跳至主要内容

Empirical Likelihood Diagnosis of Modal Linear Regression Models

Read full paper at:
http://www.scirp.org/journal/PaperInformation.aspx?PaperID=50264#.VDNZsVfHRK0

Author(s)  
In this paper, we investigate the empirical likelihood diagnosis of modal linear regression models. The empirical likelihood ratio function based on modal regression estimation method for the regression coefficient is introduced. First, the estimation equation based on empirical likelihood method is established. Then, some diagnostic statistics are proposed. At last, we also examine the performance of proposed method for finite sample sizes through simulation study.
Cite this paper
Wang, S. , Zheng, L. and Dai, J. (2014) Empirical Likelihood Diagnosis of Modal Linear Regression Models. Journal of Applied Mathematics and Physics, 2, 948-952. doi: 10.4236/jamp.2014.210107. 
 

[1] Muller, D.W. and Sawitzki, G. (1991) Excess Mass Estimates and Tests for Multimodality. Journal of the American Statistical Association, 86, 738-746.
[2] Scott, D.W. (1992) Multivariate Density Estimation: Theory, Practice and Visualization. Wiley, New York.
http://dx.doi.org/10.1002/9780470316849
[3] Friedman, J.H. and Fisher, N.I. (1999) Bump Hunting in High-Dimensional Data. Statistics and Computing, 9, 123-143.
http://dx.doi.org/10.1023/A:1008894516817
[4] Chaudhuri, P. and Marron, J.S. (1999) Sizer for Exploration of Structures in Curves. Journal of the American Statistical Association, 94, 807-823. http://dx.doi.org/10.1080/01621459.1999.10474186
[5] Fisher, N.I. and Marron, J.S. (2001) Mode Testing via the Excess Mass Estimate. Biometrika, 88, 499-517.
http://dx.doi.org/10.1093/biomet/88.2.499
[6] Davies, P.L. and Kovac, A. (2004) Densities, Spectral Densities and Modality. Annals of Statistics, 32, 1093-1136.
[7] Hall, P., Minnotte, M.C. and Zhang, C. (2004) Bump Hunting with Non-Gaussian Kernels. Annals of Statistics, 32, 2124-2141. http://dx.doi.org/10.1214/009053604000000715
[8] Ray, S. and Lindsay, B.G. (2005) The Topography of Multivariate Normal Mixtures. Annals of Statistics, 33, 2042-2065. http://dx.doi.org/10.1214/009053605000000417
[9] Yao, W. and Lindsay, B.G. (2009) Bayesian Mixture Labeling by Highest Posterior Density. Journal of American Statistical Association, 104, 758-767. http://dx.doi.org/10.1198/jasa.2009.0237
[10] Yao, W. and Li, L. (2013) A New Regression Model: Modal Linear Regression. Scandinavian Journal of Statistics, 41, 656-671. http://dx.doi.org/10.1111/sjos.12054
[11] Lee, M.J. (1989) Mode Regression. Journal of Econometrics, 42, 337-349.
http://dx.doi.org/10.1016/0304-4076(89)90057-2
[12] Yao, W., Lindsay, B. and Li, R. (2012) Local Modal Regression. Journal of Nonparametric Statistics, 24, 647-663.
http://dx.doi.org/10.1080/10485252.2012.678848
[13] Yu, K. and Aristodemou, K. (2012) Bayesian Mode Regression. Technical Report. arXiv: 1208.0579v1.
[14] Zhao, W.H., Zhang, R.Q., Liu, Y.K. and Liu, J.C. (2014) Empirical Likelihood Based Modal Regression. Statistical Papers.
[15] Thomas, D.R. and Grunkemeier, G.L. (1975) Confidence Interval Estimation of Survival Interval Estimation of Survival Probabilities for Censored Data. Journal of the American Statistical Association, 70, 865-871.
http://dx.doi.org/10.1080/01621459.1975.10480315
[16] Owen, A. (2001) Empirical Likelihood. Chapman and Hall, New York. ，
http://dx.doi.org/10.1201/9781420036152
[17] Zhu, H.T., Ibrahim, J.G., Tang, N.S. and Zhang, H.P. (2008) Diagnostic Measures for Empirical Likelihood of Generalized Estimating Equations. Biometrika, 95, 489-507. http://dx.doi.org/10.1093/biomet/asm094
[18] Xue, L.G. and Zhu, L.X. (2010) Empirical Likelihood in Nonparametric and Semiparametric Models. Science Press, Beijing.
[19] Cook, R.D. and Weisberg, S. (1982) Residuals and Influence in Regression. Chapman and Hall, New York.
[20] Wei, B.C., Lu, G.B. and Shi, J.Q. (1990) Statistical Diagnostics. Publishing House of Southeast University, Nanjing.                      eww141007lx
标签：

评论

发表评论

此博客中的热门博文

A Comparison of Methods Used to Determine the Oleic/Linoleic Acid Ratio in Cultivated Peanut (Arachis hypogaea L.)

Cultivated peanut ( Arachis hypogaea L.) is an important oil and food crop. It is also a cheap source of protein, a good source of essential vitamins and minerals, and a component of many food products. The fatty acid composition of peanuts has become increasingly important with the realization that oleic acid content significantly affects the development of rancidity. And oil content of peanuts significantly affects flavor and shelf-life. Early generation screening of breeding lines for high oleic acid content greatly increases the efficiency of developing new peanut varieties. The objective of this study was to compare the accuracy of methods used to classify individual peanut seed as high oleic or not high oleic. Three hundred and seventy-four (374) seeds, spanning twenty-three (23) genotypes varying in oil composition (i.e. high oleic (H) or normal/not high oleic (NH) inclusive of all four peanut market-types (runner, Spanish, Valencia and Virginia), were individually tested ...
发表评论
阅读全文

Location Optimization of a Coal Power Plant to Balance Costs against Plant’s Emission Exposure

Fuel and its delivery cost comprise the biggest expense in coal power plant operations. Delivery of electricity from generation to consumers requires investment in power lines and transmission grids. Placing a coal power plant or multiple power plants near dense population centers can lower transmission costs. If a coalmine is nearby, transportation costs can also be reduced. However, emissions from coal plants play a key role in worsening health crises in many countries. And coal upon combustion produces CO 2 , SO 2 , NO x , CO, Metallic and Particle Matter (PM10 & PM2.5). The presence of these chemical compounds in the atmosphere in close vicinity to humans, livestock, and agriculture carries detrimental health consequences. The goal of the research was to develop a methodology to minimize the public’s exposure to harmful emissions from coal power plants while maintaining minimal operational costs related to electric distribution losses and coal logistics. The objective was...
发表评论
阅读全文

Evaluation of the Safety and Efficacy of Continuous Use of a Home-Use High-Frequency Facial Treatment Appliance

At present, many home-use beauty devices are available in the market. In particular, many products developed for facial treatment use light, e.g., a flash lamp or a light-emitting diode (LED). In this study, the safety of 4 weeks’ continuous use of NEWA TM , a high-frequency facial treatment appliance, every alternate day at home was verified, and its efficacy was evaluated in Japanese individuals with healthy skin aged 30 years or older who complained of sagging of the facial skin.  Transepidermal water loss (TEWL), melanin levels, erythema levels, sebum secretion levels, skin color changes and wrinkle improvement in the facial skin were measured before the appliance began to be used (study baseline), at 2 and 4 weeks after it had begun to be used, and at 2 weeks after completion of the 4-week treatment period (6 weeks from the study baseline). In addition, data obtained by subjective evaluation by the subjects themselves on a visual analog scale (VAS) were also analyzed. Fur...
发表评论
阅读全文