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Consistency and asymptotic normality for a nonparametric prediction under measurement errors

Kairat Mynbaev, Carlos Martins-Filho
2015 Journal of Multivariate Analysis  
Second, we obtain asymptotic normality of the estimators under the assumption that there are two types of measurement errors on the observed values of X.  ...  Nonparametric prediction of a random variable Y conditional on the value of an explanatory variable X is a classical and important problem in Statistics.  ...  By imposing conditions on the parameters of the measurement error distributions we are able to obtain asymptotic normality of allμ k (x) under suitable centering and a non-random normalization that depends  ... 
doi:10.1016/j.jmva.2015.03.003 fatcat:bdk2qxllzfhkhmlef3mpstu5aq

Nonparametric regression to the mean

H.-G. Muller, I. Abramson, R. Azari
2003 Proceedings of the National Academy of Sciences of the United States of America  
We establish asymptotic normality and propose an intuitively appealing and simple implementation based on local sample moments that is illustrated with a data set consisting of a bivariate sample of repeated  ...  The well known basic result for the situation of a multivariate normal distribution corresponds to shrinkage to the mean and provides the best prediction for a new observation based on past observations  ...  We are grateful for the helpful and detailed comments of two reviewers. This research was supported in part by National Science Foundation Grants DMS-9971602, DMS-0204869, and 0079430.  ... 
doi:10.1073/pnas.1733547100 pmid:12902544 pmcid:PMC187831 fatcat:5w34d4kq3fdarfgrrjypio77xi

Page 3909 of Mathematical Reviews Vol. , Issue 92g [page]

1992 Mathematical Reviews  
Summary: “This paper describes a 100 x (1 — a) percent confidence interval for the mean of a bounded random variable that holds for every sample size n and avoids the error of approximation that the normality  ...  First, the recursive Wolverton-Wagner kernel estimates },(x) for the invariant density y(x) are introduced and their consistency is shown under some regularity conditions.  ... 

Page 2045 of Mathematical Reviews Vol. , Issue 88d [page]

1988 Mathematical Reviews  
Consider the model y; = g(t;) +28), i= 1,---,m, where n measure- ments y; of a “smooth” function g defined on [0,1] are made at fixed points t;, and the ¢; denote i.i.d. errors with zero ex- pectation  ...  /n), has an asymptotically normal distribution. An upper bound is given of the distance sup |P((Tn — A)/(a/n) < x) - ®(x)|, where ® is the standard normal distribution.  ... 

Page 1631 of Mathematical Reviews Vol. , Issue 91C [page]

1991 Mathematical Reviews  
go to infinity at a rate explicitly determined by a smoothness measure to en- sure consistency and asymptotic unbiasedness.  ...  Sufficient con- ditions under which this bandwidth is asymptotically optimal and normally distributed are given.  ... 

Measuring Nonlinear Granger Causality in Mean

Xiaojun Song, Abderrahim Taamouti
2017 Journal of business & economic statistics  
We derive the asymptotic normality of nonparametric estimator of causality measures, which we use to build tests for their statistical significance.  ...  They are easily and consistently estimated by replacing the unknown mean square forecast errors by their nonparametric kernel estimates.  ...  A consistent nonparametric estimator of these measures is defined et al. (2011). We need Assumptions (A.2.1) and (A.2.2) to show the asymptotic normality of nonparametric estimators.  ... 
doi:10.1080/07350015.2016.1166118 fatcat:k52rqeil7rfrlkz5yku5lgol5e

Bootstrapping Nonparametric Prediction Intervals for Conditional Value-at-Risk with Heteroscedasticity

Emmanuel Torsen, Lema Logamou Seknewna
2019 Journal of Probability and Statistics  
Using bootstrap method, we have constructed nonparametric prediction intervals for Conditional Value-at-Risk for returns that admit a heteroscedastic location-scale model where the location and scale functions  ...  The prediction interval performs well for large sample sizes and is relatively small, which is consistent with what is obtainable in the literature.  ...  Acknowledgments The authors would like to thank to the editors and two referees for their many valuable suggestions and comments which improved this paper greatly.  ... 
doi:10.1155/2019/7691841 fatcat:3letp2nupzclhjfqsvtowr5wfa

Page 1250 of Mathematical Reviews Vol. , Issue 2003B [page]

2003 Mathematical Reviews  
Under the null hypothesis of additivity asymptotic normality is established with a limiting variance which involves only the variance of the error of measurements.  ...  As a generalization of a result by [ref], it is shown that, under appropriate conditions, the classical chi-square test has an asymptotic normal distribution as the sample and the number of classes tend  ... 

Proportional Hazards Model With Covariate Measurement Error and Instrumental Variables

Xiao Song, Ching-Yun Wang
2014 Journal of the American Statistical Association  
The estimators are shown to be consistent and asymptotically normal. Performance of the estimators is evaluated via simulation studies and by an application to data from an HIV clinical trial.  ...  The instrumental variables are related to the covariates through a general nonparametric model, and no distributional assumptions are placed on the error and the underlying true covariates.  ...  Acknowledgments This research was partially supported by NIH grants R01ES017030, HL121347 (Wang and Song), CA53996 (Wang) and CA152460 (Song), NSF grant DMS-1106816 (Song), and a travel award from the  ... 
doi:10.1080/01621459.2014.896805 pmid:25663724 pmcid:PMC4315262 fatcat:2orrluolrnhedirva7szynfndq

Page 1783 of Mathematical Reviews Vol. , Issue 98C [page]

1998 Mathematical Reviews  
are consistent and asymptotically normal.” 98c:62079 62G05 Xiang, Xiaojing (1-CIGEP-BS; Summit, NJ) A kernel estimator of a conditional quantile.  ...  Summary: “A training set of data has been used to construct a rule for predicting future responses. What is the error rate of this rule?  ... 

A simple and robust estimator for linear regression models with strictly exogenous instruments

Juan Carlos Escanciano
2017 Econometrics Journal  
The paper introduces a uniformly (in the data generating process) consistent estimator under nearly minimal identifying assumptions.  ...  In an application with quarterly UK data, IIV estimates a positive and signi...cant elasticity of intertemporal substitution and an equally sensible estimate for its reciprocal, in sharp contrast to IV  ...  We formalize this …nite sample behaviour by showing that it is uniformly consistent and uniformly asymptotically normal under a wide set of data generating processes.  ... 
doi:10.1111/ectj.12087 fatcat:ctom5f7rx5cedlxmwnajl5c5hq

Page 7397 of Mathematical Reviews Vol. , Issue 94m [page]

1994 Mathematical Reviews  
The mean squared prediction error is also shown to converge to zero in probability.  ...  An asymptotic formula for ho» and for E(||,f — K(n,Mopt)) Y ||?) is developed.  ... 

Asymptotically Optimal Regression Prediction Intervals and Prediction Regions for Multivariate Data

David Olive
2013 International Journal of Statistics and Probability  
The prediction regions are for a future vector of measurements x f from a multivariate distribution.  ...  The prediction intervals are for a future response Y f given a p×1 vector x f of predictors when the regression model has the form Y i = m(x i )+e i where m is a function of x i and the errors e i are  ...  Acknowledgements The author thanks the editor and two referees for their comments that improved this article.  ... 
doi:10.5539/ijsp.v2n1p90 fatcat:oafborrtvvh5ti6e6m5llskili

Nonparametric receiver operating characteristic-based evaluation for survival outcomes

Xiao Song, Xiao-Hua Zhou, Shuangge Ma
2012 Statistics in Medicine  
In this article, we examine evaluation of markers' predictive power using the time-dependent ROC curve and a concordance measure which can be viewed as a weighted area under the time-dependent AUC (area  ...  This study significantly advances from existing time-dependent ROC studies by developing nonparametric estimators of the summary indexes and, more importantly, rigorously establishing their asymptotic  ...  Acknowledgments The research is partially supported by a UGARF grant from University of Georgia (Song), by NIH grant R21CA152460 (Song), and by Department of Veterans Affairs project grant #XVA 61-036  ... 
doi:10.1002/sim.5386 pmid:22987578 pmcid:PMC3743052 fatcat:cz6a2myl4jbddnuus5pmvrisfe

Nonparametric analysis of financial time series by the Kernel methodology

Mohamed Chikhi, Claude Diebolt
2009 Quality & Quantity: International Journal of Methodology  
The forecasting results show that Orange stock prices are short-term predictable and nonparametric NAR-ARCH model has better performance over parametric MA-APARCH model for short horizons.  ...  The linearity and Gaussianity assumptions are rejected for Orange Stock returns and informational shocks have transitory effects on returns and volatility.  ...  Despite this difficulty, the nonparametric methods are still a powerful tool for studying time series.  ... 
doi:10.1007/s11135-009-9239-6 fatcat:djtzxggp75f3tfgpdan3v4qmze
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