Estimation of wood fibre length distributions from censored data through an EM algorithm. (English) Zbl 1114.62142
The observed sample of wood cells comes from a cylindric wood sample (increment core). It contains not only fibres but also other cells (the so-called “fines”). The cells can be uncut as well as cut once or twice. The problem is to estimate the distribution of fibre lengths in a tree. Note, that the sampling procedure is biased by the fact that longer fibres are more likely to be sampled in the increment core. The authors propose a parametric model for the distribution of the observed length of cells which is a mixture of distributions of fibers and fines. A Monte Carlo version of EM-algorithm is used for estimation of the model parameters. Results of simulation studies and applications to real data are presented.
Reviewer: R. E. Maiboroda (Kyïv)
MSC:
| 62P99 | Applications of statistics |
| 65C05 | Monte Carlo methods |
| 62F10 | Point estimation |
| 65C60 | Computational problems in statistics (MSC2010) |
References:
| [1] | DOI: 10.1016/0378-3758(94)00097-F · Zbl 0821.62013 · doi:10.1016/0378-3758(94)00097-F |
| [2] | Dempster A. P., J. Roy. Statist. Soc. Ser. B 39 pp 1– (1977) |
| [3] | Franklin G. L., Nature 155 pp 51– (1945) |
| [4] | Hart C. H., Tappi Journal 50 pp 615– (1967) |
| [5] | Ilvessalo-Pfaffli M. S., Fiber atlas - identification of papermaking fibers (1995) |
| [6] | DOI: 10.2307/2335863 · doi:10.2307/2335863 |
| [7] | Liu C., Proceedings of the American Statistical Association (Statistical Computing Section) pp 109– (1997) |
| [8] | McLachlan G., The EM algorithm and extensions (1997) · Zbl 0882.62012 |
| [9] | McLachlan G., Finite mixture models (2000) · Zbl 0963.62061 · doi:10.1002/0471721182 |
| [10] | DOI: 10.2307/2337198 · doi:10.2307/2337198 |
| [11] | Morgan B. J. T., Elements of simulation (1984) · Zbl 0575.65009 · doi:10.1007/978-1-4899-3282-2 |
| [12] | DOI: 10.1515/HF.2003.038 · doi:10.1515/HF.2003.038 |
| [13] | DOI: 10.1137/1026034 · Zbl 0536.62021 · doi:10.1137/1026034 |
| [14] | DOI: 10.1111/1368-423X.00032 · Zbl 0955.91050 · doi:10.1111/1368-423X.00032 |
| [15] | Tanner M. A., Tools for statistical inference: methods for the exploration of posterior distributions and likelihood functions (1993) · Zbl 0777.62003 |
| [16] | van der Laan M. J., Scand. J. Statist. 23 pp 527– (1996) |
| [17] | DOI: 10.1111/1467-9469.00096 · Zbl 0921.62038 · doi:10.1111/1467-9469.00096 |
| [18] | van Zwet E. W., Bernoulli 10 pp 377– (2004) |
| [19] | Wijers B. J., Scand. J. Statist. 22 pp 335– (1995) |
| [20] | Wijers B. J., Nonparametric estimation for a windowed line-segment process (1997) · Zbl 0876.62029 |
| [21] | Wu C. F. J., Ann. Statist. 11 pp 95– (1983) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
