A PARTICULAR APPLICATION OF BROWNIAN MOTION TO SEQUENTIAL ANALYSIS

Abstract: This paper studies uniform distributional properties of particular stopping times for Brownian motion that are determined by a family of stopping curves indexed by p ∈ [0, 1]. These curves derive from the stopping curve for a sequential estimation problem in which the goal is to estimate a function of the Binomial parameter p that diverges as p approaches zero. The almost sure convergence and asymptotic normality of the stopping times for the Brownian analogue of this problem are obtained straightforwardly. The main result is the derivation of exponential bounds for the tail probabilities of a weighted mean square loss function expressible in terms of these stopping times. This result suffices to establish the uniform integrability of these loss functions in this continuous model, providing more importantly the methodology to prove the more difficult consistency result for the discrete Binomial problem. Brief historical comments about Brownian motion are included, as well as several open problems related to Brownian processes and sequential methods

The demography of fine roots in response to patches of water and nitrogen

Fine root demography was quantified in response to patches of increased water and nitrogen availability in a natural, second-growth, mixed hardwood forest in northern Michigan, USA. As expected, the addition of water and water plus nitrogen resulted in a significant overall increase in the production of new fine roots. New root production was much greater in response to water plus nitrogen when compared with water alone, and the duration of new root production was related to the length of resource addition in the water plus nitrogen treatments; the average difference in new root length between the 20 vs. 40 d additions of water plus nitrogen amounted to almost 600%. Roots produced in response to the additions of water and water plus nitrogen lived longer than roots in the control treatments. Thus, additions of water and water plus nitrogen influenced both the proliferation of new roots and their longevity, with both proliferation and longevity related to the type and duration of resource supply. Results suggest that root longevity and mortality may be plastic in response to changes in soil resource availability, as is well known for root proliferation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65770/1/j.1469-8137.1993.tb03905.x.pd

Making Capitalism Work: Social Capital and Economic Growth in Italy, 1970-1995

Using data on the 20 Italian regions for the period 1970-1995, I examine whether the presence of social capital, as reflected in a number of different measures collected by Putnam (1993), affects economic productivity. I find three types of effects. First, social capital, when treated as an input to regional production, has a positive and significant effect in the South, but a much weaker effect in the North. Second, some forms of social capital can significantly increase regions propensities to make physical capital investments; however, dense networks of association reduce capital investment in both the North and South. Instrumental variables estimates show that social capital affects growth both directly and through affecting investment in physical capital. Third, social capital contributes positively to the rate of total factor productivity growth in the Italian regions

distributed in U. S. A. byP.A.P.MoranThe Theory of Storage$2.50Methuen's Monographs on Applied Probability and Statistics1959WileyIthaca, N. Y.111

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Minimax one-sided Kolmogorov-type distribution-free tests

A family of distribution-free statistics along with related tests is defined and properties of its members are studied. These statistics, one of which is the Smirnov-Wald and Wolfowitz statistic, D n + yield tests of the one-sided hypotheses. The minimax and maximin tests in this family against a restricted class of alternatives of minimum power are obtained. The connection to a confidence bound of Stringer for the mean is also remarked.</jats:p