Download or read book A Simulation Study of Some Nonparametric Quantile Estimators Under Censoring written by Michelle Elaine Skelton and published by . This book was released on 1989 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Simulation Comparison of Parametric and Nonparametric Estimators of Quantiles from Right Censored Data written by Shyamalee Kumary Serasinghe and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantiles are useful in describing distributions of component lifetimes. Data, consisting of the lifetimes of sample units, used to estimate quantiles are often censored. Right censoring, the setting investigated here, occurs, for example, when some test units may still be functioning when the experiment is terminated. This study investigated and compared the performance of parametric and nonparametric estimators of quantiles from right censored data generated from Weibull and Lognormal distributions, models which are commonly used in analyzing lifetime data. Parametric quantile estimators based on these assumed models were compared via simulation to each other and to quantile estimators obtained from the nonparametric Kaplan- Meier Estimator of the survival function. Various combinations of quantiles, censoring proportion, sample size, and distributions were considered. Our simulation show that the larger the sample size and the lower the censoring rate the better the performance of the estimates of the 5th percentile of Weibull data. The lognormal data are very sensitive to the censoring rate and we observed that for higher censoring rates the incorrect parametric estimates perform the best. If you do not know the underlying distribution of the data, it is risky to use parametric estimates of quantiles close to one. A limitation in using the nonparametric estimator of large quantiles is their instability when the censoring rate is high and the largest observations are censored. Key Words: Quantiles, Right Censoring, Kaplan-Meier estimator.
Download or read book Smooth Nonparametric Quantile Estimation Under Censoring Simulations and Bootstrap Methods written by W. J. Padgett and published by . This book was released on 1986 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objectives of this paper are two-fold. One is to report results of extensive Monte Carlo simulations which demonstrate the behavior of the mean squared error of the kernel estimator with respect to bandwidth. These simulations provide a method of choosing an optimal bandwidth when the form of the lifetime and censoring distributions are known. Also, they compare the kernel-type estimator with the product-limit qauntile estimator. Five commonly used parametric lifetime distributions, two censoring mechanisms, and four different kernel functions are considered in this study, which is an extension of the brief simulations for exponential distributions reported by Padgett (1986). The second objective is to present a nonparametric method for bandwidth selection based on the bootstrap for right-censored data. This data-based procedure used the bootstrap to estimate mean squared error, and is both an extension and modification of the methods proposed by Padgett. Bandwidth selection using the bootstrap is important for small and moderately large samples since no exact expressions exist for the mean squared error of the kernel-type quantile estimator.
Download or read book A Simulation Study of Kernel type Quantile Estimators for Randomly Right censored Data written by Mei-Chu Tang and published by . This book was released on 1985 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Smooth Nonparametric Quantile Estimator from Right Censored Data written by W. J. Padgett and published by . This book was released on 1987 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on randomly right-censored data, a smooth nonparametric estimator of the quantile function of the lifetime distribution is studied. The estimator is defined to be the solution x sub n (p) to F sub n (p)) = O, where F sub n is the distribution function corresponding to a kernel estimator of the lifetime density. The strong consistency and asymptotic normality of x sub n (p) are shown. Some simulation results comparing this estimator with the product of the bandwidth required for computing F sub n is investigated using bootstrap methods. Illustrative examples are given. (Author).
Download or read book A Kernel Type Estimator of a Quantile Function from Right Censored Data written by W. J. Padgett and published by . This book was released on 1984 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arbitrarily right-censored data arise naturally in industrial life testing and medical follow-up studies. In these situations it is important to be able to obtain nonparametric estimates of various characteristics of the survival function S. Based on such right-censored data, Kaplan and Meier gave the nonparametric maximum likelihood estimator of S, called the product-limit estimator, and, among others, Reid has proposed methods of estimating the median survival time from the product-limit estimator. Recently, Nair studied the problem of confidence bands for the survival function obtained from the product-limit estimator. Also, Padgett and McNichols and McNichols and Padgett have discussed estimation of a density for the survival distribution based on right-censored data. One characteristic of the survival distribution that is of interest is the quantile function, which is useful in reliability and medical studies. The quantile function of the product-limit estimator is a step function with jumps corresponding to the uncensored observations. The purpose of this paper is to present a smoothed nonparametric estimator of the quantile function from arbitrarily right-censored data based on the kernel method. It will be shown that under general conditions this estimator, mentioned briefly by Parzen is strongly consistent, and based on the results of a small Monte-Carol simulation study, performs better than quantile function of the product-limit estimator in the sense of smaller mean squared error. In particular, better estimates of the median survival time are obtainable. In addition, an approximation to the kernel estimator will be shown to be almost surely asymptotically equivalent to it under certain conditions.
Download or read book On the Mean Squared Error of Nonparametric Quantile Estimators Under Random Right Censorship written by Y. L. Lio and published by . This book was released on 1986 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: For randomly right-censored data, new asymptotic expressions for the mean squared errors of the product-limit quantile estimator and a kernel-type quantile estimator are presented in this paper. From these results a comparison of the two quantile estimators with respect to their mean squared errors is given. (Author).
Download or read book Nonparametric Estimation of Quantiles and of Density Functions Under Censoring Discrete Failure Models and Multiple Comparisons written by W. J. Padgett and published by . This book was released on 1985 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: Major results have been obtained in the areas of nonparametric estimation of quantiles and of density functions under censoring, discrete failure models, and multiple comparisons. In particular, smooth nonparametric estimators of quantile functions from censored data were developed which give better estimates of percentiles of the lifetime distribution than the usual product-limit quantile function. Also, smooth density estimators from censored data were investigated using maximum penalized likelihood procedures. Several parametric models were proposed for the case of discrete failure data. These models provide a better fit to such data than some previously used discrete models. Finally, new methods of constructing simultaneous confidence intervals for pairwise differences of means of normal populations were developed, and the problem of selecting an asymptotically optimal design for comparing several new treatments with a control was solved. Work is continuing on the study of properties of kernel type quantile function estimators and development of goodness-of-fit tests for the model assumptions in accelerated life testing. Keywords: Nonparametric quantile estimation; Density estimation; Right-censored data; Discrete failure models; Multiple comparisons; Accelerated life testing.
Download or read book Partially Linear Models written by Wolfgang Härdle and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last ten years, there has been increasing interest and activity in the general area of partially linear regression smoothing in statistics. Many methods and techniques have been proposed and studied. This monograph hopes to bring an up-to-date presentation of the state of the art of partially linear regression techniques. The emphasis is on methodologies rather than on the theory, with a particular focus on applications of partially linear regression techniques to various statistical problems. These problems include least squares regression, asymptotically efficient estimation, bootstrap resampling, censored data analysis, linear measurement error models, nonlinear measurement models, nonlinear and nonparametric time series models.
Download or read book A Nonparametric Quantile Estimator Computation written by W. J. Padgett and published by . This book was released on 1986 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: Right-censored data arise very naturally in life testing and reliability studies. For such data, it is important to be able to obtain good nonparametric estimates of various characteristics of the unknown lifetime distribution. This report concerns the computational procedure for a kernel-type nonparametric estimator of the quantile function of the lifetimne distribution from right-censored data. This estimator was suggested by Padgett (1986), extending the complete sample results of Yang (1985). The large sample properties of the estimator, such as asymptotic normality and mean square convergence, were studied by Lio, Padgett and Yu (1986) and by Lio and Padgett (1985). In this report, a procedure for calculation of the kernel-type quantile estimate from right-censored data is described, and a listing of a computer program in FORTRAN code is provided.
Download or read book A Generalized Quantile Estimator Under Censoring written by Y. L. Lio and published by . This book was released on 1987 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on right-censored data from a lifetime distribution F sub 0, a smooth alternative to the product-limit estimator as a nonparametric quantile estimator of a population quantile is proposed. The estimator is a generalized product-limit quantile obtained by averaging appropriate subsample product-limit quantiles over all subsamples of a fixed size. Under the random censorship model and some conditions of F sub 0, it is shown that the estimator is consistent and has the same asymptotic normal distribution as the product-limit quantile estimator performs better than the product-limit quantile estimator in the sense of estimated mean squared errors.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1991 with total page 912 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Research in Progress written by and published by . This book was released on 1983 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Quantile Regression written by Roger Koenker and published by CRC Press. This book was released on 2017-10-12 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantile regression constitutes an ensemble of statistical techniques intended to estimate and draw inferences about conditional quantile functions. Median regression, as introduced in the 18th century by Boscovich and Laplace, is a special case. In contrast to conventional mean regression that minimizes sums of squared residuals, median regression minimizes sums of absolute residuals; quantile regression simply replaces symmetric absolute loss by asymmetric linear loss. Since its introduction in the 1970's by Koenker and Bassett, quantile regression has been gradually extended to a wide variety of data analytic settings including time series, survival analysis, and longitudinal data. By focusing attention on local slices of the conditional distribution of response variables it is capable of providing a more complete, more nuanced view of heterogeneous covariate effects. Applications of quantile regression can now be found throughout the sciences, including astrophysics, chemistry, ecology, economics, finance, genomics, medicine, and meteorology. Software for quantile regression is now widely available in all the major statistical computing environments. The objective of this volume is to provide a comprehensive review of recent developments of quantile regression methodology illustrating its applicability in a wide range of scientific settings. The intended audience of the volume is researchers and graduate students across a diverse set of disciplines.
Download or read book Mathematical and Statistical Applications in Life Sciences and Engineering written by Avishek Adhikari and published by Springer. This book was released on 2017-12-06 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book includes articles from eminent international scientists discussing a wide spectrum of topics of current importance in mathematics and statistics and their applications. It presents state-of-the-art material along with a clear and detailed review of the relevant topics and issues concerned. The topics discussed include message transmission, colouring problem, control of stochastic structures and information dynamics, image denoising, life testing and reliability, survival and frailty models, analysis of drought periods, prediction of genomic profiles, competing risks, environmental applications and chronic disease control. It is a valuable resource for researchers and practitioners in the relevant areas of mathematics and statistics.
Download or read book Nonparametric and Semiparametric Estimation of Instrumental Variable Method written by Anqi Cheng and published by . This book was released on 2019 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: The instrumental variable approach has been widely used for estimating the treatment effect in the presence of unmeasured confounding, e.g. randomized trials with noncompliance problems and observational studies. While most literature focus on the estimation of compliers averaged causal effect (CACE) nonparametrically or based on parametric assumptions, under the IV assumptions, fewer works focus on estimating distributional causal effect using IV. We study a novel monotone cumulative distribution function estimator of an outcome variable for compliers receiving treatment or control. The estimation procedures involve a weighted quantile regression and a post-estimation rearrangement adjustment. We show that the proposed estimator is consistent and develop large sample properties. Based on the asymptotic properties of the proposed estimator, a Wilcoxon-type statistic is proposed to test the equivalence of CDF for compliers receiving treatment and control. By comparing the influence function of the proposed estimator to the efficient influence function, we modify the proposed estimator and obtain a local efficient and robust estimator in the sense that when the unknown density functions are correctly specified, it reaches the semiparametric efficiency bound and when the unknown density functions are misspecified, it is still a consistent estimator. For the censoring outcomes, we propose a method to estimate quantile functions and survival functions for potential outcomes under independent censoring and noncompliance. Based on the martingale feature associated with the censoring data, we estimate quantile functions for compliers. Then using the possibly non-monotone quantile function, we construct a monotone and bounded estimator for the survival function. By using empirical process techniques, we establish asymptotic properties, including uniform consistency and weak convergence for the proposed estimators. For general observational studies with unmeasured confounding problems, we impose a no-interaction assumption proposed by Wang and Tchetgen Tchetgen (2018) and propose a new class of IV models that identify quantities of potential outcomes for the whole population. Our work complements current research on using instrumental variable method to estimate distributions of potential outcomes and infer heterogenous treatment effect for observational studies in the presence of unmeasured confounding, especially for the censoring outcomes. Simulation results, real data examples, and proofs are detailed in this dissertation.
Download or read book Advances in Contemporary Statistics and Econometrics written by Abdelaati Daouia and published by Springer Nature. This book was released on 2021-06-14 with total page 713 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unique collection of contributions on modern topics in statistics and econometrics, written by leading experts in the respective disciplines and their intersections. It addresses nonparametric statistics and econometrics, quantiles and expectiles, and advanced methods for complex data, including spatial and compositional data, as well as tools for empirical studies in economics and the social sciences. The book was written in honor of Christine Thomas-Agnan on the occasion of her 65th birthday. Given its scope, it will appeal to researchers and PhD students in statistics and econometrics alike who are interested in the latest developments in their field.
