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In Valais, Switzerland, Scots pines (Pinus sylvestris L.) are declining, mainly following drought. To assess the impact of drought on tree growth and survival, an irrigation experiment was initiated in 2003 in a mature pine forest, approximately doubling the annual precipitation. Tree crown transparency (lack of foliage) and leaf area index (LAI) were annually assessed. Seven irrigated and six control trees were felled in 2006, and needles, stem discs and branches were taken for growth analysis. Irrigation in 2004 and 2005, both with below-average precipitation, increased needle size, area and mass, stem growth and, with a 1-year delay, shoot length. This led to a relative decrease in tree crown transparency (−14%) and to an increase in stand LAI (+20%). Irrigation increased needle length by 70%, shoot length by 100% and ring width by 120%, regardless of crown transparency. Crown transparency correlated positively with mean needle size, shoot length and ring width and negatively with specific leaf area. Trees with high crown transparency (low growth, short needles) experienced similar increases in needle mass and growth with irrigation than trees with low transparency (high growth, long needles), indicating that seemingly declining trees were able to ‘recover’ when water supply became sufficient. A simple drought index before and during the irrigation explained most of the variation found in the parameters for both irrigated and control trees.
A nonparametric goodness-of-fit test for random variables with values in a separable Hilbert space is investigated. To verify the null hypothesis that the data come from a specific distribution, an integral type test based on a Cramér-von-Mises statistic is suggested. The convergence in distribution of the test statistic under the null hypothesis is proved and the test's consistency is concluded. Moreover, properties under local alternatives are discussed. Applications are given for data of huge but finite dimension and for functional data in infinite dimensional spaces. A general approach enables the treatment of incomplete data. In simulation studies the test competes with alternative proposals.
This paper considers a paired data framework and discusses the question of marginal homogeneity of bivariate high-dimensional or functional data. The related testing problem can be endowed into a more general setting for paired random variables taking values in a general Hilbert space. To address this problem, a Cramér–von-Mises type test statistic is applied and a bootstrap procedure is suggested to obtain critical values and finally a consistent test. The desired properties of a bootstrap test can be derived that are asymptotic exactness under the null hypothesis and consistency under alternatives. Simulations show the quality of the test in the finite sample case. A possible application is the comparison of two possibly dependent stock market returns based on functional data. The approach is demonstrated based on historical data for different stock market indices.