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- Belyaev, Yuri K, et al.
(author)
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Weakly approaching sequences of random distributions
- 2000
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In: Journal of Applied Probability. - Umeå : Umeå universitet. - 0021-9002 .- 1475-6072.
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Reports (peer-reviewed)abstract
- We introduce the notion of weakly approaching sequences of distributions, which is a generalization of the well-known concept of weak convergence of distributions. The main difference is that the suggested notion does not demand the existence of a limit distribution. A similar definition for conditional (random) distributions is presented. Several properties of weakly approaching sequences are given. The tightness of some of them is essential. The Cramér-Lévy continuity theorem for weak convergence is generalized to weakly approaching sequences of (random) distributions. It has several applications in statistics and probability. A few examples of applications to resampling are given.
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- Ekström, Magnus, 1966-, et al.
(author)
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Subsampling methods to estimate the variance of sample means based on nonstationary spatial data with varying expected values
- 2004
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In: Journal of the American Statistical Association. - : Informa UK Limited. - 0162-1459 .- 1537-274X. ; 99:465, s. 82-95
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Journal article (peer-reviewed)abstract
- Subsampling and block resampling methods have been suggested in the literature to nonparametrically estimate the variance of statistics computed from spatial data. Usually stationary data are required. However, in empirical applications, the assumption of stationarity often must be rejected. This article proposes nonparametric methods to estimate the variance of (functions of) sample means based on nonstationary spatial data using subsampling. We assume that data are observed on a lattice in some region of R-2. In the data that we consider, the information in the different picture elements (pixels) of the lattice are allowed to come from different distributions, with smoothly varying expected values, or with expected values decomposed additively into directional components. Furthermore, pixels are assumed to be locally dependent, and the dependence structure is allowed to differ over the lattice. Consistent variance estimators for (functions of) sample means, together with convergence rates in mean square, are provided under these assumptions. An example with applications to forestry, using satellite data, is discussed.
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- Mörling, Tommy, et al.
(author)
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A method to estimate fibre length distribution in conifers based on wood samples from increment cores
- 2003
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In: Holzforschung. - 0018-3830. ; 57:3, s. 248-254
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Journal article (peer-reviewed)abstract
- We propose a method to estimate fibre length distribution in conifers based on wood samples from increment cores processed by automatic optical fibre-analysers. Automatic fibre-analysers are unable to distinguish: a) fibres from other tissues, “fines”, and b) cut from uncut fibres. However, our proposed method can handle these problems if the type of distributions that fibre lengths and fines follow is known. In our study the length distributions of fines and fibres were assumed to follow truncated normal distributions, characterised by means and standard deviations of the two distributions. Parameter estimates were obtained by the maximum likelihood method. Wood samples from two 22-year-old Scots pine trees at breast height were used to evaluate the performance of the method. From stem discs at 1.5 m, adjacent samples of 5 mm increment cores and wood pieces were taken. The cores were trimmed 1 mm at each side and samples were, after maceration, analysed in a Kajaani FiberLab 3.0. The results showed that the method works well and gives a possibility to distinguish fine and fibre length distribution.
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