Tie the Straps: Uniform Bootstrap Confidence Bands for Bounded Influence Curve Estimators

Parametric bootstrapping (BS) provides an attractive alternative, both theoretically and numerically, to asymptotic theory for estimating sampling distributions. This chapter summarizes its use not only for calculating confidence intervals for estimated parameters and functions of parameters, but also to obtain log-likelihood-based confidence regions from which confidence bands for cumulative distribution and regression functions can be obtained. All such BS calculations are very easy to implement. Details are also given for calculating critical values of EDF statistics used in goodness-of-fit (GoF) tests, such as the Anderson-Darling A2 statistic whose null distribution is otherwise difficult to obtain, as it varies with different null hypotheses. A simple proof is given showing that the parametric BS is probabilistically exact for location-scale models. A formal regression lack-of-fit test employing parametric BS is given that can be used even when the regression data has no replications. Two real data examples are given.

The influence curve approach in data envelopment analysis

Mathematical Programming ◽

10.1007/bf01582884 ◽

1991 ◽

Vol 52 (1-3) ◽

pp. 147-166 ◽

Cited By ~ 7

Author(s):

Jati K. Sengupta

Keyword(s):

Data Envelopment Analysis ◽

Data Envelopment ◽

Influence Curve

Simultaneous confidence bands for nonparametric regression with missing covariate data

Annals of the Institute of Statistical Mathematics ◽

10.1007/s10463-021-00784-5 ◽

2021 ◽

Author(s):

Li Cai ◽

Lijie Gu ◽

Qihua Wang ◽

Suojin Wang

Keyword(s):

Nonparametric Regression ◽

Confidence Bands ◽

Covariate Data ◽

Missing Covariate Data ◽

Simultaneous Confidence Bands

On nonparametric regression for bivariate circular long-memory time series

Statistical Papers ◽

10.1007/s00362-021-01228-1 ◽

2021 ◽

Author(s):

Jan Beran ◽

Britta Steffens ◽

Sucharita Ghosh

Keyword(s):

Time Series ◽

Nonparametric Regression ◽

Long Range ◽

Long Memory ◽

Regression Function ◽

Confidence Bands ◽

Long Range Dependence ◽

Asymptotic Results ◽

Memory Time ◽

Circular Time Series

AbstractWe consider nonparametric regression for bivariate circular time series with long-range dependence. Asymptotic results for circular Nadaraya–Watson estimators are derived. Due to long-range dependence, a range of asymptotically optimal bandwidths can be found where the asymptotic rate of convergence does not depend on the bandwidth. The result can be used for obtaining simple confidence bands for the regression function. The method is illustrated by an application to wind direction data.

Assessing bias, precision, and agreement in method comparison studies

Statistical Methods in Medical Research ◽

10.1177/0962280219844535 ◽

2019 ◽

Vol 29 (3) ◽

pp. 778-796 ◽

Cited By ~ 1

Author(s):

Patrick Taffé

Keyword(s):

Measurement Method ◽

Method Comparison ◽

Estimation Procedure ◽

Measurement Methods ◽

Repeated Measurements ◽

Confidence Bands ◽

The Other ◽

Reference Standard ◽

Simultaneous Confidence Bands ◽

Index Of Agreement

Recently, a new estimation procedure has been developed to assess bias and precision of a new measurement method, relative to a reference standard. However, the author did not develop confidence bands around the bias and standard deviation curves. Therefore, the goal in this paper is to extend this methodology in several important directions. First, by developing simultaneous confidence bands for the various parameters estimated to allow formal comparisons between different measurement methods. Second, by proposing a new index of agreement. Third, by providing a series of new graphs to help the investigator to assess bias, precision, and agreement between the two measurement methods. The methodology requires repeated measurements on each individual for at least one of the two measurement methods. It works very well to estimate the differential and proportional biases, even with as few as two to three measurements by one of the two methods and only one by the other. The repeated measurements need not come from the reference standard but from either measurement methods. This is a great advantage as it may sometimes be more feasible to gather repeated measurements with the new measurement method.

Nonparametric Confidence Bands for a Quantile Comparison Function

Technometrics ◽

10.1198/004017005000000184 ◽

2005 ◽

Vol 47 (3) ◽

pp. 364-371 ◽

Cited By ~ 10

Author(s):

F Lombard

Keyword(s):

Confidence Bands ◽

Comparison Function

Bounded-influence estimators for the tobit model

Journal of Econometrics ◽

10.1016/0304-4076(90)90075-5 ◽

1990 ◽

Vol 44 (1-2) ◽

pp. 107-126 ◽

Cited By ~ 13

Author(s):

Franco Peracchi

Keyword(s):

Tobit Model ◽

Bounded Influence

Conditionally Unbiased Bounded-Influence Estimation in General Regression Models, with Applications to Generalized Linear Models

Journal of the American Statistical Association ◽

10.1080/01621459.1989.10478791 ◽

1989 ◽

Vol 84 (406) ◽

pp. 460-466 ◽

Cited By ~ 10

Author(s):

Hans R. Künsch ◽

Leonard A. Stefanski ◽

Raymond J. Carroll

Keyword(s):

Generalized Linear Models ◽

Regression Models ◽

Linear Models ◽

Bounded Influence ◽

General Regression