1,720,987 research outputs found
Testing model assumptions in multivariate linear regression models
No full textIn the multivariate nonparametric regression model Y = g(t)+ epsilon the problem of testing linearity of the regression function g and homoscedasticity of the distribution of the error epsilon is considered. For both problems a simple test is derived which is based on estimating the L-2-distance between the model space and the space induced by the hypothesis. The resulting statistics can be shown to be asymptotically normal, even under fixed alternatives. This extends and unifies recent results of Dette and Munk (1998a,b) to the multivariate case. A small simulation study on the finite sample behaviour of the proposed tests is reported and their properties are illustrated by analyzing a data example
Estimating the variance in nonparametric regression - what is a reasonable choice?
No full textThe exact mean-squared error (MSE) of estimators of the variance in nonparametric regression based on quadratic forms is investigated. In particular, two classes of estimators are compared: Hall, Kay and Titterington's optimal difference-based estimators and a class of ordinary difference-based estimators which generalize methods proposed by Rice and Gasser, Sroka and Jennen-Steinmetz. For small sample sizes the MSE of the first estimator is essentially increased by the magnitude of the integrated first two squared derivatives of the regression function. It is shown that in many situations ordinary difference-based estimators are more appropriate for estimating the variance, because they control the bias much better and hence have a much better overall performance. It is also demonstrated that Rice's estimator does not always behave well. Data-driven guidelines are given to select the estimator with the smallest MSE
Opportunity to integrate machine management data, soil, terrain and climatic variables to estimate tree harvester and forwarder performance
Full text linkA review of variance estimators with extensions to multivariate nonparametric regression models
No full textA review of variance estimators with extensions to multivariate nonparametric regression models
No full text
On Difference-Based Variance Estimation in Nonparametric Regression When the Covariate is High Dimensional
No full textWe consider the problem of estimating the noise variance in homoscedastic nonparametric regression models. For low dimensional covariates t is an element of R-d, d=1, 2, difference-based estimators have been investigated in a series of papers. For a given length of such an estimator, difference schemes which minimize the asymptotic mean-squared error can be computed for d=1 and d=2. However, from numerical studies it is known that for finite sample sizes the performance of these estimators may be deficient owing to a large finite sample bias. We provide theoretical support for these findings. In particular, we show that with increasing dimension d this becomes more drastic. If dgreater than or equal to4, these estimators even fail to be consistent. A different class of estimators is discussed which allow better control of the bias and remain consistent when dgreater than or equal to4. These estimators are compared numerically with kernel-type estimators (which are asymptotically efficient), and some guidance is given about when their use becomes necessary
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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