Estimate error of frequency-dependentQintroduced by linear regression and its nonlinear implementation

A Generalization Error Estimate for Nonlinear Systems

5.6 Linear and Nonlinear Perspectives of Forecast Error Estimate Using the First Passage Time

Traditionally, the prediction skill of atmospheric models is verified through small amplitude stability analysis. The Lyapunov exponent (LE) and singular vector (SV) decomposition methods are the two popular approaches (e.g. Lorenz, 1984, Dalcher and Kalnay, 1987; Farrell and Ioannou, 1996; Vannitsem and Nicolis, 1997 and others). The model stability is defined as sensitivity to small errors in...

Kernel Density Based Linear Regression Estimate

For linear regression models with non-normally distributed errors, the least squares estimate (LSE) will lose some efficiency compared to the maximum likelihood estimate (MLE). In this article, we propose a kernel density based regression estimate (KDRE) that is adaptive to the unknown error distribution. The key idea is to approximate the likelihood function by using a nonparametric kernel den...

A Subspace Error Estimate for Linear Systems

This paper proposes a new method for estimating the error in the solution of linear systems. A condition number is defined for a linear function of the solution components. This definition of the condition number is quite versatile. It reduces to the component condition number proposed by Chandrasekaran and Ipsen [SIAM J. Matrix Anal. Appl., 16 (1995), pp. 93–112] and to Skeel’s definition of c...

Linear regression, the normal distribution of error values or normal distribution of the dependent variable?

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