This paper proposes a bias reduction of the coefficients' estimator for linear regression models when observations are randomly censored and the error distribution is unknown. The proposed bias correction is applied to the weighted least squares estimator proposed by Stute [28] [W. Stute: Consistent estimation under random censorship when covariables are present. J. Multivariate Anal. \emph{45} (1993), 89-103.], and it is based on model-based bootstrap resampling techniques that also allow us to work with censored data. Our bias-corrected estimator proposal is evaluated and its behavior assessed in simulation studies concluding that both the bias and the mean square error are reduced with the new proposal.
The GMDH MIA algorithm uses linear regression for adaptation. We show that Gauss-Markov conditions are not met here and thus estimations of network parameters are biased. To eliminate this we propose to use cloning of neuron parameters in the GMDH network with genetic selection and cloning (GMC GMDH) that can outperform other powerful methods. It is demonstrated on tasks from the Machine Learning Repository.
We applied the grey system theory to evaluation of chlorophyll (Chl) degradation in Chamaecyparis Sieb. & Zucc. var. formosana (Hayata) Rehder needle-leaf in the Yuanyang Lake Nature Preserve of northern Taiwan. Pigment analysis was finished within 12 h after collecting the samples. Four grey prediction models for the degradation of Chl a, Chl b, and for the change of Chl a/b ratio and water content were established and compared with the results of linear and exponential regression analysis. The residual error and accuracy range show that the grey prediction process is much better than regression analysis. The degradation of Chl a and b contains two phases, one being fast and the other slow. and C. M. Yang ... [et al.].
A bicubic model for local smoothing of surfaces is constructed on the base of pivot points. Such an approach allows reducing the dimension of matrix of normal equations more than twice. The model enables to increase essentially the speed and stability of calculations. The algorithms, constructed by the aid of the offered model, can be used both in applications and the development of global methods for smoothing and approximation of surfaces.
The paper deals with the recently proposed autotracking piecewise cubic approximation (APCA) based on the discrete projective transformation, and neural networks (NN). The suggested new approach facilitates the analysis of data with complex dependence and relatively small errors. We introduce a new representation of polynomials that can provide different local approximation models. We demonstrate how APCA can be applied to especially noisy data thanks to NN and local estimations. On the other hand, the new approximation method also has its impact on neural networks. We show how APCA helps to decrease the computation time of feed forward NN.
The aim of the present experiment was to evaluate the currently used allometric models for Vitis vinifera L., as well as to develop a simple and accurate model using linear measurements [leaf length (L.) and leaf width (W)] for estimating the individual leaf area (LA) of nine grapevine genotypes. For model construction, a total of 1,630 leaves coming from eight genotypes in 2010 was sampled during different leaf developmental stages and encompassed the full spectrum of leaf sizes. The model with single measurement of L could be considered an interesting option because it requires measurement of only one variable, but at the expense of accuracy. To find a model to estimate individual LA accurately for grapevine plants of all genotypes, both measurements of L and W should be involved. The proposed linear model [LA = 0,465 + 0,914 (L x W)] was adopted for its accuracy: the highest coefficient of determination (>0,98), the smallest mean square error, the smallest prediction sum of squares, and the reasonable close prediction sum of squares value to error sum of squares. To validate the LW model, an independent data set of 200 leaves coming from another genotype in 2011 was used. Correlation coefficients showed that there was a highly reliable relationships between predicted leaf area and the observed leaf area, giving an overestimation of 0.8% in the prediction. and Obsahuje seznam literatury
The least absolute shrinkage and selection operator (LASSO) is a popular technique for simultaneous estimation and model selection. There have been a lot of studies on the large sample asymptotic distributional properties of the LASSO estimator, but it is also well-known that the asymptotic results can give a wrong picture of the LASSO estimator's actual finite-sample behaviour. The finite sample distribution of the LASSO estimator has been previously studied for the special case of orthogonal models. The aim in this work is to generalize the finite sample distribution properties of LASSO estimator for a real and linear measurement model in Gaussian noise. In this work, we derive an expression for the finite sample characteristic function of the LASSO estimator, we then use the Fourier slice theorem to obtain an approximate expression for the marginal probability density functions of the one-dimensional components of a linear transformation of the LASSO estimator.