergent importance of controlling factors for LZ and SV can explain the different CHL trends for the two systems.This study expanded our understanding of the long-term changes of CHL in the SCS and provided a reference for investigating changes in the marine ecosystem.

Tail spillover effects between cryptocurrencies and uncertainty in the gold,oil,and stock markets

This study investigates tail dependence among five major cryptocurrencies,namely Bitcoin,Ethereum,Litecoin,Ripple,and Bitcoin Cash,and uncertainties in the gold,oil,and equity markets.Using the cross-quantilogram method and quantile connectedness approach,we identify cross-quantile interdependence between the analyzed variables.Our results show that the spillover between cryptocurrencies and volatility indices for the major traditional markets varies substantially across quantiles,implying that diversification benefits for these assets may differ widely across normal and extreme market conditions.Under normal market conditions,the total connectedness index is moderate and falls below the elevated values observed under bearish and bullish market conditions.Moreover,we show that under all market conditions,cryptocurrencies have a leadership influence over the volatility indices.Our results have important policy implications for enhancing financial stability and deliver valuable insights for deploying volatility-based financial instruments that can potentially provide cryptocurrency investors with suitable hedges,as we show that cryptocurrency and volatility markets are insignificantly(weakly)connected under normal(extreme)market conditions.