Strong convergence of the functional nonparametric relative error regression estimator under right censoring

2020 ◽  
Vol 70 (6) ◽  
pp. 1469-1490
Author(s):  
Omar Fetitah ◽  
Ibrahim M. Almanjahie ◽  
Mohammed Kadi Attouch ◽  
Ali Righi
Keyword(s):  
Censored Data ◽  
Relative Error ◽  
Complete Convergence ◽  
Explanatory Variable ◽  
Asymptotic Properties ◽  
Right Censoring ◽  
Regression Estimator ◽  
Nonparametric Estimator ◽  
The Mean ◽  
Censored Response

AbstractIn this paper, we investigate the asymptotic properties of a nonparametric estimator of the relative error regression given a functional explanatory variable, in the case of a scalar censored response, we use the mean squared relative error as a loss function to construct a nonparametric estimator of the regression operator of these functional censored data. We establish the strong almost complete convergence rate and asymptotic normality of these estimators. A simulation study is performed to illustrate and compare the higher predictive performances of our proposed method to those obtained with standard estimators.

Asymptotic properties of the overall sound pressure level of subsonic jet flows using isotropy as a paradigm

2010 ◽  
Vol 664 ◽  
pp. 510-539 ◽  
Author(s):  
M. Z. AFSAR
Keyword(s):  
Reynolds Stress ◽  
Sound Pressure Level ◽  
Small Angle ◽  
Sound Pressure ◽  
Asymptotic Properties ◽  
Jet Noise ◽  
Pressure Level ◽  
Mean Flow ◽  
The Mean ◽  
Jet Axis

Measurements of subsonic air jets show that the peak noise usually occurs when observations are made at small angles to the jet axis. In this paper, we develop further understanding of the mathematical properties of this peak noise by analysing the properties of the overall sound pressure level with an acoustic analogy using isotropy as a paradigm for the turbulence. The analogy is based upon the hyperbolic conservation form of the Euler equations derived by Goldstein (Intl J. Aeroacoust., vol. 1, 2002, p. 1). The mean flow and the turbulence properties are defined by a Reynolds-averaged Navier–Stokes calculation, and we use Green's function based upon a parallel mean flow approximation. Our analysis in this paper shows that the jet noise spectrum can, in fact, be thought of as being composed of two terms, one that is significant at large observation angles and a second term that is especially dominant at small observation angles to the jet axis. This second term can account for the experimentally observed peak jet noise (Lush, J. Fluid Mech., vol. 46, 1971, p. 477) and was first identified by Goldstein (J. Fluid Mech., vol. 70, 1975, p. 595). We discuss the low-frequency asymptotic properties of this second term in order to understand its directional behaviour; we show, for example, that the sound power of this term is proportional to the square of the mean velocity gradient. We also show that this small-angle shear term does not exist if the instantaneous Reynolds stress source strength in the momentum equation itself is assumed to be isotropic for any value of time (as was done previously by Morris & Farrasat, AIAA J., vol. 40, 2002, p. 356). However, it will be significant if the auto-covariance of the Reynolds stress source, when integrated over the vector separation, is taken to be isotropic in all of its tensor suffixes. Although the analysis shows that the sound pressure of this small-angle shear term is sensitive to the statistical properties of the turbulence, this work provides a foundation for a mathematical description of the two-source model of jet noise.

scholarly journals Strong uniform consistency rates of conditional quantile estimation in the single functional index model under random censorship

2018 ◽  
Vol 6 (1) ◽  
pp. 197-227 ◽  
Author(s):  
Nadia Kadiri ◽  
Abbes Rabhi ◽  
Amina Angelika Bouchentouf
Keyword(s):  
Cumulative Distribution Function ◽  
Complete Convergence ◽  
Asymptotic Properties ◽  
Cumulative Distribution ◽  
Index Structure ◽  
Functional Index ◽  
Conditional Quantile ◽  
Index Model ◽  
Strong Uniform Consistency ◽  
Mixing Sequence

AbstractThe main objective of this paper is to non-parametrically estimate the quantiles of a conditional distribution in the censorship model when the sample is considered as an -mixing sequence. First of all, a kernel type estimator for the conditional cumulative distribution function (cond-cdf) is introduced. Afterwards, we estimate the quantiles by inverting this estimated cond-cdf and state the asymptotic properties when the observations are linked with a single-index structure. The pointwise almost complete convergence and the uniform almost complete convergence (with rate) of the kernel estimate of this model are established. This approach can be applied in time series analysis.

scholarly journals Nonparametric Instrumental Variable Methods for Dynamic Treatment Evaluation

2020 ◽  
Vol 102 (2) ◽  
pp. 355-367
Author(s):  
Gerard J. van den Berg ◽  
Petyo Bonev ◽  
Enno Mammen
Keyword(s):  
Instrumental Variable ◽  
Causal Effect ◽  
Asymptotic Properties ◽  
Right Censoring ◽  
Unemployment Duration ◽  
Dynamic Selection ◽  
Average Causal Effect ◽  
Variable Approach ◽  
Dynamic Treatment ◽  
Job Finding

We develop an instrumental variable approach for identification of dynamic treatment effects on survival outcomes in the presence of dynamic selection, noncompliance, and right-censoring. The approach is nonparametric and does not require independence of observed and unobserved characteristics or separability assumptions. We propose estimation procedures and derive asymptotic properties. We apply our approach to evaluate a policy reform in which the pathway of unemployment benefits as a function of the unemployment duration is modified. Those who were unemployed at the reform date could choose between the old and the new regime. We find that the new regime has a positive average causal effect on the job finding rate.

Right-censoring bias in trials shared at the Project Data Sphere platform.

2021 ◽  
Vol 39 (15_suppl) ◽  
pp. e13543-e13543
Author(s):  
Enrique Barrajon ◽  
Antonio López Jiménez ◽  
Laura Barrajon
Keyword(s):  
Clinical Trials ◽  
Disease Free Survival ◽  
Right Censoring ◽  
Development Environment ◽  
Free Survival ◽  
R Language ◽  
Event Time ◽  
The Mean ◽  
Project Data ◽  
Comparative Trials

e13543 Background: Independent of the bias inherent to the design and execution of clinical trials, bias may be the result of patient censoring. A bias index (BI) was developed to detect right-censoring bias and tested in datasets availabe at Project Data Sphere, a data sharing research platform maintained by the CEO Roundtable on Cancer, Inc.,* a nonprofit corporation to improve outcomes for cancer patients by openly sharing deidentified data. Methods: Project Data Sphere platform was searched for clinical comparative trials with available experimental and comparator survival datasets: overall survival (OS) and event-free survival (EFS: disease-free survival, DFS, or progresssion-free survival, PFS). The R language and the integrated development environment Rstudio were used to import and manage the datasets. BI was defined in the events time domain as the adjusted proportion of censor times below the mean event time. Comparison of BI in different datasets were made with the two-sided Wilcoson unpaired test. A weighted regression model was applied to estimate the influence of bias on survival results as measured by the hazard ratio (HR). Results: Out of 184 trials, 19 trials offered both comparator and experimental arms, 3 of them not based on survival analysis and 4 of them with 2 substudies, providing 72 datasets based on OS and/or EFS, for a total of 16532 patients (90.8% of the 18198 patients in published trials). BI over the theshold was found in 24% of EFS datasets (versus 0% in OS datasets, Wilcoxon p = 0.0007), especially in PFS (35% vs 0% in DFS datasets, p = 0.00004). Nearly two thirds of the variance in the HR of EFS datasets was explained by the HR of OS datasets (adj.R2 = 0.638, p = 1.5e-5), approaching to what was found in the corresponding publications (adj.R2 = 0.751, p = 7.81e-5). Though the trials sample is small, introducing the BI of control and experimental datasets in the model decreases the residual standard error (3.831 vs 3.958) and increases the correlation (adj.R2 = 0.99, p < 2.2e-16), resulting in the model: HR(EFR) = 0.985 HR(OS) + 0.36 BI(exper) – 0.42 BI(control). Conclusions: This study is a proof of concept that right-censoring bias may be detected and estimated in clinical trials, especially in PFS datasets, and opens the possibility for correcting biased estimations in survival and increasing the precision in the prediction of OS from preliminary EFS. (*) This abstract is based on research using information obtained from ProjectDataSphere.org, which is maintained by Project Data Sphere LLC. Neither Project Data Sphere nor the owners of any information from the web site have contributed to, approved or are in any way responsible for the contents of this abstract.

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