Large sample and finite sample behavior of robust estimators

2019 ◽  
pp. 173-199
Author(s):  
Jana Jurečková ◽  
Jan Picek ◽  
Martin Schindler
Keyword(s):  
Robust Estimators ◽  
Finite Sample ◽  
Large Sample

scholarly journals Gradient and Likelihood Ratio Tests in Cure Rate Models

2016 ◽  
Vol 5 (4) ◽  
pp. 9 ◽  
Author(s):  
Hérica P. A. Carneiro ◽  
Dione M. Valença
Keyword(s):  
Likelihood Ratio ◽  
Asymptotic Properties ◽  
Information Matrix ◽  
Survival Models ◽  
Finite Sample ◽  
Cure Rate ◽  
Time Model ◽  
Cure Rate Models ◽  
Large Sample ◽  
Finite Samples

In some survival studies part of the population may be no longer subject to the event of interest. The called cure rate models take this fact into account. They have been extensively studied for several authors who have proposed extensions and applications in real lifetime data. Classic large sample tests are usually considered in these applications, especially the likelihood ratio. Recently  a new test called \textit{gradient test} has been proposed. The gradient statistic shares the same asymptotic properties with the classic likelihood ratio and does not involve knowledge of the information matrix, which can be an advantage in survival models. Some simulation studies have been carried out to explore the behavior of the gradient test in finite samples and compare it with the classic tests in different models. However little is known about the properties of these large sample tests in finite sample for cure rate models. In this work we  performed a simulation study based on the promotion time model with Weibull distribution, to assess the performance of likelihood ratio and gradient tests in finite samples. An application is presented to illustrate the results.

scholarly journals Causal inference for recurrent event data using pseudo-observations

Biostatistics ◽  
2020 ◽  
Author(s):  
Chien-Lin Su ◽  
Robert W Platt ◽  
Jean-François Plante
Keyword(s):  
Goodness Of Fit ◽  
Variance Estimation ◽  
Recurrent Event ◽  
Event Data ◽  
Robust Estimators ◽  
Recurrent Event Data ◽  
Finite Sample ◽  
Data Set ◽  
Asymptotically Normal ◽  
Doubly Robust

Summary Recurrent event data are commonly encountered in observational studies where each subject may experience a particular event repeatedly over time. In this article, we aim to compare cumulative rate functions (CRFs) of two groups when treatment assignment may depend on the unbalanced distribution of confounders. Several estimators based on pseudo-observations are proposed to adjust for the confounding effects, namely inverse probability of treatment weighting estimator, regression model-based estimators, and doubly robust estimators. The proposed marginal regression estimator and doubly robust estimators based on pseudo-observations are shown to be consistent and asymptotically normal. A bootstrap approach is proposed for the variance estimation of the proposed estimators. Model diagnostic plots of residuals are presented to assess the goodness-of-fit for the proposed regression models. A family of adjusted two-sample pseudo-score tests is proposed to compare two CRFs. Simulation studies are conducted to assess finite sample performance of the proposed method. The proposed technique is demonstrated through an application to a hospital readmission data set.

scholarly journals Large sample behaviour of some well-known robust estimators under long-range dependence

Statistics ◽  
2011 ◽  
Vol 45 (1) ◽  
pp. 59-71 ◽  
Author(s):  
C. Lévy-Leduc ◽  
H. Boistard ◽  
E. Moulines ◽  
M. S. Taqqu ◽  
V. A. Reisen
Keyword(s):  
Long Range ◽  
Long Range Dependence ◽  
Robust Estimators ◽  
Large Sample

scholarly journals HIGHER-ORDER ACCURATE, POSITIVE SEMIDEFINITE ESTIMATION OF LARGE-SAMPLE COVARIANCE AND SPECTRAL DENSITY MATRICES

2011 ◽  
Vol 27 (4) ◽  
pp. 703-744 ◽  
Author(s):  
Dimitris N. Politis
Keyword(s):  
Spectral Density ◽  
Positive Semidefinite ◽  
Higher Order ◽  
Individual Element ◽  
Finite Sample ◽  
Order Accuracy ◽  
Optimal Bandwidth ◽  
Large Sample ◽  
Spectral Density Matrix ◽  
Sample Covariance

A new class of large-sample covariance and spectral density matrix estimators is proposed based on the notion of flat-top kernels. The new estimators are shown to be higher-order accurate when higher-order accuracy is possible. A discussion on kernel choice is presented as well as a supporting finite-sample simulation. The problem of spectral estimation under a potential lack of finite fourth moments is also addressed. The higher-order accuracy of flat-top kernel estimators typically comes at the sacrifice of the positive semidefinite property. Nevertheless, we show how a flat-top estimator can be modified to become positive semidefinite (even strictly positive definite) while maintaining its higher-order accuracy. In addition, an easy (and consistent) procedure for optimal bandwidth choice is given; this procedure estimates the optimal bandwidth associated with each individual element of the target matrix, automatically sensing (and adapting to) the underlying correlation structure.

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