Robustness Theory and Application

A preeminent expert in the field explores new and exciting methodologies in the ever-growing field of robust statistics

Used to develop data analytical methods, which are resistant to outlying observations in the data, while capable of detecting outliers, robust statistics is extremely useful for solving an array of common problems, such as estimating location, scale, and regression parameters. Written by an internationally recognized expert in the field of robust statistics, this book addresses a range of well-established techniques while exploring, in depth, new and exciting methodologies. Local robustness and global robustness are discussed, and problems of non-identifiability and adaptive estimation are considered. Rather than attempt an exhaustive investigation of robustness, the author provides readers with a timely review of many of the most important problems in statistical inference involving robust estimation, along with a brief look at confidence intervals for location. Throughout, the author meticulously links research in maximum likelihood estimation with the more general M-estimation methodology. Specific applications and R and some MATLAB subroutines with accompanying data sets—available both in the text and online—are employed wherever appropriate.

Providing invaluable insights and guidance, Robustness Theory and Application:

• Offers a balanced presentation of theory and applications within each topic-specific discussion
• Features solved examples throughout which help clarify complex and/or difficult concepts
• Meticulously links research in maximum likelihood type estimation with the more general M-estimation methodology
• Delves into new methodologies which have been developed over the past decade without stinting on coverage of “tried-and-true” methodologies
• Includes R and some MATLAB subroutines with accompanying data sets, which help illustrate the power of the methods described

Robustness Theory and Application is an important resource for all statisticians interested in the topic of robust statistics. This book encompasses both past and present research, making it a valuable supplemental text for graduate-level courses in robustness.

Nyckelord:

Statistics; robustness; robust statistics; linear series; time series analysis; robust statistics examples; robust statistics new methodologies; frontiers in robust statistics; estimating location parameters; estimating scale parameters; estimating regression coefficients; estimation of model-states in models expressed in state-space form; Kalman filter; robust measure of central tendency; the median absolute deviation; interquartile range; trimmed estimators; winsorised estimators; m-estimators; robust estimator; probability spaces; distribution functions; frechet differentiability; efficiency for multivariate parameters; Stochastic Frechet Expansions; Differentiability; bias reduction; variance estimation; the jackknife bias and variance estimation; the newton algorithm; problems in robust statistics; robust statistics R subroutines; robust statistics data sets; gamma distributions and quality assurance