837 research outputs found
Comparison of hyperbolic and constant width simultaneous confidence bands in multiple linear regression under MVCS criterion
No full textA simultaneous confidence band provides useful information on the plausible range of the unknown regression model, and different confidence bands can often be constructed for the same regression model. For a simple regression line, Liu and Hayter (2007) propose use of the area of the confidence set corresponding to a confidence band as an optimality criterion in comparison of confidence bands; the smaller the area of the confidence set, the better the corresponding confidence band. This minimum area confidence set (MACS) criterion can begeneralized to a minimum volume confidence set (MVCS) criterion in the study of confidence bands for a multiple linear regression model. In this paper hyperbolic and constant width confidence bands for a multiple linear regression model over a particular ellipsoidal region of the predictor variables are compared under the MVCS criterion. It is observed that whether one band is better than the other depends on the magnitude of one particular angle that determines the size of the predictor variable region. When the angle and so the size of the predictor variable region is small, the constant width band is better than the hyperbolic band but only marginally. When the angle and so the size of the predictor variable region is large the hyperbolic band can be substantially better than the constant width band
Random Walk
No full textRandom walks (RW’s) appeared in the mathematical and statistical literature in 1905 when Karl
Pearson, in a letter to the journal Nature, introduced the name for the first time. They are a simple kind of stochastic
processes and describe the random movements of an object in a set of possible positions. RW’s are Markov processes
as the conditional distribution of a future state given the present and the past depends only on the present state. As
a consequence the classification of Markov chains as irreducible, recurrent and periodic can be applied to characterize
their limiting behavior. An important role in this regard is played by asymptotic results in probability theory concerning
sums of i.i.d. random variables, such as the laws of large numbers and the central limit theorem. At present a large
number of papers in environmental sciences make explicit or implicit use of RW based models. Their application
has mainly to do with studies of animal movements and microscopic motility and of particle diffusion in fluids. The
implicit use of RW models arises when computational algorithms or complex, possibly hierarchical, statistical models
are employed
Comparison of hyperbolic and constant width simultaneous confidence bands in multiple linear regression under MVCS criterion
No full textA simultaneous confidence band provides useful information on the plausible range of the unknown regression model, and different confidence bands can often be constructed for the same regression model. For a simple regression line, Liu and Hayter [W. Liu, A.J. Hayter, Minimum area confidence set optimality for confidence bands in simple linear regression, J. Amer. Statist. Assoc. 102 (477) (2007) pp. 181–190] proposed the use of the area of the confidence set corresponding to a confidence band as an optimality criterion in comparison of confidence bands; the smaller the area of the confidence set, the better the corresponding confidence band. This minimum area confidence set (MACS) criterion can be generalized to a minimum volume confidence set (MVCS) criterion in the study of confidence bands for a multiple linear regression model. In this paper hyperbolic and constant width confidence bands for a multiple linear regression model over a particular ellipsoidal region of the predictor variables are compared under the MVCS criterion. It is observed that whether one band is better than the other depends on the magnitude of one particular angle that determines the size of the predictor variable region. When the angle and hence the size of the predictor variable region is small, the constant width band is better than the hyperbolic band but only marginally. When the angle and hence the size of the predictor variable region is large the hyperbolic band can be substantially better than the constant width band
Minimum area confidence set optimality for confidence bands in simple linear regression
No full textThe average width of a simultaneous confidence band has been used by several authors (e.g. Naiman, 1983, 1984, Piegorsch, 1985a) as a criterion for the comparison of different confidence bands. In this paper, the area of the confidence set corresponding to a confidence band is used as a new criterion. For simple linear regression, comparisons have been carried out under this new criterion between hyperbolic bands, two-segment bands, and three-segment bands, which include constant width bands as special cases. It is found that if one requires a confidence band over the whole range of the covariate, then the best confidence band is given by the Working & Hotelling hyperbolic band. Furthermore, if one needs a confidence band over a finite interval of the covariate, then a restricted hyperbolic band can again be recommended, although a three-segment band may be very slightly superior in certain cases
Letter from W.W. Lessing, Relocation Officer, War Relocation Authority, to Mrs. George H. Nakamura, November 25, 1945
No full textCorrespondence from W.W. Lessing to Dorothy Nakamura regarding grants for former incarcerees returning to their former homes after World War II.The Japanese American Archival Collection documents the people, places, and daily life of Japanese Americans, primarily those who lived in the once thriving community of pre-war Florin in the Sacramento region, as well as the conditions in American incarceration camps during World War II. The approximately 7,000 original items include personal and official letters, photographs, diaries, arts and crafts, newsletters, textiles, camps artifacts, yearbooks and other publications
Food Web Modeling
No full textMany features of a food web are semi- to fully quantitative and are subject to uncertainty. Various techniques have been developed to describe these features. Others have been developed to model food web dynamics for purposes that include prediction. Yet, few approaches facilitate systematic, unified conclusions to be readily drawn about the food web's characteristics. Even fewer address the uncertainty that is inherent in the behavior of organisms within the web and in the surrounding environment. Recently, statistical modeling techniques have been adapted to food web research; they allow the investigator to simultaneously address multiple questions about the food web of interest under a unified quantitative framework, while fully exploiting the important role that uncertainty plays in food web ecology. This article reviews some conventional methods for drawing insights into food webs, and discusses recent statistical developments in food web research. Some details of the latter on network flows are provided
Letter from W.W. [Escherich], to Virginia Lowers, March 1, 1946.
No full textIn this letter [Escherich] informs Miss Lowers about his promotion to captain of a ship, as well events that took place during his trips to Maui, Tientsin China, and Okinawa, including brief descriptions about landscapes and climates.Gerth Archives Japanese American History Collection contains books, pamphlets, flyers, photographs, booklets, correspondence, periodicals, and oversized material related to Japanese Americans. Subjects in the collection include incarceration camps, Southbay local history, World War II propaganda, Japanese American families, incarceration camp pilgrimages, and other topics
Has J. G. Mendel been “Too accurate” in his experiments? the χ2 test and its significance to the evaluation of genetic segregation
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