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TESTING OF CORRELATION AND HETEROSCEDASTICITY IN nonlinear regression models WITH DBL(p,q,1) RANDOM ERRORS

Acta Mathematica Scientia 2008年第3期28卷 613-632页

作者：刘应安韦博成 College of Information Science and Technology Nanjing Forestry University Department of Mathematics SoutheastUniversity

Chaos theory has taught us that a system which has both nonlinearity and random input will most likely produce irregular data. If random errors are irregular data, then random error process will raise nonlinearity （Kantz and Schreiber （1997））. Tsai （1986） introduced a composite test for autocorrelation and heteroscedasticity in linear models with AR（1） errors. Liu （2003） introduced a composite test for correlation and heteroscedasticity in nonlinear models with DBL（p, 0, 1） errors. Therefore, the important problems in regression model axe detections of bilinearity, correlation and heteroscedasticity. In this article, the authors discuss more general case of nonlinear models with DBL（p, q, 1） random errors by score test. Several statistics for the test of bilinearity, correlation, and heteroscedasticity are obtained, and expressed in simple matrix formulas. The results of regression models with linear errors are extended to those with bilinear errors. The simulation study is carried out to investigate the powers of the test statistics. All results of this article extend and develop results of Tsai （1986）, Wei, et al （1995）, and Liu, et al （2003）.

关键词： DBL(p q 1) random errors nonlinear regression models score test heteroscedasticity correlation

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ON CONFIDENCE REGIONS OF SEMIPARAMETRIC nonlinear regression models(A GEOMETRIC APPROACH)

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Acta Mathematica Scientia 2000年第1期20卷 68-75页

作者：朱仲义唐年胜韦博成 Department of Applied Mathematics. Southeast University Nanjing 210096 China

A geometric framework is proposed for semiparametric nonlinear regression models based on the concept of least favorable curve, introduced by Severini and Wong (1992). The authors use this framework to drive three kinds of improved approximate confidence regions for the parameter and parameter subset in terms of curvatures. The results obtained by Hamilton et al. (1982), Hamilton (1986) and Wei (1994) are extended to semiparametric nonlinear regression models.

关键词： confidence regions curvatures nonlinear regression models score statistic semiparametric models

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Residuals and Influence in nonlinear regression for Repeated Measurement Data

Residuals and Influence in Nonlinear Regression for Repeated...

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作者： Ali Munsir 南京理工大学

学位级别：硕士

All observations don't have equal significance in regression *** of observations is an important aspect of model *** this dissertation,we use diagnostics method to detect residuals and influential points in nonlinear regression for repeated measurement *** distance,likelihood distance and Gauss newton method have been proposed to identify the outliers in nonlinear regression analysis and parameter *** of these techniques based on graphical representations of residuals,hat matrix and case deletion *** results show us detection of single and multiple outliers cases in repeated measurement data by *** and Likelihood *** use these techniques to explore performance of residuals and influence in nonlinear regression model.

关键词： Hat matrix Cook distance Likelihood distance Residual nonlinear regression models Hierarchical

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