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Regularized Least Square Regression with Unbounded and Dependent Sampling

Xiaorong Chu, Hongwei Sun
2013 Abstract and Applied Analysis  
The standard bound assumption for output data is abandoned and the learning algorithm is implemented with samples drawn from dependent sampling process with a more general output data condition.  ...  This paper mainly focuses on the least square regression problem for the -mixing and -mixing processes.  ...  It mainly studies the half supervised coefficient regularization with indefinite kernels and unbounded sampling, where the unbounded condition is ∫ 2 ≤̂2 for some constant̂> 0.  ... 
doi:10.1155/2013/139318 fatcat:ecz5g5bj4bcapoduyzpur3uvhy

An Extensive Examination of Regression Models with a Binary Outcome Variable

Suneel Chatla, Galit Shmueli
2017 Journal of the AIS  
We compare its performance to logit and probit under different sample sizes, error distributions, and more.  ...  We find that coefficient directions, statistical significance, and marginal effects yield results similar to logit and probit.  ...  We are grateful to the AE and the three reviewers for their helpful comments and suggestions that helped improve this paper.  ... 
doi:10.17705/1jais.00455 fatcat:psz3szwokfhn5bj6pzxmdylamq

Comparison of the modified unbounded penalty and the LASSO to select predictive genes of response to chemotherapy in breast cancer

Olivier Collignon, Jeongseop Han, Hyungmi An, Seungyoung Oh, Youngjo Lee
2018 PLoS ONE  
Recently Lee and Oh developed a novel random-effect covariate selection method called the modified unbounded penalty (MUB) regression, whose penalization function can equal minus infinity at 0 in order  ...  In practice the LASSO regression of Tibshirani, which penalizes the likelihood of the model by the L1 norm of the regression coefficients, has become the gold-standard to reach these objectives.  ...  Wessels from the Netherlands Cancer Institute and Delft University of Technology for sharing the data used in this research paper as well as for its fruitful advice.  ... 
doi:10.1371/journal.pone.0204897 pmid:30273405 pmcid:PMC6166949 fatcat:o3vbkzn235euhdymwwrejntfpe

Learning Theory

Ding-Xuan Zhou, Qiang Wu, Yiming Ying
2014 Abstract and Applied Analysis  
Acknowledgments The guest editors wish to express their sincere gratitude to the authors and reviewers who contributed greatly to the success of this special issue.  ...  Cai investigated a coefficient-based least squares regression problem with indefinite kernels from nonidentical unbounded sampling processes, which extends the existing related results. W. Gao and T.  ...  Chen and J. Wu, where they studied the ranking problem with L1-regularization associated with a convex loss. P. Ye and Y.  ... 
doi:10.1155/2014/138960 fatcat:xlgia2cr2ffcpkckizvf74tu4e

Coefficient-Based Regression with Non-Identical Unbounded Sampling

Jia Cai
2013 Abstract and Applied Analysis  
We investigate a coefficient-based least squares regression problem with indefinite kernels from non-identical unbounded sampling processes.  ...  Here non-identical unbounded sampling means the samples are drawn independently but not identically from unbounded sampling processes.  ...  The work described in this paper is supported partially by National Natural Science Foundation of China (Grant no. 11001247) and Doctor Grants of Guangdong University of Business Studies (Grant no. 11BS11001  ... 
doi:10.1155/2013/134727 fatcat:tdccsw6fsrerldlut6act7mvw4

Robust measures of association in the correlation model

Lee D. Witt, Joseph W. McKean, Joshua D. Naranjo
1994 Statistics and Probability Letters  
In the correlation model, the classical coefficient of multiple determination J?' is a measure of association between the dependent random variable Y and the random vector of independent variables x.  ...  In the regression model robust estimates of the regression coefficients are less sensitive to outlying points than least squares estimates.  ...  McKean and Naranjo was partially supported by NSF Grant DMS-9103916. We appreciate the helpful comments from an anonymous referee.  ... 
doi:10.1016/0167-7152(94)90017-5 fatcat:iqdc2ritdbhxlkwuctqm5mmk2m

Contribution of the activities of CYP3A, CYP2D6, CYP1A2 and other potential covariates to the disposition of methadone in patients undergoing methadone maintenance treatment

Mohammad-Reza Shiran, Martin S. Lennard, Mohammad-Zafar Iqbal, Oldwale Lagundoye, Nicholas Seivewright, Geoffrey T. Tucker, Amin Rostami-Hodjegan
2009 British Journal of Clinical Pharmacology  
CYP3A activity explained 22, 16, 15 and 23% of the variation in unbound (R)-, unbound (S)-, total (RS)-and total (S)-methadone clearances, respectively.  ...  Population pharmacokinetics and subsequent multiple regression analysis were used to calculate methadone oral clearance and to identify its covariates.  ...  As a drug with a low extraction ratio [17] , the hepatic clearance of methadone following intravenous (i.v.) administration is dependent on its unbound fraction and intrinsic clearance [13] .  ... 
doi:10.1111/j.1365-2125.2008.03312.x pmid:19133059 pmcid:PMC2668081 fatcat:v5pex4rnefb4zh2t2kegrtorty

Rates of convergence of the Adaptive LASSO estimators to the Oracle distribution and higher order refinements by the bootstrap

A. Chatterjee, S. N. Lahiri
2013 Annals of Statistics  
In this paper, we investigate the rate of convergence of the ALASSO estimator to the oracle distribution when the dimension of the regression parameters may grow to infinity with the sample size.  ...  It is shown that the rate critically depends on the choices of the penalty parameter and the initial estimator, among other factors, and that confidence intervals (CIs) based on the oracle limit law often  ...  We generated the variables (c i , ϵ i ) as iid bivariate normal vectors with zero mean vector and identity covariance matrix. The sample size considered was n = 200.  ... 
doi:10.1214/13-aos1106 fatcat:edoizpwjdrbt5jfho4hf62dwvi

Page 1997 of Mathematical Reviews Vol. , Issue 99c [page]

1991 Mathematical Reviews  
When a LAU parameter or paramet- ric function has an unbounded range, it is shown under general regularity conditions that any valid confidence set with level | — a for this parameter must be unbounded  ...  ., IV regressions with poor instruments), it is observed that likelihood-based methods (e.g., likelihood-ratio tests and confidence sets) combined with projection techniques can easily yield valid tests  ... 

Page 8699 of Mathematical Reviews Vol. , Issue 99m [page]

1999 Mathematical Reviews  
Summary: “We consider likelihood-based inference from multi- variate regression models with independent Student-¢ errors with unknown degrees of freedom.  ...  Consider a linear regression model with regression parameter vec- tor # and a normally distributed error term.  ... 

Positive-shrinkage and Pretest Estimation in Multiple Regression: A Monte Carlo study with Applications [article]

SM Enayetur Raheem, S. Ejaz Ahmed
2011 arXiv   pre-print
Performance of positive-shrinkage and pretest estimators are compared with unrestricted estimator under varying degree of uncertainty of the prior information.  ...  Thus, pretest estimator chooses between the restricted and unrestricted estimators depending on the outcome of the preliminary test.  ...  Ahmed (1997) gave a detailed description of shrinkage estimation, and discussed large sample estimation techniques in a regression model with non-normal errors.  ... 
arXiv:1109.2527v1 fatcat:aa7743b66nbpnfmnzmr66qihy4

Nonconcave Penalized Likelihood With NP-Dimensionality

Jianqing Fan, Jinchi Lv
2011 IEEE Transactions on Information Theory  
This fills a long-standing gap in the literature where the dimensionality is allowed to grow slowly with the sample size.  ...  In this paper, we show that in the context of generalized linear models, such methods possess model selection consistency with oracle properties even for dimensionality of nonpolynomial (NP) order of sample  ...  ACKNOWLEDGMENT We sincerely thank the Associate Editor and referee for their constructive comments that significantly improved the paper.  ... 
doi:10.1109/tit.2011.2158486 pmid:22287795 pmcid:PMC3266747 fatcat:qmmy5bdtcbfbngve3yrsi2foea

Identification of regular and chaotic isothermal trajectories of a shape memory oscillator using the 0–1 test

Davide Bernardini, Giuseppe Rega, Grzegorz Litak, Arkadiusz Syta
2012 Proceedings of the Institution of mechanical engineers. Proceedings part K, journal of multi-body dynamics  
The analysis is based on the computation of the control parameter K that approaches asymptotically 0 or 1 for regular and chaotic motions, respectively.  ...  The presented approach is independent of the integration procedure, being based on the characteristic sampling distance between the points of the analysed time series.  ...  Consequently, the regression analysis [18, 19, 20] of the linear growth of M (n, c) (Eq. 6) with increasing n is performed using the linear correlation coefficient which determines the value of the searching  ... 
doi:10.1177/1464419312447498 fatcat:ljnuf4vjufcnnkrjlakfus7rcq

Valid Confidence Intervals and Inference in the Presence of Weak Instruments

Eric Zivot, Richard Startz, Charles R. Nelson
1998 International Economic Review  
We investigate confidence intervals and inference for the instrumental variables model with weak instruments.  ...  We show that the practice of "pre-testing" by looking at the significance of the first-stage regression and then making inference based on the Wald statistic leads to extremely poor results when the instruments  ...  Since an unbounded confidence set occurs when the coefficient a in ( 8 ) is less than zero, we are able to link unboundedness with goodness-of-fit statistics for the first stage regression as follows:  ... 
doi:10.2307/2527355 fatcat:33vmit6alfcznl5vdl5jqpox5e

Modeling Regression Quantile Process Using Monotone B-Splines

Yuan Yuan, Nan Chen, Shiyu Zhou
2016 Technometrics  
In this paper, we proposed a regression quantile process estimation method based on monotone B-splines.  ...  The proposed method can easily ensure the validity of the regression quantile process, and offers a concise framework for variable selection and adaptive complexity control.  ...  Acknowledgments: We would like to thank the editor, associate editor, and two anonymous referees for their constructive comments and suggestions that have considerably improved the paper.  ... 
doi:10.1080/00401706.2016.1211553 fatcat:3wmlb5yqvjf7zlcwte3ccrrvmq
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