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A novel approach to the construction of absolutely continuous distributions over the unit interval is proposed. Considering two absolutely continuous random variables with positive support, this method conditions on their convolution to generate a new random variable in the unit interval. This approach is demonstrated using some popular choices of positive random variables, such as the exponential, Lindley, and gamma. Some existing distributions, like the uniform, the beta, and the Kummer-beta, are formulated with this method. Several new structures of density functions having potential for future applications in real-life problems are also provided. One of the new distributions, namely the LCG, is considered for detailed study along with a related distribution, namely the GCL. The moments, hazard rate, cumulative distribution function, stress-strength reliability, random sample generation using the quantile function, method of moments along with maximum likelihood estimation, and regression modeling are discussed for both the distributions. Real-life applications of the proposed models and the corresponding regression models show promising results. [ABSTRACT FROM AUTHOR]

Traditional ordinary least square (OLS) regression is commonly utilized to develop regression-ratio type estimators with traditional and non traditional measures of location. However, when data are contaminated by outliers, the ordinary least square estimates become inappropriate, and the alternative approach is to use the robust regression method. To solve this issue, the use of robust regression tools for mean estimation is a commonly settled practice. In the present study, we have proposed an efficient family of exponential quantile regression-ratio type estimators by using the auxiliary information for estimating the finite population mean under simple random sampling scheme. Here it is worth noting that quantile regression is robust to outliers. Mathematical expressions such as bias, mean squared error (MSE), and minimum mean squared error are derived up to first order of approximation. To support theoretical findings, two real data collections originating from different sources are used for numerical illustration. The results are showing the superiority of proposed exponential quantile robust regression family of estimators as compared to the existing estimators under simple random sampling scheme. [ABSTRACT FROM AUTHOR]

AbstractIn this study, we consider 2- and 3-step estimators for censored quantile regression models with fixed effects. In the first step of these estimators, the informative subset is determined through the estimation of censoring probability. While previous studies often employ symmetric link functions for estimating the censoring probability, these may not accurately identify the best subset when the distribution of the censoring probability is skewed. Given the prevalence of asymmetrically censored data in empirical analyses, we propose using an asymmetric link function for more accurate subset determination. We conduct Monte Carlo simulations and empirical analysis to assess our proposed methods. Our Monte Carlo simulations and empirical analysis confirm that an asymmetric link function offers a better fit for asymmetrically censored data. For symmetrically censored data, the symmetric link function performs better in moderate and large samples, while the asymmetric link function performs slightly better in small samples. These findings underscore the importance of considering both the censoring probability distribution and sample size in panel quantile regression. [ABSTRACT FROM AUTHOR]

Recently, quantile-based structural equation model has enjoyed increasing popularity in various fields and applications. As we know, structural equation model consists of structural model and measurement model in total. In our quantile-based measurement model, the observed variables are considered to be manifestations of an underlying construct with changing relationships going from the latent variable to its observed variables at different quantiles. Based on our model, we propose a quantile-based partial least square algorithm with bag of little bootstraps. All of our model and algorithm are compared to our quantile-based partial least square algorithms with traditional bootstrap in simulations, and applied to part of IMD (International Institute for Management Development) World Competitiveness Yearbook datasets. [ABSTRACT FROM AUTHOR]

AbstractIn this article, the robust estimation for a class of semiparametric spatial autoregressive models has been investigated. By combining the QR decomposition technique for matrix and the weighted composite quantile regression method, we propose a robust estimation procedure for the parametric and non parametric components. Under certain regularity conditions, asymptotic properties of the resulting estimators are proved. Several simulation analyses have been conducted for further illustrating the performance of the proposed method, and the simulation results demonstrate that the proposed method improve the robustness of the models. [ABSTRACT FROM AUTHOR]

AbstractWe, in this article, focus on functional partially linear quantile regression, where the observations are missing at random, which allows the response or covariates or response and covariates simultaneously missing. Estimation of the unknown function is done based on reproducing kernel method. Under suitable assumptions, we discuss consistency with rates of the estimators, and establish asymptotic normality of the estimator for the parameter. At the same time, we study hypothesis test of the parameter, and prove asymptotic distributions of restricted estimators of the parameter and test statistic under null hypothesis and local alternative hypothesis, respectively. Also, we study variable selection of the linear part of the model. By simulation and real data, finite sample performance of the proposed methods is analyzed. [ABSTRACT FROM AUTHOR]

Abstract–In the regression analysis, ordinary least square techniques is commonly used. However, the data's outcomes may be untrustworthy if there is an outliers in it. In order to deal with the outliers problem, robust quantile regression methods have been frequently presented as alternatives to OLS for a long time. In this article, primarily a exponential ratio-type estimators is suggested. After that, robust quantile regression estimators are proposed, that is a useful strategy. The application of robust quantile regression empowered the efficiency of the estimators especially for outliers in the data. The MSE equations of the various estimators are computed and compared to OLS approaches. Numerical illustration and simulations studies are performed to support our theoretical findings. [ABSTRACT FROM AUTHOR]

In this article, we investigate various asymptotic properties (bias, variance, mean squared error, mean integrated squared error, asymptotic normality, uniform strong consistency) for Bernstein estimators of quantiles and cumulative distribution functions when the variable of interest is subject to random right-censored. In this work, we extend to the case of censored data the results of Leblanc and Babu, Canty and Chaubey. A simulation study is considered to show the performance of the proposed estimator. [ABSTRACT FROM AUTHOR]

In this article, we consider smooth estimators for the quantile density function (qdf) for a sequence { X n , n ≥ 1 } of stationary non negative associated random variables with a common marginal distribution function. The qdf is given by q (u) = Q ′ (u) , u ∈ (0 , 1) , Q (u) representing the corresponding quantile function. The smooth estimators of q (u) considered here are adapted from those of Q (u) considered in Chaubey, Dewan, and Li (2021). A few asymptotic properties of these estimators are established parallel to those in the i.i.d. case. A numerical study comparing the mean squared errors of various estimators indicates the advantages and a few limitations of various estimators. The smoothing parameter is selected based on the BCV and RLCV (a variation of likelihood cross-validation) criteria. It is concluded, based on the numerical studies, that the RLCV criterion may produce over-smoothing, hence BCV criterion may be preferable. The numerical studies also suggest that, overall, the estimator proposed by Soni, Dewan, and Jain (2012) seems to have some advantage over the other estimators considered in this article. [ABSTRACT FROM AUTHOR]

This article is concerned with the asymptotic theory of estimates of unknown parameters in autoregressive quantile processes. We assume random errors form a strictly stationary ϕ -mixing sequences. In view of the approach of argmins and blocking argument, we prove the parameter estimators satisfy the functional moderate deviation principle (MDP). Further, we give the law of the iterated logarithm under some standard conditions. Based on the contraction principle, the moderate deviation principles of L-estimators on the autoregression quantile (ARQ) and autoregression rank scores (ARRS's) are also discussed. This method can be extended to a fair range of different statistical estimation problems. [ABSTRACT FROM AUTHOR]

In some experiments such as stress testing and industrial quality control experiments, only values which are larger or smaller than all previous ones are observed. Study of such extremes are of great importance. An extensive research on record values using distribution function are available in literature; however, a quantile-based study on the same have not been considered so far. Motivated with these, in this article, we introduce a quantile function approach of record values, which is an equivalent and alternative to the traditional distribution function approach. We study various properties of quantile-based measures of record values. We also obtain some stochastic comparison and ageing properties of quantile-based record values. The L-moment estimation method of hazard quantile function of record values is explained using a real-data example. [ABSTRACT FROM AUTHOR]

Non-additive measures are important for many applications. In this paper we propose an extension of the non-additive measure using the concept of Kerridge inaccuracy and cumulative Tsallis entropy. Several properties including non-linear transformation, bounds and characterizations are obtained using this measure. We also study different properties of the quantile version of the proposed measure. Finally, we numerically illustrate the usefulness of the measure and its quantile form using kernel density estimators. [ABSTRACT FROM AUTHOR]

In this article, we consider functions having the properties of both the cumulative distribution function and the quantile function. Due to these characteristics, we term such functions quantile cumulative distribution functions. The comparison distribution function defined by Parzen (1982) for comparing the probability distributions of two populations is an example of such a function. We discuss some properties of the quantile cumulative distribution function and its usefulness in generating new continuous probability distributions on the unit interval. An overview of some of their applications is also presented to emphasize the importance of the quantile cumulative distribution function. [ABSTRACT FROM AUTHOR]

This paper presents a flexible family of 2- and 3-parameter distributions whose support is the closed interval [0,1], with explicit density, cumulative density, and quantile functions. These distributions are suited to modeling quantiles, thereby expanding the toolbox of distributions for doubly-bounded random variables. The densities at the boundaries are determined by dispersion and skew parameters, and a third parameter exclusively influences location. The paper also discusses practical issues of parameter estimation and assesses estimation bias, Type I error-rate accuracy, and parameter-estimate collinearity. It also provides three examples of applications to real data using new packages implementing the distributions in R and Stata. [ABSTRACT FROM AUTHOR]

Composite quantile regression methods have been shown to be effective techniques in improving the prediction accuracy. In this article, we propose a Bayesian weighted composite quantile regression estimation procedure to estimate unknown regression coefficients and autoregressive parameters in the linear regression models with autoregressive errors. A Bayesian joint hierarchical model is established using the working likelihood of the asymmetric Laplace distribution. Adaptive Lasso-penalized type priors are used on regression coefficients and autoregressive parameters of the model to conduct inference and variable selection simultaneously. A Gibbs sampling algorithm is developed to simulate the parameters from the posterior distributions. The proposed method is illustrated by some simulation studies and analyzing a real data set. Both simulation studies and real data analysis indicate that the proposed approach performs well. [ABSTRACT FROM AUTHOR]

The random coefficient autoregressive (RCAR) processes are very useful to model time series in applications. It is commonly observed that the random autoregressive coefficient is assumed to be an independent identically distributed (i.i.d.) random variable sequence. To make the RCAR model more practical, this paper considers a new RCAR(1) model driven by explanatory variable and observations. We use the conditional least squares, the quantile regression and the conditional maximum likelihood methods to estimate the model parameters. The consistency and asymptotic normality of the proposed estimates are established. Simulation studies are conducted for the evaluation of the developed approaches and two applications to real-data examples are provided. The results show that the proposed procedures perform well for the simulations and application. [ABSTRACT FROM AUTHOR]

We propose two new regressions, one parametric and other partially linear based on an extended Birnbaum–Saunders distribution. This distribution includes, as special cases, the exponentiated Birnbaum–Saunders, odd log-logistic Birnbaum–Saunders and Birnbaum–Saunders distributions. Several mathematical properties are presented. We adopt the maximum likelihood method to estimate the parameters of the parametric regression model and the penalized maximum likelihood method to estimate the parameters of the partially linear regression model. We study the behavior of the estimators through Monte Carlo simulations considering different scenarios and also extended the quantile residuals for the new regression models to verify the versatility of the parametric regression model. An analysis is carried out using average price data (R$) received by producers and wholesalers collected by Hortifruti/Cepea-Esalq/USP (Brazil). Similarly, the flexibility of the partially linear regression model is proved through an analysis with data on the average price of a hectare of rural property with improvements in the city of Itapeva-SP, Brazil. These applications empirically show that the proposed regression models have a better quality of fit than other existing regression models in the literature. [ABSTRACT FROM AUTHOR]

Missing information is a typical issue in sampling surveys. The analysts have perceived that statistical inference possibly ruined due to occurrence of non-response. Ratio type regression estimators under simple random sampling (SRS) scheme for estimating the population mean are commonly used when some of the data suffered with the issue of missingness. It is worth noting that this class is based on ordinary least square regression coefficient which is not suitable when extreme values present in the data set. In this research, primarily a modified class of estimators is presented by adapting the idea of Zaman and Bulut. Later on, a class of quantile regression type estimators is defined which is an effective technique in presence of extreme observations. The utilization of quantile regression in the idea of Zaman and Bulut's work empowered the proposed class of estimators for the estimation of population mean especially for missingness in the data. For mean square error (MSE), the hypothetical equations are also formulated for adapted and proposed estimators, on the basis of three possible cases of missingness. To justify the proposed work these hypothetical innovations are illustrated by the numerical demonstrations. [ABSTRACT FROM AUTHOR]

Tecator dataset has been widely used in the content of functional data analysis. As far as we know, this dataset is only considered under mean regression, which is easily affected by outliers. However, there are 8 more fat samples and 17 more protein samples in this dataset, so, in this paper, we explore this dataset by quantile regression, which is a robust method. Single-index partially functional linear quantile regression is proposed, and B-splines are used to estimate the unknown link function in the single-index component and the unknown slope function in the functional linear component. We establish the convergence rates and asymptotic normality of the estimators. Simulation studies and a real data application are presented to illustrate the performance of the proposed methodologies. [ABSTRACT FROM AUTHOR]

The study of Shannon differential entropy function and its associated measures using quantile function are of recent interest among researchers. However, a bivariate extension of the same have not been considered so far. Recently, a new method of deriving bivariate quantile function and their properties in the context of reliability modeling is available in literature. Motivated by this, the present paper introduces and obtain some properties of quantile-based entropy function in the bivariate case. We also examine various properties of bivariate quantile entropy function for residual random variables. Finally, we illustrate the bivariate quantile-based residual entropy function using a suitable lifetime data. [ABSTRACT FROM AUTHOR]

By establishing a connection between a quantile regression and an asymmetric Laplace distribution (ALD), this paper considers the maximum likelihood estimation of parameters of a quantile autoregression model with Markovian switching (MSQAR), where the error terms obey ALD whose scale parameter depends on regime shifts. By utilizing the mixture representation of ALD, we develop an effective ML approach for estimating parameters of MSQAR models, and obtain closed-form estimators of unknown parameters via the EM algorithm. Consistency and asymptotic normality of estimators are shown by extending some techniques adopted in Douc, Moulines, and Rydén (2004). Also, we extend some asymptotic results of estimators to the case where the conditional quantile regression model is misspecified. Furthermore, the proposed approach is illustrated by simulations and empirical data. Simulation results show that the procedure performs well in finite samples, and the empirical analysis not only supports the existence of regime-switching in the quantile autoregression model, but also has a good performance on data fitting. [ABSTRACT FROM AUTHOR]

We propose a reparameterized regression for the median of an extended Maxwell distribution that can be used when the response variable has a positive support. We obtain some structural properties of the distribution. The parameter estimates are obtained by maximum likelihood and Bayesian methods. Some influence measures and quantile residuals are defined. Several Monte Carlo simulations are reported for inference purposes. The new regression is applied to an experimental data set. [ABSTRACT FROM AUTHOR]

Based on Bayesian method, we investigate single-index quantile regression with missing observation. In particular, using spline approximation for the link function, we construct quasi-posterior distribution of the index vector based on asymmetric Laplace likelihood with missing observation, and establish asymptotically normality of the posterior estimator of the index parameters. At the same time, we use a hierarchical model based on spike and slab Gaussian priors to do variable selection and study consistency of the variable selection. Finite sample performance of the proposed methods is analyzed via simulation and real data too. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a class of distributions with bilinear mean residual quantile function. We study various distributional properties and reliability characteristics of the proposed class. Characterizations of the model are presented and the method of L-moments is employed to estimate parameters of the class of distributions. Finally, we illustrate the usefulness of the proposed claim to a real data set. [ABSTRACT FROM AUTHOR]

A behavioral mean-risk portfolio selection problem in continuous time is formulated and studied in this article. Based on the standard mean-variance portfolio selection problem, the cumulative distribution function of the cash flow is distorted by a probability distortion function. This probability distortion function represents the risk preference in a different way. Then the problem is no longer a convex optimization problem. This feature distinguishes it from the conventional linear-quadratic (LQ) problems. The stochastic optimal LQ control theory no longer applies. We take the quantile function of the terminal cash flow as the decision variable. The corresponding optimal terminal cash flow can be recovered by the optimal quantile function. Then the efficient strategy is the hedging strategy of the optimal terminal cash flow. [ABSTRACT FROM AUTHOR]

Quantile regression predicts the τ-quantile of the conditional distribution of a response variable given the explanatory variable for τ ∈ (0, 1). The aim of this paper is to establish the asymptotic distribution of the quantile estimator obtained by penalized spline method. A simulation and an exploration of real data are performed concerned with our results. [ABSTRACT FROM AUTHOR]

In this article, we introduce two quantile autoregressive models with explanatory variables. The Bayesian quantile estimation method is considered in estimating the model parameters based on an asymmetric Laplace likelihood. By introducing the latent variables, we developed the two Gibbs sampling algorithms for the proposed models. The numerical simulation implies that the Gibbs sampling algorithms converges fast and the Bayesian quantile estimators are robust. A real example is given to discuss the relationship of the gold price and three exogenous variables. Both the simulations and the data example indicate that the proposed methods are feasible, reliable and appropriate for analyzing the gold price time series. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In survival or reliability studies, the quantile density function is an important characteristic in understanding the survival or aging process. In this various types of studies, a typical problem encountered in the data collection stage is that the samples may be censored from the right. In this article, we consider the problem of nonparametric estimation of a quantile density with right-censored data. A new adaptive wavelet estimator of this function is defined and its asymptotic properties are studied. In order to evaluate the performance of our estimator, small Monte Carlo simulations are carried out. Results show that the proposed estimators work well especially when the sample size is small and their calculations are simple. Finally, a real data example is provided. [ABSTRACT FROM AUTHOR]

In many applications of hierarchical latent variable model, manifest variables could be missing due to various reasons. Improper missing data techniques or data imputation algorithms may lead to incredible data sets and inaccurate estimates. In our paper, we propose two types of imputation partial least square (PLS) algorithms to deal with missing data problems in hierarchical latent variable model. One is the imputation PLS algorithms based on linear regression (IPLSL), the other is the imputation PLS algorithms based on quantile regression (IPLSQ). In IPLSL, we apply the idea of complete case analysis (CC), inverse probability weighting (IPW) and fractional imputation (FI) to one kind of PLS algorithm which is different from the existing repeated indicators approach, two-step approach and hybrid approach. In IPLSQ, we also apply CC, IPW and FI to a modified PLS algorithm based on quantile regression. Compared with IPLSL, IPLSQ has the advantages in capturing overall view of structural relationships at different quantiles and highlighting the changing relations according to the explored quantile of interest. Together with mean and median imputation, we investigate the performances of our IPLSL and IPLSQ algorithms through simulation studies and then apply them to national science and technology innovation capability study based on part of World Bank database and Global Innovation Index report. [ABSTRACT FROM AUTHOR]

This paper studies a penalized quantile regression for spatial panel model with fixed effects, where a penalized method is used to control additional variability by shrinking the individual fixed effects to a common value with a tuning parameter. The bias is reduced by employing the instrumental variables quantile regression method. Limiting properties of the proposed estimator are derived, say consistency and asymptotic normality. Monte Carlo simulations results are provided to illustrate the finite sample behavior of the proposed estimation methods. The use of the procedures is illustrated through an empirical application to analyze a spatial panel data related to military expenditure from 144 countries over 15 years. [ABSTRACT FROM AUTHOR]

In many data analytic problems, repeated measurements with a large number of covariates are collected and conditional quantile modeling for such correlated data are often of significant interest, especially in medical applications. We propose a quadratic inference functions based approach to take into account the correlations within clusters and use smoothing to make the objective function amenable to computation. We show that the asymptotic properties of the estimators are the same whether or not smoothing is applied, established in the "diverging p, large n" setting. The cluster sizes are also allowed to diverge with sample size n. Simulation results are presented to demonstrate the effectiveness of the proposed estimator by taking into account the within-cluster correlations and we use a longitudinal data set to illustrate the method. [ABSTRACT FROM AUTHOR]

In this paper, we make use of meta-elliptical copula functions to build a new multivariate distribution with fixed marginal distributions and dependence structure to analyze bounded data. Specifically, we present a flexible p-elliptical multivariate probability distribution in the hypercube (0 , 1) p p with fixed marginal GF-quantile distributions. We then present some illustrative examples and a meta-elliptical multivariate regression model as a flexible alternative to the multivariate normal regression model on unit intervals. A simulation study and real-life data analysis using a Bayesian framework with the extreme-value quantile functions show the flexibility of the proposed meta-multivariate normal regression model for modeling the observed proportion response variables. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a robust estimator of the tail index of a Pareto-type distribution. The estimator is obtained through the use of the minimum density power divergence with an exponential regression model for log-spacings of top order statistics. The proposed estimator is compared to existing minimum density power divergence estimators of the tail index based on fitting an extended Pareto distribution and exponential regression model on log-ratio of spacings of order statistics. We derive the influence function and gross error sensitivity of the proposed estimator of the tail index to study its robustness properties. In addition, a simulation study is conducted to assess the performance of the estimators under different contaminated samples from different distributions. The results show that our proposed estimator of the tail index has better mean square errors and is less sensitive to an increase in the number of top order statistics. In addition, the estimation of the exponential regression model yields estimates of second-order parameters that can be used for estimation of extreme events such as quantiles and exceedance probabilities. The proposed estimator is illustrated with practical datasets on insurance claims and calcium content in soil samples. [ABSTRACT FROM AUTHOR]

Nonignorable missing data presents a great challenge in statistical applications, since the observed likelihood is not identifiable without any further restrictions. In this paper, we make inference about the differences between the corresponding parameters of two independent samples with nonignorable missing renponse. To address the identifiability issue, we consider a parametric propensity model and utilize group label information as an instrument. Two-step generalized method of moments is applied to estimate the parameters of the propensity based on the instrumental estimating equations, and then population parameters are estimated based on the inverse probability weighting with the estimated propensity. The asymptotic properties of the resulting estimators are established. The finite-sample performance of the differences for the population means, distribution functions and quantiles is studied through simulations, and an application to Korean Labor and Income Panel Study (KLIPS) data set is also presented. [ABSTRACT FROM AUTHOR]

The problems of interval estimation of, and testing a hypothesis on the quantile θ = μ + η σ 1 (for given η) have been considered when independent random samples are available from two normal populations with a common mean μ and possibly unknown and unequal variances. The asymptotic confidence interval (ACI) for the quantile has been derived using the Fisher information matrix. Further, parametric bootstrap approaches such as boot-p, boot-t as well as the generalized p-value method have been adopted to obtain the confidence intervals numerically. For hypothesis testing several tests such as the one based on the Computational Approach Test (CAT), the likelihood ratio test (LRT), a test using an estimator of quantile, and tests based on generalized p-value approach have been proposed. Finally, the sizes (powers) of all the proposed tests have been computed using Monte-Carlo simulation procedure. Also the confidence intervals have been compared through average length (AL), coverage probability (CP), and a new measure called - the probability coverage density (PCD). [ABSTRACT FROM AUTHOR]

In medical research, it is important to compare quantiles of certain measures obtained from treatment and control groups, with the quantile ratio showing the effect of the treatment. In particular, inference of the quantile ratio based on large sample methods can be studied using a normal model. In this paper, we develop noninformative priors such as probability matching priors and reference priors for quantile ratios in normal models. It has been proved that the one-at-a-time reference prior satisfies a first-order matching criterion, while the Jeffreys' and two-group reference priors do not when the variances are equal. Through simulation study and an example based on real data, we also confirm that the proposed probability matching priors match the target coverage probabilities in a frequentist sense even when the sample size is small. [ABSTRACT FROM AUTHOR]

The role of quantile functions in modeling various forms of statistical data is well established. Generally classical procedures like method of moments, L-moments, percentiles etc are employed in estimating the parameters of the model. In the present work an attempt is made to infer parameters in the Bayesian framework with special emphasis to distributions in which the quantile functions do not posses tractable distribution functions. The procedure is illustrated for some distributions and real life data. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of the nonparametric analysis by the relative-error regression when the explanatory of a variable is of infinite dimension. Based on k-Nearest Neighbors procedure (kNN), we construct an estimator and establish its asymptotic properties. Precisely, we show its Uniform consistency in Number of Neighbors (UNN) with the precision of the convergence rate. Some empirical studies are also performed to highlight the impact of this asymptotic result in nonparametric functional statistics. [ABSTRACT FROM AUTHOR]

Medical costs are often skewed to the right, heteroscedastic, and having a sophisticated relation with covariates. Moreover, medical cost datasets are always massive, such as in the New York Statewide Planning and Research Cooperative System Expenditure Study. Different observations can depend on each other as the spatial distribution of diseases induces complex correlation among patients coming from nearby communities. Therefore, it is not enough if only focus on the mean function regression models with low-dimensional covariates, small sample size and identically independent observations. In this paper, we propose a new quantile regression model to analyze medical costs. A network term is introduced to account for the dependence among different observations. We also consider variable selection for massive datasets. An adaptive lasso penalized variable selection method is applied in a parallel manner, the resulting estimators are combined through minimizing an extra penalized loss function. Simulation studies are conducted to illustrate the performance of the estimation method. We apply our method to the analysis of the New York State's Statewide Planning and Research Cooperative System, 2013. [ABSTRACT FROM AUTHOR]

In this paper, we propose a scale-scale plot to compare multivariate distributions. These scale-scale plots can be viewed as a multivariate analog of quantile-quantile plots and we illustrate their use as a visualization tool to validate distributional assumptions for multivariate data as well as to compare the distributions of two multivariate samples. We discuss some characterizations of the proposed plots under elliptically symmetric distributions and based on those results, propose some visual tests of location and scale as further applications of these scale-scale plots. For the test of location problem, we present a small power study using simulations. [ABSTRACT FROM AUTHOR]

This paper proposes a new efficient composite quantile regression (CQR) estimating function for the semivarying models with longitudinal data, which can incorporate the correlation structure between repeated measures via the Gaussian copula. Because the objective function is non-smooth and non-convex, the induced smoothing method is used to reduce computational burdens. It is proved that the smoothed estimator is asymptotically equivalent to the original estimator. Furthermore, a smooth-threshold efficient CQR estimating equation variable selection method is proposed. Because the new method can incorporate the correlation structure and inherit the good properties of CQR, it has the advantages of both robustness and high estimation efficiency. Simulation studies and real data analysis are also included to illustrate the finite sample performance of our methods. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the partially linear varying-coefficient quantile regression model with observations missing at random (MAR), which include the responses or the responses and covariates MAR. Based on the local linear estimation of the varying-coefficient function in the model, we construct empirical log-likelihood ratio functions for unknown parameter in the linear part of the model, which are proved to be asymptotically weighted chi-squared distributions, further the adjusted empirical log-likelihood ratio functions are verified to converge to standard chi-squared distribution. The asymptotic normality of maximum empirical likelihood estimator for the parameter is also established. In order to do variable selection, we consider penalized empirical likelihood by using smoothly clipped absolute deviationv (SCAD) penalty, and the oracle property of the penalized likelihood estimator of the parameter is proved. Furthermore, Monte Carlo simulation and a real data analysis are undertaken to test the performance of the proposed methods. [ABSTRACT FROM AUTHOR]

The consistency of various estimators under the semi-parametric linear regression model and the standard right censorship model (SPLRRC model) has been studied under various assumptions since the 1970s. These assumptions are somewhat sufficient conditions for the identifiability of the parameters under the SPLRRC model. Since then, it has been a difficult open problem in survival analysis to find the necessary and sufficient condition for the identifiability of the parameters under the SPLRRC model. The open problem is solved in this paper. It is of interest to investigate whether the common estimators under this model are consistent under the identifiability condition. Under the latter condition, we show that the Buckley–James estimator and quantile regression estimator can be inconsistent and present partial results on the consistency of the semi-parametric maximum likelihood estimator. [ABSTRACT FROM AUTHOR]

In quantile regression, the quantile function is often discontinuous so that it is needful to detect the jump points. In the existing literature, it is generally assumed the jump number to be known. In most applications, however, it is not uncommon that the jump number is often unknown so that the existing methods of detecting jump discontinuities are no longer applicable. In this paper, we first propose a new procedure of detecting jump by using the local polynomial techniques for the case of the unknown jump number. We then propose the estimators of jump points, jump sizes and jump number, and study their asymptotic properties. Finally, we conduct simulation studies to assess the finite sample performance of our proposed estimators and present their biases and standard errors to demonstrate that our proposed method performs well in a wide range of practical settings. [ABSTRACT FROM AUTHOR]

Quantile regression has great flexibility in describing the effect of covariate on response. In this paper, based on the censored median regression proposed by Zhou, we develop a new weighted quantile regression of nonlinear models when the response is randomly censored. Our method can be applied to more complicated quantile regression models at any quantile within (0, 1), which contains censored median regression. Furthermore, the consistency and asymptotic normality of the proposed estimator are derived under appropriate assumptions. Finally, the finite sample performance of the proposed estimator is examined by numerical simulation. [ABSTRACT FROM AUTHOR]

The present paper introduces a new method for constructing a flexible family of distributions defined by a quantile function. We derive a new class of distributions, which is an extension of the class of distributions with linear mean residual quantile function. Various distributional properties and reliability characteristics are discussed. The estimation of parameters using the method of percentiles is studied. The model is applied to a real-life data. [ABSTRACT FROM AUTHOR]

This article introduces a Bayesian estimating method for a bent line quantile regression model. Within the Bayesian framework, regression coefficients and threshold can be simultaneously estimated, addressing the problem of optimizing the loss function in frequentist approaches, while the statistical inference on the threshold is direct. Simulation studies and two real data examples show that the Bayesian method demonstrates better sample performance. [ABSTRACT FROM AUTHOR]

We introduce a local linear estimation of the conditional quantile of a censored scalar response variable, given a functional covariate. The rates of the pointwise and the uniform almost-complete convergences, of the conditional distribution estimator, are established. Then, we deduce the uniform almost-complete convergence of the obtained conditional quantile estimator. A simulation study is used to investigate the performance of a studied new estimator with respect to the kernel method. [ABSTRACT FROM AUTHOR]

In this paper, we consider the weighted composite quantile regression for the linear model when the data are right censored and the censoring indicators are missing at random. The adaptive penalized procedures are proposed to discuss variable selection in the model. Under appropriate assumptions, the asymptotic normality and oracle property of these estimators are also established. The simulation studies are conducted to illustrate the finite sample performance of the proposed methods. [ABSTRACT FROM AUTHOR]