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Accounting for Intrinsic Nonlinearity in Nonlinear Regression Parameter Inference Regions

非线性回归参数推断区域中的内在非线性

Joint confidence and likelihood regions for the parameters in nonlinear regression models can be defined using the geometric concepts of sample space and solution locus. Using a quadratic approximation to the solution locus, instead of the usual linear approximation, it is shown that these inference regions correspond to ellipsoids on the tangent plane at the least squares point. Accurate approximate inference regions can be obtained by mapping these ellipsoids into the…

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Parameter Transformations for Improved Approximate Confidence Regions in Nonlinear Least Squares

通过参数变换改善非线性最小二乘的近似置信域

In a previous paper, it was shown that parameter-effects nonlinearities of a nonlinear regression model-experimental design-parameterization combination can be quantified by means of a parameter-effects curvature array $A$ based on second derivatives of the model function. In this paper, the individual terms of $A$ are interpreted and local compensation methods are suggested. A method of computing the parameter-effects array corresponding to a transformed set of parameters…

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Relative Curvature Measures of Nonlinearity

衡量非线性程度的相对曲率指标

Summary Simple relative curvature measures of nonlinearity are developed to measure the extent of the nonlinearity in a model-experimental design-parameterization combination. We review the geometric aspects of linear and nonlinear least squares and, using the geometric concept of curvature, compute the maximum relative intrinsic curvature of the solution locus as well as the maximum relative parameter-effects curvature. The relative curvatures are independent of scale…

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Interpreting Partial Autocorrelation Functions of Seasonal Time Series Models

季节性时间序列模型偏自相关函数的解释

A simple approach to understanding the behaviour of the partial autocorrelation function of seasonal time series is presented, based on a partial autocorrelation pattern. This pattern, which acts as a signature of the regular component of the model, is a simple composite of the autocorrelation and partial autocorrelation functions of the regular component.

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Interpreting partial autocorrelation functions of seasonal time series models

季节性时间序列模型偏自相关函数的解释

A simple approach to understanding the behaviour of the partial autocorrelation function of seasonal time series is presented, based on a partial autocorrelation pattern. This pattern, which acts as a signature of the regular component of the model, is a simple composite of the autocorrelation and partial autocorrelation functions of the regular component.

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