Correct Point Estimator and Confidence Interval for RMSEA Given Categorical Data

2019 ◽  
Vol 27 (5) ◽  
pp. 678-695 ◽  
Author(s):  
Keke Lai
Keyword(s):  
Confidence Interval ◽  
Categorical Data ◽  
Point Estimator ◽  
Correct Point

scholarly journals Parametric Interval Estimation of the Geeta Distribution

2018 ◽  
Vol 8 (1) ◽  
pp. 1
Author(s):  
Betty C. Korir ◽  
Josphat K. Kinyanjui
Keyword(s):  
Confidence Interval ◽  
Interval Estimation ◽  
Random Variable ◽  
Moment Generating Function ◽  
Distribution Model ◽  
Unknown Parameters ◽  
Sample Mean ◽  
Population Mean ◽  
Point Estimator ◽  
Interval Estimators

It is well known that the sample mean is the estimator of a population mean in mathematical statistics from a given population of interest as a point estimator which assume a single number that is obtained by taking a random sample of a specified size from the entire population, depending on whether the population mean and variance is known or unknown. In the interval estimation, the sample mean is accompanied with a plus or a minus margin of an error that is assumed that the estimator is contained within the range of values with certain degree of confidence. This paper investigated and obtained the interval estimators of the unknown constants of Geeta distribution model through the construction of confidence interval using; the pivotal quantity method, the shortest-length confidence interval, unbiased confidence interval estimators, Bayesian confidence interval estimators and statistical method. Geeta distribution is a new discrete random variable distribution defined over all the positive integers, with two unknown parameters. The properties and characteristics of the Geeta distribution model were discussed and reviewed that is, the existence of the mean, variance, moment generating function and that the sum of all probabilities is unity. These are common properties of any given probability density function.

scholarly journals The Use Of Statistical Sampling And A Single-Point Estimator To Establish Punitive Fines In Compliance Auditing: A Cautionary Note

2011 ◽  
Vol 7 (1) ◽  
Author(s):  
Steven W. Lamb ◽  
William H. Svihla ◽  
Jeffrey S. Harper
Keyword(s):  
Confidence Interval ◽  
Single Point ◽  
Statistical Sampling ◽  
Font Size ◽  
Cautionary Note ◽  
Point Estimator ◽  
Compliance Audit ◽  
Current Practices

<p class="MsoNormal" style="text-align: justify; margin: 0in 0.5in 0pt; mso-pagination: widow-orphan;"><span style="mso-bidi-font-weight: bold;"><span style="font-size: x-small;"><span style="font-family: Times New Roman;">This paper describes current practices relating to statistical sampling used by auditors performing compliance audits.<span style="mso-spacerun: yes;">&nbsp; </span>An example audit case is presented where a compliance audit is performed using statistical sampling.<span style="mso-spacerun: yes;">&nbsp; </span>Fines for non-compliance are based upon the sample results.<span style="mso-spacerun: yes;">&nbsp; </span>While the practice is quite common and generally accepted, there are significant ramifications associated with the use of a single-point estimator.<span style="mso-spacerun: yes;">&nbsp; </span>Approximately half of the time, an auditee will be charged more than is actually deserved.<span style="mso-spacerun: yes;">&nbsp; </span>We explore the shortcomings associated with the use of a single-point estimator and the appropriateness of the use of a one-tailed confidence interval to provide greater assurance that fines are appropriate and reasonable.</span></span></span></p>

scholarly journals Optimal estimators of the position of a mass extinction when recovery potential is uniform

Paleobiology ◽  
2009 ◽  
Vol 35 (3) ◽  
pp. 447-459 ◽  
Author(s):  
Steve C. Wang ◽  
David J. Chudzicki ◽  
Philip J. Everson
Keyword(s):  
Confidence Interval ◽  
Mass Extinction ◽  
Measurement Scale ◽  
Standard Errors ◽  
Optimal Point ◽  
Average Width ◽  
Recovery Potential ◽  
Coverage Probabilities ◽  
Point Estimator ◽  
Optimal Estimators

Numerous methods have been developed to estimate the position of a mass extinction boundary while accounting for the incompleteness of the fossil record. Here we describe the point estimator and confidence interval for the extinction that are optimal under the assumption of uniform preservation and recovery potential, and independence among taxa. First, one should pool the data from all taxa into one combined “supersample.” Next, one can then apply methods proposed by Strauss and Sadler (1989) for a single taxon. This gives the optimal point estimator in the sense that it has the smallest variance among all possible unbiased estimators. The corresponding confidence interval is optimal in the sense that it has the shortest average width among all possible intervals that are invariant to measurement scale. These optimality properties hold even among methods that have not yet been discovered. Using simulations, we show that the optimal estimators substantially improve upon the performance of other existing methods. Because the assumptions of uniform recovery and independence among taxa are strong ones, it is important to assess to what extent they are satisfied by the data. We demonstrate the use of probability plots for this purpose. Finally, we use simulations to explore the sensitivity of the optimal point estimator and confidence interval to nonuniformity and lack of independence, and we compare their performance under these conditions with existing methods. We find that nonuniformity strongly biases the point estimators for all methods studied, inflates their standard errors, and degrades the coverage probabilities of confidence intervals. Lack of independence has less effect on the accuracy of point estimates as long as recovery potential is uniform, but it, too, inflates the standard errors and degrades confidence interval coverage probabilities.

Development of apical pits in chloride cells of the gills of Pimephales promelas after chronic exposure to acid water

1983 ◽  
Vol 41 ◽  
pp. 462-463
Author(s):  
Richard L. Leino ◽  
Jon G. Anderson ◽  
J. Howard McCormick
Keyword(s):  
Confidence Interval ◽  
Chronic Exposure ◽  
Lake Superior ◽  
Pimephales Promelas ◽  
Chloride Cells ◽  
Fathead Minnows ◽  
Secondary Lamellae ◽  
Untreated Water ◽  
Water Ph ◽  
Flow Through

Groups of 12 fathead minnows were exposed for 129 days to Lake Superior water acidified (pH 5.0, 5.5, 6.0 or 6.5) with reagent grade H2SO4 by means of a multichannel toxicant system for flow-through bioassays. Untreated water (pH 7.5) had the following properties: hardness 45.3 ± 0.3 (95% confidence interval) mg/1 as CaCO3; alkalinity 42.6 ± 0.2 mg/1; Cl- 0.03 meq/1; Na+ 0.05 meq/1; K+ 0.01 meq/1; Ca2+ 0.68 meq/1; Mg2+ 0.26 meq/1; dissolved O2 5.8 ± 0.3 mg/1; free CO2 3.2 ± 0.4 mg/1; T= 24.3 ± 0.1°C. The 1st, 2nd and 3rd gills were subsequently processed for LM (methacrylate), TEM and SEM respectively.Three changes involving chloride cells were correlated with increasing acidity: 1) the appearance of apical pits (figs. 2,5 as compared to figs. 1, 3,4) in chloride cells (about 22% of the chloride cells had pits at pH 5.0); 2) increases in their numbers and 3) increases in the % of these cells in the epithelium of the secondary lamellae.

Efficacy of Vitamin D on Chronic Heart Failure Among Adults

2020 ◽  
Vol 90 (1-2) ◽  
pp. 49-58 ◽  
Author(s):  
Wang Chunbin ◽  
Wang Han ◽  
Cai Lin
Keyword(s):  
Heart Failure ◽  
Vitamin D ◽  
Chronic Heart Failure ◽  
Left Ventricular Ejection Fraction ◽  
Confidence Interval ◽  
Left Ventricular ◽  
Left Ventricular Ejection ◽  
Controlled Trials ◽  
Ventricular Ejection Fraction ◽  
Randomized Controlled

Abstract. Vitamin D deficiency commonly occurs in chronic heart failure. Whether additional vitamin D supplementation can be beneficial to adults with chronic heart failure remains unclear. We conducted a meta-analysis to derive a more precise estimation. PubMed, Embase, and Cochrane databases were searched on September 8, 2016. Seven randomized controlled trials that investigated the effects of vitamin D on cardiovascular outcomes in adults with chronic heart failure, and comprised 592 patients, were included in the analysis. Compared to placebo, vitamin D, at doses ranging from 2,000 IU/day to 50,000 IU/week, could not improve left ventricular ejection fraction (Weighted mean difference, WMD = 3.31, 95% confidence interval, CL = −0.93 to 7.55, P < 0.001, I2 = 92.1%); it also exerts no beneficial effects on the 6 minute walk distance (WMD = 18.84, 95% CL = −24.85 to 62.52, P = 0.276, I2 = 22.4%) and natriuretic peptide (Standardized mean difference, SMD = −0.39, 95% confidence interval CL = −0.48 to 0.69, P < 0.001, I2 = 92.4%). However, a dose-response analysis from two studies demonstrated an improved left ventricular ejection fraction with vitamin D at a dose of 4,000 IU/day (WMD = 6.58, 95% confidence interval CL = −4.04 to 9.13, P = 0.134, I2 = 55.4%). The results showed that high dose vitamin D treatment could potentially benefit adults with chronic heart failure, but more randomized controlled trials are required to confirm this result.

Confidence Interval Pictures Can Give Better Inference Than Significance Testing

2006 ◽  
Author(s):  
Geoff Cumming ◽  
Melissa Coulson ◽  
Michelle Healey ◽  
Fiona Fidler
Keyword(s):  
Confidence Interval ◽  
Significance Testing

Using Connectionist Modules for Decision Support

1990 ◽  
Vol 29 (03) ◽  
pp. 167-181 ◽  
Author(s):  
G. Hripcsak
Keyword(s):  
Decision Support ◽  
Standard Deviation ◽  
Confidence Interval ◽  
Posterior Probability ◽  
Back Propagation ◽  
Connectionist Model ◽  
Test Set ◽  
The Third ◽  
Independent Test ◽  
Better Than

AbstractA connectionist model for decision support was constructed out of several back-propagation modules. Manifestations serve as input to the model; they may be real-valued, and the confidence in their measurement may be specified. The model produces as its output the posterior probability of disease. The model was trained on 1,000 cases taken from a simulated underlying population with three conditionally independent manifestations. The first manifestation had a linear relationship between value and posterior probability of disease, the second had a stepped relationship, and the third was normally distributed. An independent test set of 30,000 cases showed that the model was better able to estimate the posterior probability of disease (the standard deviation of residuals was 0.046, with a 95% confidence interval of 0.046-0.047) than a model constructed using logistic regression (with a standard deviation of residuals of 0.062, with a 95% confidence interval of 0.062-0.063). The model fitted the normal and stepped manifestations better than the linear one. It accommodated intermediate levels of confidence well.

Does Low Protein Concentration of Tissue-type Plasminogen Activator Predict a Low Risk of Spontaneous Deep Vein Thrombosis?

1995 ◽  
Vol 74 (02) ◽  
pp. 718-721 ◽  
Author(s):  
Jørgen Gram ◽  
Johannes Sidelmann ◽  
Jørgen Jespersen
Keyword(s):  
Deep Vein Thrombosis ◽  
Confidence Interval ◽  
Plasminogen Activator ◽  
Fibrinolytic Activity ◽  
Protein Concentration ◽  
Tissue Type ◽  
Vein Thrombosis ◽  
Low Protein ◽  
Deep Vein ◽  
Pai 1

SummaryMany reports have demonstrated an abnormal fibrinolysis in a subset of patients with deep vein thrombosis. We have studied systemic global fibrinolytic activity and protein concentrations of tissue-type plasminogen activator (t-PA) and plasminogen activator inhibitor type 1 (PAI-1) in plasma of 25 young patients with a previous instance of spontaneous deep vein thrombosis documented by phlebography and in 50 healthy controls. The two populations were comparable with respect to a number of base-line variables (age, height, weight, etc.), while the patients had significantly lower fibrinolytic activity (p <0.02), and significantly higher protein concentrations of t-PA (p <0.0001) and PAI-1 (p <0.0006).We used probit scale plots to identify the consequence of different cut-off points to separate patients from controls. Reasonable separation could be obtained for t-PA with a cut-off point of 5.2 ng/ml and for PAI-1 18 ng/ml. The sensitivity and specificity for these cut-off points were for t-PA 73% (95% confidence interval 63%-84%) and for PAI-1 67% (confidence interval 55%-77%). The negative predictive value with a cut-off point t-PA concentration of 5.2 ng/ml was 85% (95% confidence interval 70%-94%). We observed a significantly negative association between concentration of t-PA and fibrinolytic activity (rs = -0.47; p <0.005) and also between PAI-1 and fibrinolytic activity (rs = -0.78; p <0.005).We conclude that a young healthy population is characterized by low protein concentration of t-PA (and PAI-1) compared with young patients with a previous instance of spontaneous vein thrombosis, and we tentatively state that a low protein concentration of t-PA predicts a low risk of spontaneous deep vein thrombosis.

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