Strictly conservative expected values in the case of heteroscedastic errors and their application to evidential breath alcohol confidence intervals for concentration measurements

2018 ◽  
Vol 32 (7) ◽  
pp. e3029 ◽  
Author(s):  
Veli-Matti Taavitsainen ◽  
Kirsi Muuriaisniemi-Skippari ◽  
Teemu Gunnar ◽  
Heikki Ihalainen
Keyword(s):  
Confidence Intervals ◽  
Breath Alcohol ◽  
Heteroscedastic Errors ◽  
Expected Values ◽  
Concentration Measurements

scholarly journals Robust Confidence Intervals for PM2.5 Concentration Measurements in the Ecuadorian Park La Carolina

Sensors ◽  
2020 ◽  
Vol 20 (3) ◽  
pp. 654 ◽  
Author(s):  
Wilmar Hernandez ◽  
Alfredo Mendez ◽  
Rasa Zalakeviciute ◽  
Angela Maria Diaz-Marquez
Keyword(s):  
Air Pollution ◽  
Standard Deviation ◽  
Confidence Intervals ◽  
Quality Index ◽  
Urban Park ◽  
Absolute Deviation ◽  
The Mean ◽  
Concentration Measurements ◽  
Pm2.5 Concentration

In this article, robust confidence intervals for PM2.5 (particles with size less than or equal to 2.5   μ m ) concentration measurements performed in La Carolina Park, Quito, Ecuador, have been built. Different techniques have been applied for the construction of the confidence intervals, and routes around the park and through the middle of it have been used to build the confidence intervals and classify this urban park in accordance with categories established by the Quito air quality index. These intervals have been based on the following estimators: the mean and standard deviation, median and median absolute deviation, median and semi interquartile range, a -trimmed mean and Winsorized standard error of order a , location and scale estimators based on the Andrew’s wave, biweight location and scale estimators, and estimators based on the bootstrap- t method. The results of the classification of the park and its surrounding streets showed that, in terms of air pollution by PM2.5, the park is not at caution levels. The results of the classification of the routes that were followed through the park and its surrounding streets showed that, in terms of air pollution by PM2.5, these routes are at either desirable, acceptable or caution levels. Therefore, this urban park is actually removing or attenuating unwanted PM2.5 concentration measurements.

Evaluating the Variability of Duplicate Breath Alcohol Analyses as a Function of Subject Age

1993 ◽  
Vol 33 (2) ◽  
pp. 110-114
Author(s):  
R G Gullberg
Keyword(s):  
Confidence Intervals ◽  
Age Groups ◽  
Elderly Subjects ◽  
Breath Sampling ◽  
Breath Alcohol ◽  
The Mean ◽  
Acceptable Agreement

The influence of the person's age upon reproducibility in duplicate breath alcohol analyses is investigated. A total of n = 30,324 duplicate results (with both ≥0.01 g/210L) were selected and divided into eight age groups from 10–19, 20–29, and up through 80+. Two duplicate agreement criteria, +/- 10% of the mean and +/- 0.02 g/210L, were evaluated according to age. A X2trend analysis was employed and resulted in: +/- 10% of mean criteria, P < 0.001 and +/- 0.02 g/210L criteria, P > 0.05. The proportions of duplicates not conforming to the two agreement standards along with 95% confidence intervals were: +/- 10% of mean, 0.026 (0.024 to 0.028) and +/- 0.02 g/210 L, 0.052 (0.050 to 0.054). Depending on the agreement criteria selected there will be proportional differences, but neither appears to be importantly influenced by the subject's age. The breath sampling criteria employed in the instrument studied does not appear to inhibit acceptable agreement, even in elderly subjects where the risk of respiratory disfunction increases.

scholarly journals Simultaneous Inference on All Linear Combinations of Means with Heteroscedastic Errors

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Xin Yan ◽  
Xiaogang Su
Keyword(s):  
Confidence Intervals ◽  
Error Rate ◽  
Pairwise Comparisons ◽  
Simultaneous Inference ◽  
Familywise Error Rate ◽  
Linear Combinations ◽  
Simultaneous Confidence Intervals ◽  
Nominal Level ◽  
Equal Variance ◽  
Heteroscedastic Errors

We proposed a statistical method to construct simultaneous confidence intervals on all linear combinations of means without assuming equal variance where the classical Scheffé's simultaneous confidence intervals no longer preserve the familywise error rate (FWER). The proposed method is useful when the number of comparisons on linear combinations of means is extremely large. The FWERs for proposed simultaneous confidence intervals under various configurations of mean variances are assessed through simulations and are found to preserve the predefined nominal level very well. An example of pairwise comparisons on heteroscedastic means is given to illustrate the proposed method.

A Perspective on the Construction of Nonsymmetric Uncertainty Intervals

1997 ◽  
Vol 119 (4) ◽  
pp. 804-807
Author(s):  
Paul K. Maciejewski
Keyword(s):  
Confidence Intervals ◽  
New Method ◽  
True Value ◽  
Expected Values ◽  
Normally Distributed

This paper presents a new method for constructing nonsymmetric uncertainty intervals, one that is based on estimates of “expected values” and “variances” associated with deterministic errors that one constructs from estimates of “upper bias limits” and “lower bias limits” for measured variables. On the assumption that upper bias limits and lower bias limits specified by the user correspond to 95 percent confidence intervals for normally distributed deterministic errors, the uncertainty intervals determined by the new method reduce to approximate 95 percent confidence intervals for the true value of the measured variables.

Simultaneous Confidence Intervals for the Linear Functions of Expected Mean Squares Used in Generalizability Theory

1986 ◽  
Vol 11 (3) ◽  
pp. 197-205
Author(s):  
John F. Bell
Keyword(s):  
Linear Model ◽  
Confidence Intervals ◽  
Random Effects ◽  
Variance Components ◽  
Generalizability Theory ◽  
Linear Functions ◽  
Simultaneous Confidence Intervals ◽  
Balanced Design ◽  
Expected Values ◽  
Bonferroni's Inequality

This paper demonstrates a method, derived by Khuri (1981) , of constructing simultaneous confidence intervals for functions of expected values of mean squares obtained when analyzing a balanced design by a random effects linear model. The method may be applied to obtain confidence intervals for the variance components and other linear functions of the expected mean squares used in generalizability theory, with probability of simultaneous coverage guaranteed to be greater than or equal to the specified confidence coefficient. The Khuri intervals are compared with the approximate intervals obtained by using Satterthwaite’s (1941 , 1946) method in conjunction with Bonferroni’s inequality.

Quantitative Diameter Measurements of Chromatin and TMV Fibers in the Freeze-Dried State

1988 ◽  
Vol 46 ◽  
pp. 170-171
Author(s):  
B. D. Athey ◽  
A. L. Stout ◽  
M. F. Smith ◽  
J. P. Langmore
Keyword(s):  
Reliable Method ◽  
Fiber Diameter ◽  
Quantitative Agreement ◽  
One Dimension ◽  
Fiber Axis ◽  
Two Dimensional ◽  
Fiber Density ◽  
Variable Diameter ◽  
Freeze Dried ◽  
Expected Values

Although there is general agreement that Inactive chromosome fibers consist of helically packed nucleosomes, the pattern of packing is still undetermined. Only one of the proposed models, the crossed-linker model, predicts a variable diameter dependent on the length of DNA between nucleosomes. Measurements of the fiber diameter of negatively-stained and frozen- hydrated- chromatin from Thyone sperm (87bp linker) and Necturus erythrocytes (48bp linker) have been previously reported from this laboratory. We now introduce a more reliable method of measuring the diameters of electron images of fibrous objects. The procedure uses a modified version of the computer program TOTAL, which takes a two-dimensional projection of the fiber density (represented by the micrograph itself) and projects it down the fiber axis onto one dimension. We illustrate this method using high contrast, in-focus STEM images of TMV and chromatin from Thyone and Necturus. The measured diameters are in quantitative agreement with the expected values for the crossed-linker model for chromatin structure

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