Author: Gabriela Florentina Nane
Publisher:
ISBN: 9789461862006
Category :
Languages : en
Pages :

Get Book Here

Book Description

Author: Piet Groeneboom
Publisher: Cambridge University Press
ISBN: 0521864011
Category : Business & Economics
Languages : en
Pages : 429

Get Book Here

Book Description
This book introduces basic concepts of shape constrained inference and guides the reader to current developments in the subject.

Author: Shabnam Fani
Publisher:
ISBN:
Category : Failure time data analysis
Languages : en
Pages : 126

Get Book Here

Book Description
The main problem studied in this thesis is to analyse and model time-to- event data, particularly when the survival times of subjects under study are not exactly observed. One of the primary tasks in the analysis of survival data is to study the distribution of the event times of interest. In order to avoid strict assumptions associated with a parametric model, we resort to nonparametric methods for estimating a function. Although other nonparametric approaches, such as Kaplan-Meier, kernel-based, and roughness penalty methods, are popular tools for solving function estimation problems, they suffer from some non-trivial issues like the loss of some important information about the true underlying function, difficulties with bandwidth or tuning parameter selection. In contrast, one can avoid these issues at the cost of enforcing some qualitative shape constraints on the function to be estimated. We confine our survival analysis studies to estimating a hazard function since it may make a lot of practical sense to impose certain shape constraints on it. Specifically, we study the problem of nonparametric estimation of a hazard function subject to convex shape restrictions, which naturally entails monotonicity constraints. In this thesis, three main objectives are addressed. Firstly, the problem of nonparametric maximum-likelihood estimation of a hazard function under convex shape restrictions is investigated. We introduce a new nonparametric approach to estimating a convex hazard function in the case of exact observations, the case of interval-censored observations, and the mixed case of exact and interval-censored observations. A new idea to handle the problem of choosing the minimum of a convex hazard function estimate is proposed. Based on this, a new fast algorithm for nonparametric hazard function estimation under convexity shape constraints is developed. Theoretical justification for the convergence of the new algorithm is provided. Secondly, nonparametric estimation of a hazard function under smoothness and convex shape assumptions is studied. Particularly, our nonparametric maximum-likelihood approach is generalized for smooth estimation of a function by applying a higher-order smoothness assumption of an estimator. We also evaluate the performance of the estimators using simulation studies and real-world data. Numerical studies suggest that the shape-constrained estimators generally outperform their unconstrained competitors. Moreover, the empirical results indicate that the smooth shape-restricted estimator has more capability to model human mortality data compared to the piecewise linear continuous estimator, specifically in the infant mortality phase. Lastly, our nonparametric estimation of a hazard function approach under convex shape restrictions is extended to the Cox proportional hazards model. A new algorithm is also developed to estimate both convex baseline hazard function and the effects of covariates on survival times. Numerical studies reveal that our new approaches generally dominate the traditional partial likelihood method in the case of right-censored data and the fully semiparametric maximum likelihood estimation method in the case of interval-censored data. Overall, our series of studies show that the shape-restricted approach tends to provide more accurate estimation than its unconstrained competitors, and further investigations in this direction can be highly fruitful.

Author: Ari David Gross
Publisher:
ISBN:
Category :
Languages : en
Pages : 444

Get Book Here

Book Description

Author: P. Groeneboom
Publisher:
ISBN: 9781139020893
Category : Estimation theory
Languages : en
Pages :

Get Book Here

Book Description

Author: Luc Duchateau
Publisher: Springer Science & Business Media
ISBN: 038772835X
Category : Mathematics
Languages : en
Pages : 329

Get Book Here

Book Description
Readers will find in the pages of this book a treatment of the statistical analysis of clustered survival data. Such data are encountered in many scientific disciplines including human and veterinary medicine, biology, epidemiology, public health and demography. A typical example is the time to death in cancer patients, with patients clustered in hospitals. Frailty models provide a powerful tool to analyze clustered survival data. In this book different methods based on the frailty model are described and it is demonstrated how they can be used to analyze clustered survival data. All programs used for these examples are available on the Springer website.

Author: Mark Anthony Wolters
Publisher:
ISBN:
Category :
Languages : en
Pages : 314

Get Book Here

Book Description
Nonparametric density estimators are used to estimate an unknown probability density while making minimal assumptions about its functional form. Although the low reliance of nonparametric estimators on modelling assumptions is a benefit, their performance will be improved if auxiliary information about the density's shape is incorporated into the estimate. Auxiliary information can take the form of shape constraints, such as unimodality or symmetry, that the estimate must satisfy. Finding the constrained estimate is usually a difficult optimization problem, however, and a consistent framework for finding estimates across a variety of problems is lacking. It is proposed to find shape-constrained density estimates by starting with a pilot estimate obtained by standard methods, and subsequently adjusting its shape until the constraints are satisfied. This strategy is part of a general approach, in which a constrained estimation problem is defined by an estimator, a method of shape adjustment, a constraint, and an objective function. Optimization methods are developed to suit this approach, with a focus on kernel density estimation under a variety of constraints. Two methods of shape adjustment are examined in detail. The first is data sharpening, for which two optimization algorithms are proposed: a greedy algorithm that runs quickly but can handle a limited set of constraints, and a particle swarm algorithm that is suitable for a wider range of problems. The second is the method of adjustment curves, for which it is often possible to use quadratic programming to find optimal estimates. The methods presented here can be used for univariate or higher-dimensional kernel density estimation with shape constraints. They can also be extended to other estimators, in both the density estimation and regression settings. As such they constitute a step toward a truly general optimizer, that can be used on arbitrary combinations of estimator and constraint.

Author: Mervyn J. Silvapulle
Publisher: John Wiley & Sons
ISBN: 1118165632
Category : Mathematics
Languages : en
Pages : 560

Get Book Here

Book Description
An up-to-date approach to understanding statistical inference Statistical inference is finding useful applications in numerous fields, from sociology and econometrics to biostatistics. This volume enables professionals in these and related fields to master the concepts of statistical inference under inequality constraints and to apply the theory to problems in a variety of areas. Constrained Statistical Inference: Order, Inequality, and Shape Constraints provides a unified and up-to-date treatment of the methodology. It clearly illustrates concepts with practical examples from a variety of fields, focusing on sociology, econometrics, and biostatistics. The authors also discuss a broad range of other inequality-constrained inference problems that do not fit well in the contemplated unified framework, providing a meaningful way for readers to comprehend methodological resolutions. Chapter coverage includes: Population means and isotonic regression Inequality-constrained tests on normal means Tests in general parametric models Likelihood and alternatives Analysis of categorical data Inference on monotone density function, unimodal density function, shape constraints, and DMRL functions Bayesian perspectives, including Stein’s Paradox, shrinkage estimation, and decision theory

Author: Klaas van Breugel
Publisher: Springer
ISBN: 3319701940
Category : Technology & Engineering
Languages : en
Pages : 241

Get Book Here

Book Description
This work is an overview of the state of art on Ageing of Materials and structures in the world. Ageing of materials is a natural phenomenon. Each material we use will age. This ageing will influence the performance of the object where the materials is used. Furthermore, the ageing will be affected by the surroundings in which the object is placed. The main focus of the book is on materials used in infrastructure, energy, buildings and industry. The book in effect establishes the definition of ageing and its main research topics that are relevant for society.

Author: Lazlo Györfi
Publisher: Springer
ISBN: 146123686X
Category : Mathematics
Languages : en
Pages : 157

Get Book Here

Book Description
Because of the sheer size and scope of the plastics industry, the title Developments in Plastics Technology now covers an incredibly wide range of subjects or topics. No single volume can survey the whole field in any depth and what follows is, therefore, a series of chapters on selected topics. The topics were selected by us, the editors, because of their immediate relevance to the plastics industry. When one considers the advancements of the plastics processing machinery (in terms of its speed of operation and conciseness of control), it was felt that several chapters should be included which related to the types of control systems used and the correct usage of hydraulics. The importance of using cellular, rubber-modified and engineering-type plastics has had a major impact on the plastics industry and therefore a chapter on each of these subjects has been included. The two remaining chapters are on the characterisation and behaviour of polymer structures, both subjects again being of current academic or industrial interest. Each of the contributions was written by a specialist in that field and to them all, we, the editors, extend our heartfelt thanks, as writing a contribution for a book such as this, while doing a full-time job, is no easy task.