Propriedades e aspectos geométricos de estimadores tipo James-Stein e do estimador de Hartigan

The James-Stein estimator is a biased shrinkage estimator with uniformly smaller risk than the risk of the sample mean estimator for the mean of multivariate normal distribution, except in the one-dimensional or two-dimensional cases. In this work we have used more heuristic arguments and intensified the geometric treatment of the theory of James-Stein estimator. New type James-Stein shrinking estimators are proposed and the Mahalanobis metric used to address the James-Stein estimator. . To evaluate the performance of the estimator proposed, in relation to the sample mean estimator, we used the computer simulation by the Monte Carlo method by calculating the mean square error. The result indicates that the new estimator has better performance relative to the sample mean estimator.

Aspectos nutricionais do baru (Dipteryx alata Vog.) em casa de vegetação e em campo

With the objective of evaluating the response of baru (Dipteryx alata Vog.) to nutrient limitation and to the different levels of fertilization, seven experiments were conducted. Experiment 1: Nutritional limitation in greenhouse. We employed 12 treatments in a completely randomized design with eight replicates. Experiment 2: Levels of liming and P in greenhouse. The experimental design was completely randomized in a factorial scheme with four levels of liming (V23.2% (natural soil), V45%, V65% and V85%) and four doses of P (0, 100, 300 and 500 mg kg -1 of P). Experiment 3: Doses of N in greenhouse. We used seven treatments (0, 75, 150, 225, 300, 375 and 450 mg kg -1 of N) in a completely randomized design. Experiment 4: Doses of K in greenhouse. We used seven treatments (0, 75, 150, 225, 300, 375 and 450 mg kg -1 ) in a completely randomized design. Experiment 5: Levels of liming under field conditions. We used four treatments (V6.7% (natural soil), V35%, V55% and V75%) in a randomized blocks design. Experiment 6: doses of P under field conditions. We used five treatments (0, 23.67, 53.34, 106.67 and 213.36 kg ha -1 of P 2O5) in a randomized blocks design. Experiment 7: Doses of N under field conditions. We used five treatments (0, 30, 60, 120 and 240 kg ha -1 of N) in Latin square. In greenhouse, the evaluations were conducted at eight months (for experiments 1 and 2) and 12 months (for experiments 3 and 4) after seeding, when the measurements of height and root collar diameter of the seedlings. Subsequently, the plants were harvested and separated into shoot and root system, for weighing and evaluating dry biomass gain. In the field, the evaluations were conducted at six, 12, 18, 24 and 30 months (for experiments 5 and 6) and at six, 12 and 18 months (for experiment 7). In these experiments, we evaluated the survival of the seedlings, height of the plants and diameter of the stem at soil height. The data obtained were submitted to analysis of variance, mean tests and regression analysis. In conclusion, during the phase of seedling formation, the species is little demanding in S and B, negatively responds to liming, positively responds to phosphate fertilization and does not respond to nitrogen and potassium fertilization. In the field, in general, the species does not respond to the application of P or to liming, and is negatively influenced by the application of elevated doses of nitrogen.