Seija Sirkiä

Tests and estimates of shape based on spatial signs and ranks

Nonparametric procedures for testing and estimation of the shape matrix in the case of multivariate elliptic distribution are considered. Testing for sphericity is an important special case. The tests and estimates are based on the spatial sign and rank covariance matrices. The estimates based on the spatial sign covariance matrix and symmetrized spatial sign covariance matrix are Tylers [A distribution-free M-estimator of multivariate scatter, Ann. Statist. 15 (1987), pp. 234–251] shape matrix and and Dümbgens [On Tylers M-functional of scatter in high dimension, Ann. Inst. Statist. Math. 50 (1998), pp. 471–491] shape matrix, respectively. The test based on the spatial sign covariance matrix is the sign test statistic in the class of nonparametric tests proposed by Hallin and Paindaveine [Semiparametrically efficient rank-based inference for shape. I. Optimal rank-based tests for sphericity, Ann. Statist. 34 (2006), pp. 2707–2756]. New tests and estimates based on the spatial rank covariance matrix are proposed. The shape estimates introduced in the paper play an important role in the inner standardisation of the spatial sign and rank tests for multivariate location. Limiting distributions of the tests and estimates are reviewed and derived, and asymptotic efficiencies as well as finite-sample efficiencies of the proposed tests are compared with those of the classical modified Johns [Some optimal multivariate tests, Biometrika 58 (1971), pp. 123–127; The distribution of a statistic used for testing sphericity of normal distributions, Biometrika 59 (1972), pp. 169–173] test and the van der Waerden test (Hallin and Paindaveine, [Semiparametrically efficient rank-based inference for shape. I. Optimal rank-based tests for sphericity, Ann. Statist. 34 (2006), pp. 2707–2756]). The symmetrised spatial sign- and rank-based estimates and tests seem to have a very high efficiency in the multivariate normal case, and they are much better than the classical estimate (shape matrix based on the regular covariance matrix) and test (Johns test) for distributions with heavy tails.

Identity and potential pathogenicity of Phytophthora species found on symptomatic Rhododendron plants in a Finnish nursery

Abstract In this study, microbial isolations were made from symptomatic Rhododendron plants from a large Finnish nursery, known to be harbouring Phytophthora based on PCR screenings. The nearby waterways were also sampled. A diversity of common Nordic plants was screened for Phytophthora susceptibility. Isolates recovered from Rhododendron plants included P. ramorum, P. cactorum, P. plurivora, P. pini and Pestalotiopsis sp. Baits floated in water samples from nearby waterways did not become infected with Phytophthora. In infection trials, all Phytophthora detected here were pathogenic to Rhododendron but nonpathogenic to Pinus sylvestris and Quercus robur. Phytophthora plurivora infected Betula pendula, Alnus glutinosa, Picea abies, Viburnum lentago, Vaccinium myrtillus, V. uliginosum, V. angustifolium and Fragaria × ananassa, the latter four species being new host records for this pathogen. Phytophthora ramorum caused small lesions on B. pendula, A. glutinosa and V. uliginosum, and more serious symptoms in Rhododendron, Viburnum lentago, V. lantana, Vaccinium myrtillus and V. angustifolium. Phytophthora pini was pathogenic to most plants tested, including Rhododendron, V. lentago and P. abies. In spite of an annual eradication programme in the nursery, P. ramorum was detected in annual samples taken during 2004–2010. Microsatellite analysis revealed that all isolates of P. ramorum belonged to the EU1 lineage.

Vulnerability to pine sawfly damage decreases with site fertility but the opposite is true with Scleroderris canker damage; results from Finnish ICP Forests and NFI data

Key messageThe probability of pine sawfly damage was highest in drier sites, while Gremmeniella abietina damage showed an opposite pattern. ICP Forests and rolling National Forest Inventory (NFI) data have good potential for quantifying patterns in damage occurrence, but region-wise NFIs may produce biased results.ContextFactors affecting the occurrence of important biotic damage on Pinus sylvestris were studied with data from large-scale forest monitoring networks.AimsWe tested how much the probability of damage caused by pine sawflies (Neodiprion sertifer Geoffr. and Diprion pini L.) and G. abietina (Lagerb. (Morelet)) differed between different forest site types and the effects of relevant climatic factors on damage probabilities.MethodsLong-term damage observations from ICP Forests Level 1 monitoring and National Forest Inventory (NFI) data were used. In addition to the traditional frequentist approach, we used a hierarchical Bayesian (HB) framework with the ICP Forests data to model the probabilities of pine sawfly outbreaks starting and continuing.ResultsThe probability of pine sawfly damage was highest in drier sites while the probabilities for G. abietina damage showed an opposite pattern. The HB analysis revealed clear differences between forest site types in the probability of outbreak starting, but the differences in the probabilities of outbreaks continuing were not clear.ConclusionICP Forests and rolling NFI data have good potential for quantifying patterns in damage occurrence, but annually region-wise NFIs may produce biased results.

Independent component analysis based on symmetrised scatter matrices

A new method for separating the mixtures of independent sources has been proposed recently in [Oja et al. (2006). Scatter matrices and independent component analysis. Austrian J. Statist., to appear]. This method is based on two scatter matrices with the so-called independence property. The corresponding method is now further examined. Simple simulation studies are used to compare the performance of so-called symmetrised scatter matrices in solving the independence component analysis problem. The results are also compared with the classical FastICA method. Finally, the theory is illustrated by some examples.