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.

Joint empirical likelihood confidence regions for a finite number of quantiles under strong mixing samples

In this paper, we obtain the joint empirical likelihood confidence regions for a finite number of quantiles under strong mixing samples. As an application of this result, the empirical likelihood confidence intervals for the difference of any two quantiles are also obtained.

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.

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.

Semi-empirical Likelihood Confidence Intervals for the Differences of Quantiles with Missing Data

Detecting population （group） differences is useful in many applications, such as medical research. In this paper, we explore the probabilistic theory for identifying the quantile differences .between two populations. Suppose that there are two populations x and y with missing data on both of them, where x is nonparametric and y is parametric. We are interested in constructing confidence intervals on the quantile differences of x and y. Random hot deck imputation is used to fill in missing data. Semi-empirical likelihood confidence intervals on the differences are constructed.

Empirical Likelihood Method for Quantiles with Response Data Missing at Random

Empirical likelihood is a nonparametric method for constructing confidence intervals and tests, notably in enabling the shape of a confidence region determined by the sample data. This paper presents a new version of the empirical likelihood method for quantiles under kernel regression imputation to adapt missing response data. It eliminates the need to solve nonlinear equations, and it is essy to apply. We also consider exponential empirical likelihood as an alternative method. Numerical results are presented to compare our method with others.

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.

Empirical Likelihood for Quantiles Under Associated Samples

The construction of confidence intervals for quantiles of a population under a associated sample is studied by using the blockwise technique. It is shown that the blockwise empirical likelihood （EL） ratio statistic is asymptotically X2-type distributed, which is used to obtain EL-based confidence intervals for quantiles of a population.

Empirical Likelihood Confidence Intervals for the Differences of Quantiles with Missing Data

Suppose that there are two nonparametric populations x and y with missing data on both of them. We are interested in constructing confidence intervals on the quantile differences of x and y. Random imputation is used. Empirical likelihood confidence intervals on the differences are constructed.

Nonparametric estimation of quantiles for a class of stationary processes

We study smoothed quantile estimator for a class of stationary processes. We obtain the convergency rates and the Bahadur representation, as well as the asymptotic normality for this estimator by the method of m-dependent approximation. Our results can be used in the study of the estimation of value-at-risk(Va R) and applied to many time series which have important applications in econometrics.

Joint Empirical Likelihood Confidence Regions for a Finite Number of Quantiles Under Negatively Associated Samples

In this paper, the authors obtain the joint empirical likelihood confidence regions for a finite number of quantiles under negatively associated samples. As an application of this result, the empirical likelihood confidence intervals for the difference of any two quantiles are also developed.

Nonparametric Estimation of Extreme Conditional Quantiles with Functional Covariate

Estimation of the extreme conditional quantiles with functional covariate is an important problem in quantile regression. The existing methods, however, are only applicable for heavy-tailed distributions with a positive conditional tail index. In this paper, we propose a new framework for estimating the extreme conditional quantiles with functional covariate that combines the nonparametric modeling techniques and extreme value theory systematically. Our proposed method is widely applicable, no matter whether the conditional distribution of a response variable Y given a vector of functional covariates X is short, light or heavy-tailed. It thus enriches the existing literature.

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.