The quantile-based flattened logistic distribution: Some properties and applications

In this paper, the quantile-based flattened logistic distribution has been studied. Some classical and quantile-based properties of the distribution have been obtained. Closed form expressions of L-moments, L-moment ratios and expectation of order statistics of the distribution have been obtained. A quantile-based analysis concerning the method of matching L-moments estimation is employed to estimate the parameters of the proposed model. We further derive the asymptotic variance–covariance matrix of the matching L-Moments estimators of the proposed model. Finally, we apply the proposed model to simulated as well as two real life datasets and compare the fit with the logistic distribution.     

Living Arrangements, Employment Status, and the Economic Well-Being of Mothers: Evidence from Brazil, Chile, and the U.S

Using data from Brazil, Chile, and the U.S., we estimate country specific models of household income that characterize mothers according to their marital status, living arrangement, and employment status. We assess the predicted economic well-being of each type of mother relative to a benchmark of married mothers in the same country, and at various points in the income distribution. We find dramatic cross-country differences in the distribution of mothers across categories, but few differences in each type's relative economic status. In all three countries and at all points in the income distribution, mothers who are the only adults in their households have the lowest levels of predicted income, while married mothers—followed closely by cohabitors—have the highest levels.     

Local dependence estimation using semiparametric archimedean copulas

The authors define a new semiparametric Archimedean copula family which has a flexible dependence structure. The generator of the family is a local interpolation of existing generators. It has locally‐defined dependence parameters. The authors present a penalized constrained least‐squares method to estimate and smooth these parameters. They illustrate the flexibility of their dependence model in a bi‐variate survival example.     

Unexpected but authentic use of an ethnically–marked dialect

Recent work on language crossing in the U.S. has examined the temporary appropriation of African American Vernacular English by white youth in an effort to participate in the current popularity and prestige of hip–hop culture, or in order to highlight racial boundaries. While such verbal behavior probably encompasses most white use of AAVE, it is not the only way in which whites (or other non–blacks) can use the variety. This paper presents a case study of the language of a 23 year old white female who makes consistent use of many distinctive linguistic features associated with AAVE. I argue that the interaction of ideologies of race, class, localness and language allow her to be considered an ingroup member despite her biographical race. This suggests that there is a tension between academic linguistic theory and actual speaker practice in assigning authenticity to individuals, and I conclude that language ideologies and other forms of qualitative evidence should be taken into account by sociolinguists looking at the link between language and race.     

A Semi-Parametric Quantile Function Estimator for Use in Bootstrap Estimation Procedures

In this note we develop a new quantile function estimator called the tail extrapolation quantile function estimator. The estimator behaves asymptotically exactly the same as the standard linear interpolation estimator. For finite samples there is small correction towards estimating the extreme quantiles. We illustrate that by employing this new estimator we can greatly improve the coverage probabilities of the standard bootstrap percentile confidence intervals. The method does not reqiure complicated calculations and hence it should appeal to the statistical practitioner.     

Sampling Strategies for Toxic Air Contaminants

Annual concentrations of toxic air contaminants are of primary concern from the perspective of chronic human exposure assessment and risk analysis. Despite recent advances in air quality monitoring technology, resource and technical constraints often impose limitations on the availability of a sufficient number of ambient concentration measurements for performing environmental risk analysis. Therefore, sample size limitations, representativeness of data, and uncertainties in the estimated annual mean concentration must be examined before performing quantitative risk analysis. In this paper, we discuss several factors that need to be considered in designing field-sampling programs for toxic air contaminants and in verifying compliance with environmental regulations. Specifically, we examine the behavior of SO2, TSP, and CO data as surrogates for toxic air contaminants and as examples of point source, area source, and line source-dominated pollutants, respectively, from the standpoint of sampling design. We demonstrate the use of bootstrap resampling method and normal theory in estimating the annual mean concentration and its 95% confidence bounds from limited sampling data, and illustrate the application of operating characteristic (OC) curves to determine optimum sample size and other sampling strategies. We also outline a statistical procedure, based on a one-sided t-test, that utilizes the sampled concentration data for evaluating whether a sampling site is compliance with relevant ambient guideline concentrations for toxic air contaminants.     

Data skeletons: simultaneous estimation of multiple quantiles for massive streaming datasets with applications to density estimation

We consider the problem of density estimation when the data is in the form of a continuous stream with no fixed length. In this setting, implementations of the usual methods of density estimation such as kernel density estimation are problematic. We propose a method of density estimation for massive datasets that is based upon taking the derivative of a smooth curve that has been fit through a set of quantile estimates. To achieve this, a low-storage, single-pass, sequential method is proposed for simultaneous estimation of multiple quantiles for massive datasets that form the basis of this method of density estimation. For comparison, we also consider a sequential kernel density estimator. The proposed methods are shown through simulation study to perform well and to have several distinct advantages over existing methods.     

Sampling design proportional to order statistic of auxiliary variable

The sampling designs dependent on sample moments of auxiliary variables are well known. Lahiri (Bull Int Stat Inst 33:133–140, 1951) considered a sampling design proportionate to a sample mean of an auxiliary variable. Sing and Srivastava (Biometrika 67(1):205–209, 1980) proposed the sampling design proportionate to a sample variance while Wywiał (J Indian Stat Assoc 37:73–87, 1999) a sampling design proportionate to a sample generalized variance of auxiliary variables. Some other sampling designs dependent on moments of an auxiliary variable were considered e.g. in Wywiał (Some contributions to multivariate methods in, survey sampling. Katowice University of Economics, Katowice, 2003a); Stat Transit 4(5):779–798, 2000) where accuracy of some sampling strategies were compared, too.These sampling designs cannot be useful in the case when there are some censored observations of the auxiliary variable. Moreover, they can be much too sensitive to outliers observations. In these cases the sampling design proportionate to the order statistic of an auxiliary variable can be more useful. That is why such an unequal probability sampling design is proposed here. Its particular cases as well as its conditional version are considered, too. The sampling scheme implementing this sampling design is proposed. The inclusion probabilities of the first and second orders were evaluated. The well known Horvitz–Thompson estimator is taken into account. A ratio estimator dependent on an order statistic is constructed. It is similar to the well known ratio estimator based on the population and sample means. Moreover, it is an unbiased estimator of the population mean when the sample is drawn according to the proposed sampling design dependent on the appropriate order statistic.     

Confidence Intervals for Current Status Data

Abstract.  The likelihood ratio statistic for testing pointwise hypotheses about the survival time distribution in the current status model can be inverted to yield confidence intervals (CIs). One advantage of this procedure is that CIs can be formed without estimating the unknown parameters that figure in the asymptotic distribution of the maximum likelihood estimator (MLE) of the distribution function. We discuss the likelihood ratio-based CIs for the distribution function and the quantile function and compare these intervals to several different intervals based on the MLE. The quantiles of the limiting distribution of the MLE are estimated using various methods including parametric fitting, kernel smoothing and subsampling techniques. Comparisons are carried out both for simulated data and on a data set involving time to immunization against rubella. The comparisons indicate that the likelihood ratio-based intervals are preferable from several perspectives.     

分位数回归及应用简介

文章介绍了分位数回归法的概念、算法及主流统计软件R和SAS计算时的语法,并通过实例与以普通最小二乘法为基础的线性回归进行了对比,展现了分位数回归的巨大魅力。