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43
Plotting Squared Radii
 Biometrika
, 1978
"... One way of testing data for multivariate normality is to plot the ordered squared radii against their expected values. It is suggested that the approximation to the null distribution offered by the beta distribution is a useful improvement on that afforded by the chisquared distribution. Some key w ..."
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One way of testing data for multivariate normality is to plot the ordered squared radii against their expected values. It is suggested that the approximation to the null distribution offered by the beta distribution is a useful improvement on that afforded by the chisquared distribution. Some key words: Multivariate normality; Order statistics; Squared radius. The scaled residuals of n observations yi on a ^dimensional random variable y may be defined as where # and S are respectively the sample mean vector and covariance matrix. Then the squared radii are r? = zjzt = (y<One aspect of the multivariate normality of y can thus be tested (Healy, 1968) by plotting the ordered r \ against their expected order statistics, or an approximation thereto. Under the hypothesis that y has a multivariate normal distribution the marginal distributions of the r \ are proportional to that of a beta variable of the first kind, being (Gnanadesikan & Kettenring, 1972) (n — l)in~1B{^p,^(n — p — 1)}. For sufficiently large n, the correlations
Permanents, order statistics, outliers, and robustness
 Revista Matemática Complutense
, 2007
"... In this paper, we consider order statistics and outlier models, and focus primarily on multipleoutlier models and associated robustness issues. We first synthesise recent developments on order statistics arising from independent and nonidentically distributed random variables based primarily on t ..."
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In this paper, we consider order statistics and outlier models, and focus primarily on multipleoutlier models and associated robustness issues. We first synthesise recent developments on order statistics arising from independent and nonidentically distributed random variables based primarily on the theory of permanents. We then highlight various applications of these results in evaluating the robustness properties of several linear estimators when multiple outliers are possibly present in the sample. Key words: order statistics, permanents, logconcavity, outliers, singleoutlier model,
Probability inequalities and limit theorems for generalized Lstatistics
 Lithuanian Math. J
, 2003
"... Abstract. We obtain exponential upper bounds for tails of distributions of generalized Lstatistics based on a sample from an exponential distribution. We prove the asymptotic normality of generalized Lstatistics based on a sample from the uniform distribution on [0, 1] and of Lstatistics with dec ..."
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Abstract. We obtain exponential upper bounds for tails of distributions of generalized Lstatistics based on a sample from an exponential distribution. We prove the asymptotic normality of generalized Lstatistics based on a sample from the uniform distribution on [0, 1] and of Lstatistics with decomposed kernels (without any restrictions on the sample distribution type).
Fatigue Damage Prediction in Deepwater Marine Risers due to VortexInduced Vibration
, 2011
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Fisher Information Test of Normality
, 1998
"... An extremal property of normal distributions is that they have the smallest Fisher Information for location among all distributions with the same variance. A new test of normality proposed by Terrell (1995) utilizes the above property by finding that density of maximum likelihood constrained on havi ..."
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An extremal property of normal distributions is that they have the smallest Fisher Information for location among all distributions with the same variance. A new test of normality proposed by Terrell (1995) utilizes the above property by finding that density of maximum likelihood constrained on having the expected Fisher Information under normality based on the sample variance. The test statistic is then constructed as a ratio of the resulting likelihood against that of normality. Since the asymptotic distribution of this test statistic is not available, the critical values for n = 3 to 200 have been obtained by simulation and smoothed using polynomials. An extensive power study shows that the test has superior power against distributions that are symmetric and leptokurtic (longtailed). Another advantage of the test over existing ones is the direct depiction of any deviation from normality in the form of a density estimate. This is evident when the test is applied to several real data sets. Testing of normality in residuals is also investigated. Various approaches in dealing with residuals being possibly heteroscedastic and correlated suffer from a loss of power. The approach with the fewest undesirable features is to use the Ordinary Least
Diurnal movements and behaviour of Heaviside’s dolphins, Cephalorhynchus heavisidii, with some comparative data for dusky dolphins, Lagenorhynchus obscurus
"... comparative data for dusky dolphins, ..."
APPROXIMATIONS FOR EXPECTED VALUES OF NORMAL ORDER STATISTICS WITH AN APPLICATION TO GOODNESSOFFIT BY
, 1984
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A Randomized Controlled Trial of Cognitive Training Using a Visual Speed of Processing Intervention in Middle Aged and Older Adults
"... Background: Agerelated cognitive decline is common and may lead to substantial difficulties and disabilities in everyday life. We hypothesized that 10 hours of visual speed of processing training would prevent agerelated declines and potentially improve cognitive processing speed. Methods: Within ..."
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Background: Agerelated cognitive decline is common and may lead to substantial difficulties and disabilities in everyday life. We hypothesized that 10 hours of visual speed of processing training would prevent agerelated declines and potentially improve cognitive processing speed. Methods: Within two age bands (50–64 and$65) 681 patients were randomized to (a) three computerized visual speed of processing training arms (10 hours onsite, 14 hours onsite, or 10 hours athome) or (b) an onsite attention control group using computerized crossword puzzles for 10 hours. The primary outcome was the Useful Field of View (UFOV) test, and the secondary outcomes were the Trail Making (Trails) A and B Tests, Symbol Digit Modalities Test (SDMT), Stroop Color and Word Tests, Controlled Oral Word Association Test (COWAT), and the Digit Vigilance Test (DVT), which were assessed at baseline and at one year. 620 participants (91%) completed the study and were included in the analyses. Linear mixed models were used with Blom rank transformations within age bands. Results: All intervention groups had (p,0.05) small to medium standardized effect size improvements on UFOV (Cohen’s d=20.322 to 20.579, depending on intervention arm), Trails A (d=20.204 to 20.265), Trails B (d=20.225 to 20.320), SDMT (d = 0.263 to 0.351), and Stroop Word (d = 0.240 to 0.271). Converted to years of protection against agerelated cognitive declines, these effects reflect 3.0 to 4.1 years on UFOV, 2.2 to 3.5 years on Trails A, 1.5 to 2.0 years on Trails B, 5.4 to
LIST OF TABLES.................................... v
, 2013
"... Threshold value estimation in the presence of covariate measurement error ..."
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Threshold value estimation in the presence of covariate measurement error