基于半参数统计模型的弗明翰心脏病数据研究
|
摘要
对于弗明翰心脏病数据,线性模型往往不能很好地拟合,而利用半参数统计模型能提炼出较准确的信息;对于半参数统计模型——单指标模型和单指标变系数模型,一般利用局部回归方法进行联系函数的估计,估计方程估计方法进行指标系数的估计;在此理论基础上,对弗明翰数据进行拟合并作出分析和比较;结果表明:单指标模型和单指标变系数模型都能较好地拟合并解释弗明翰心脏病数据,但由于单指标变系数模型比单指标模型多考虑了一些因素,所以单指标变系数模型相对来说能更多地提取一些数据中隐藏的信息,能更客观地解释弗明翰心脏病数据的现实意义。
For the Framingham data,the linear models may not fit it very well and the semi-parametric statistical models can be used to extract more accurate information. For the semi-parametric statistical modelssingle-index model and varying-coefficient single-index model,we use the local linear regression to estimate the link function and the estimating equation to estimate the index coefficient generally. On the basis of the theory,we fit the Framingham data and make analysis and comparison. The result shows that both single-index model and varying-coefficient single-index model can fit and explain the data very well. However,varying-coefficient singleindex model considers more factors than the single-index model,so that the varying-coefficient single-index model can extract more information from the data and can more objectively explain the realistic significance of it.
For the Framingham data,the linear models may not fit it very well and the semi-parametric statistical models can be used to extract more accurate information. For the semi-parametric statistical modelssingle-index model and varying-coefficient single-index model,we use the local linear regression to estimate the link function and the estimating equation to estimate the index coefficient generally. On the basis of the theory,we fit the Framingham data and make analysis and comparison. The result shows that both single-index model and varying-coefficient single-index model can fit and explain the data very well. However,varying-coefficient singleindex model considers more factors than the single-index model,so that the varying-coefficient single-index model can extract more information from the data and can more objectively explain the realistic significance of it.
引文
[1] CARROLL R J. Generalized Partially Single-Index Models[J]. Journal of the American Statistical Association,1997(92):477—489
[2] HARDL E W,HALL P,ICHIMURA H. Optimal Smoothing in Single-Index Models[J]. The Annals of Statistics,1993(21):157—178
[3] WEISBERG S,WELSH A H. Adapting for the Missing Link[J]. The Annous of Statistics,1994(22):1674—1700
[4] DELECROIX M,HARDL W,HRISTACHE M. Efficient Estimation in Conditional Single-Index Regression[J].Journal of Multivariate Analysis,2003(862):213—226
[5] DELECROIX M,HARDL W. On Semi-parametric Mestimation in Single-Index Regression[J]. Journal of Statistical Planning and Inference,2006(136):730—769
[6] XIA Y C,LI W K. On Single-Index Coefficient Regression Models[J]. Journal of the American Statistical Association,1999(94):1275—1285
[7] HUANG Z S,ZHANG R Q. Profile Empirical-Likelihood Inferences for The Single-Index-Coefficient Regression Model[J]. Statistics and Computing,2013(23):455—465
[8] KANNEL,W B et al. Overall and Coronary Heart Disease Mortality Rates in Relation to Major Risk Factors in 325,348 MenScreened for MRFIT[J]. American Heart Journal,1986(112):825—836
[9]薛留根.现代统计模型[M].北京:科学出版社,2012XUE L G. Modern Statistical Model[M]. Beijing:The Science Publishing Company,2012
[2] HARDL E W,HALL P,ICHIMURA H. Optimal Smoothing in Single-Index Models[J]. The Annals of Statistics,1993(21):157—178
[3] WEISBERG S,WELSH A H. Adapting for the Missing Link[J]. The Annous of Statistics,1994(22):1674—1700
[4] DELECROIX M,HARDL W,HRISTACHE M. Efficient Estimation in Conditional Single-Index Regression[J].Journal of Multivariate Analysis,2003(862):213—226
[5] DELECROIX M,HARDL W. On Semi-parametric Mestimation in Single-Index Regression[J]. Journal of Statistical Planning and Inference,2006(136):730—769
[6] XIA Y C,LI W K. On Single-Index Coefficient Regression Models[J]. Journal of the American Statistical Association,1999(94):1275—1285
[7] HUANG Z S,ZHANG R Q. Profile Empirical-Likelihood Inferences for The Single-Index-Coefficient Regression Model[J]. Statistics and Computing,2013(23):455—465
[8] KANNEL,W B et al. Overall and Coronary Heart Disease Mortality Rates in Relation to Major Risk Factors in 325,348 MenScreened for MRFIT[J]. American Heart Journal,1986(112):825—836
[9]薛留根.现代统计模型[M].北京:科学出版社,2012XUE L G. Modern Statistical Model[M]. Beijing:The Science Publishing Company,2012