Exact Confidence Intervals for Parameters in Linear Models With Parameter Constraints

2021 ◽  
Author(s):  
Viktor Witkovsky ◽  
Gejza Wimmer
Keyword(s):  
Confidence Intervals ◽  
Linear Models ◽  
Exact Confidence Intervals ◽  
Parameter Constraints

scholarly journals Multi-year analyses on three populations reveal the first stable QTLs for tolerance to rain-induced fruit cracking in sweet cherry (Prunus avium L.)

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
José Quero-García ◽  
Philippe Letourmy ◽  
José Antonio Campoy ◽  
Camille Branchereau ◽  
Svetoslav Malchev ◽  
...  
Keyword(s):  
Confidence Intervals ◽  
Sweet Cherry ◽  
Prunus Avium ◽  
Linear Models ◽  
Basic Research ◽  
Fruit Weight ◽  
Phenotypic Variance ◽  
Fruit Cracking ◽  
The Stability ◽  
Sweet Cherry Cultivars

AbstractRain-induced fruit cracking is a major problem in sweet cherry cultivation. Basic research has been conducted to disentangle the physiological and mechanistic bases of this complex phenomenon, whereas genetic studies have lagged behind. The objective of this work was to disentangle the genetic determinism of rain-induced fruit cracking. We hypothesized that a large genetic variation would be revealed, by visual field observations conducted on mapping populations derived from well-contrasted cultivars for cracking tolerance. Three populations were evaluated over 7–8 years by estimating the proportion of cracked fruits for each genotype at maturity, at three different areas of the sweet cherry fruit: pistillar end, stem end, and fruit side. An original approach was adopted to integrate, within simple linear models, covariates potentially related to cracking, such as rainfall accumulation before harvest, fruit weight, and firmness. We found the first stable quantitative trait loci (QTLs) for cherry fruit cracking, explaining percentages of phenotypic variance above 20%, for each of these three types of cracking tolerance, in different linkage groups, confirming the high complexity of this trait. For these and other QTLs, further analyses suggested the existence of at least two-linked QTLs in each linkage group, some of which showed confidence intervals close to 5 cM. These promising results open the possibility of developing marker-assisted selection strategies to select cracking-tolerant sweet cherry cultivars. Further studies are needed to confirm the stability of the reported QTLs over different genetic backgrounds and environments and to narrow down the QTL confidence intervals, allowing the exploration of underlying candidate genes.

SHORT EXACT CONFIDENCE INTERVALS FOR THE POISSON MEAN

2001 ◽  
Vol 30 (2) ◽  
pp. 257-261 ◽  
Author(s):  
John Byrne ◽  
Paul Kabaila
Keyword(s):  
Confidence Intervals ◽  
Exact Confidence Intervals

scholarly journals Confidence and coverage for Bland–Altman limits of agreement and their approximate confidence intervals

2016 ◽  
Vol 27 (5) ◽  
pp. 1559-1574 ◽  
Author(s):  
Andrew Carkeet ◽  
Yee Teng Goh
Keyword(s):  
Confidence Intervals ◽  
Small Sample ◽  
Interval Methods ◽  
Tolerance Interval ◽  
Confidence Limits ◽  
Sample Sizes ◽  
Limits Of Agreement ◽  
Approximate Methods ◽  
Exact Confidence Intervals ◽  
Tolerance Factors

Bland and Altman described approximate methods in 1986 and 1999 for calculating confidence limits for their 95% limits of agreement, approximations which assume large subject numbers. In this paper, these approximations are compared with exact confidence intervals calculated using two-sided tolerance intervals for a normal distribution. The approximations are compared in terms of the tolerance factors themselves but also in terms of the exact confidence limits and the exact limits of agreement coverage corresponding to the approximate confidence interval methods. Using similar methods the 50th percentile of the tolerance interval are compared with the k values of 1.96 and 2, which Bland and Altman used to define limits of agreements (i.e. [Formula: see text]+/− 1.96Sd and [Formula: see text]+/− 2Sd). For limits of agreement outer confidence intervals, Bland and Altman’s approximations are too permissive for sample sizes <40 (1999 approximation) and <76 (1986 approximation). For inner confidence limits the approximations are poorer, being permissive for sample sizes of <490 (1986 approximation) and all practical sample sizes (1999 approximation). Exact confidence intervals for 95% limits of agreements, based on two-sided tolerance factors, can be calculated easily based on tables and should be used in preference to the approximate methods, especially for small sample sizes.

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