Application of Confidence Regions to Ice Ridge Keel Data Statistical Assessment

2017 ◽  
Author(s):  
Petr Zvyagin ◽  
Jaakko Heinonen
Keyword(s):  
Confidence Region ◽  
Random Variable ◽  
Confidence Regions ◽  
Small Sample ◽  
Unknown Parameters ◽  
Minimum Area ◽  
Statistical Assessment ◽  
Gulf Of Bothnia ◽  
The Mean ◽  
Small Sample Sizes

Sets of measurements of underwater ridge parts usually contain a limited amount of data. Outcomes need to be made while relying on small sample sizes. In this event, the chance of making inaccurate estimations increases. This paper proposes to use stochastic confidence regions in the estimation of the unknown parameters of keel depths. A model for a random variable with a lognormal distribution for keel depths is assumed. Regions for the mean and standard deviation of keel depths are obtained from Mood’s and minimum-area confidence regions for parameters of the normally distributed random variable. Conservative safety probability of non-exceeding the critical keel depth in one random interaction of the ridge with structure is estimated. An algorithm for statistically assessment of ice ridge keel data by means of confidence region building is here offered. The assessment of a set of ridge keel depths for the Gulf of Bothnia (Baltic Sea) is performed.

scholarly journals Generalized Inferences about the Mean Vector of Several Multivariate Gaussian Processes

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Pilar Ibarrola ◽  
Ricardo Vélez
Keyword(s):  
Gaussian Processes ◽  
Confidence Region ◽  
Confidence Regions ◽  
Covariance Matrices ◽  
Nuisance Parameters ◽  
Vector Parameter ◽  
Multivariate Gaussian ◽  
The Mean ◽  
Unknown Vector ◽  
Mean Vector

We consider in this paper the problem of comparing the means of several multivariate Gaussian processes. It is assumed that the means depend linearly on an unknown vector parameterθand that nuisance parameters appear in the covariance matrices. More precisely, we deal with the problem of testing hypotheses, as well as obtaining confidence regions forθ. Both methods will be based on the concepts of generalizedpvalue and generalized confidence region adapted to our context.

scholarly journals Empirical likelihood confidence regions of the parameters in a partially single-index varying-coefficient model

2019 ◽  
Vol 17 (1) ◽  
pp. 728-741
Author(s):  
Xing Xiang ◽  
Wanrong Liu
Keyword(s):  
Confidence Region ◽  
Confidence Regions ◽  
Varying Coefficient Model ◽  
Adjustment Factor ◽  
Unknown Parameters ◽  
Chi Square ◽  
Varying Coefficient ◽  
Single Index ◽  
Log Likelihood ◽  
Likelihood Ratio Statistics

Abstract In this paper, we investigate a partially single-index varying-coefficient model, and suggest two empirical log-likelihood ratio statistics for the unknown parameters in the model. The first statistic is asymptotically distributed as a weighted sum of independent chi-square variables under some mild conditions. It is proved that another statistic, with adjustment factor, is asymptotically standard chi-square under some suitable conditions. These useful statistics could be used to construct the confidence regions of the parameters. A simulation study indicates that, with the increase of sample size, the coverage probability of the confidence region constructed by us gradually approaches the theoretical value.

scholarly journals Confidence-based Contractor, Propagation and Potential Clouds for Differential Equations

2021 ◽  
Author(s):  
Julien Alexandre Dit Sandretto
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Confidence Level ◽  
Confidence Region ◽  
Random Variable ◽  
Confidence Regions ◽  
Initial Value ◽  
Confidence Levels ◽  
Interval Approach

A novel interval contractor based on the confidence assigned to a random variable is proposed in this paper. It makes possible to consider at the same time an interval in which the quantity is guaranteed to be, and a confidence level to reduce the pessimism induced by interval approach. This contractor consists in computing a confidence region. Using different confidence levels, a particular case of potential cloud can be computed. As application, we propose to compute the reachable set of an ordinary differential equation under the form of a set of confidence regions, with respect to confidence levels on initial value.

Effects of bait type and deployment strategy on uptake by free-living badgers

2007 ◽  
Vol 34 (6) ◽  
pp. 454 ◽  
Author(s):  
Francesca Cagnacci ◽  
Giovanna Massei ◽  
David P. Cowan ◽  
Neil Walker ◽  
Richard J. Delahay
Keyword(s):  
Wildlife Management ◽  
Social Groups ◽  
Fertility Control ◽  
Meles Meles ◽  
Small Sample ◽  
Free Living ◽  
Statistical Assessment ◽  
Deployment Strategy ◽  
Uptake Rates ◽  
Small Sample Sizes

Baits are increasingly used in wildlife management to deliver orally administered vaccines and contraceptives. The efficacy and cost-effectiveness of vaccination or fertility-control campaigns can be substantially affected by bait uptake rates. This study assessed whether bait type and deployment strategy affected bait uptake by free-living badgers (Meles meles L.). Six social groups of badgers were presented with three bait types (meat, fruit, cereals) and two deployment strategies (dispersed single baits versus aggregated multiple baits at fixed baiting stations) for six weeks. In each social group, the type of bait and deployment strategy were rotated every week so that by the end of the test every group had experienced all combinations. On three days, biomarkers (ethyl iophenoxic acid, propyl iophenoxic acid and rhodamine B) were added to the baits to determine the proportion of badgers ingesting these baits. The results indicated that both bait type and deployment strategy affected the proportion of baits eaten by badgers and the number of badgers gaining access to baits. Meat and fruit baits were taken significantly more frequently than cereals, and dispersed meat baits had the highest rates of disappearance. Biomarker levels suggested that the proportion of badgers that gained access to all baits was substantially lower when baits were aggregated, although small sample sizes prevented statistical assessment of this effect. The results suggest that dispersed single baits are likely to be consumed in greater proportions by a higher number of individual badgers than multiple baits at fixed stations.

OBTAINING POINT ESTIMATORS OF PARAMETERS FROM CONFIDENCE INTERVALS OR JOINT CONFIDENCE REGIONS

2007 ◽  
Vol 14 (01) ◽  
pp. 21-28
Author(s):  
ZHENMIN CHEN
Keyword(s):  
Maximum Likelihood ◽  
Population Distribution ◽  
Confidence Region ◽  
Interval Estimation ◽  
Likelihood Estimation ◽  
Confidence Regions ◽  
Point Estimation ◽  
Estimation Of Parameters ◽  
Unknown Parameters ◽  
Point Estimators

There are several different ways to obtain point estimators for the parameters of a population distribution. The maximum likelihood estimation and moment estimation are the most commonly used ones. Using point estimators only to estimate unknown parameters is somewhat risky because the probability that the estimation is wrong is almost 100%. Interval estimation, on the other hand, can reduce this risk considerably. The purpose of this paper is to propose a new method for obtaining point estimation of parameters. The point estimators discussed here are obtained by squeezing a confidence interval or joint confidence region of the parameters. The proposed method is easy to use in some cases. The estimators obtained by using this method possess some unbiasedness property. It is also shown that the point estimator obtained by this method is more reasonable than the maximum likelihood estimator when the population distribution is skewed.

scholarly journals A Simple Normal Approximation for Weibull Distribution with Application to Estimation of Upper Prediction Limit

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
H. V. Kulkarni ◽  
S. K. Powar
Keyword(s):  
Monte Carlo ◽  
Weibull Distribution ◽  
Shape Parameter ◽  
Normal Approximation ◽  
Random Variable ◽  
Industrial Applications ◽  
Small Sample ◽  
Prediction Limit ◽  
Coverage Probabilities ◽  
Small Sample Sizes

We propose a simple close-to-normal approximation to a Weibull random variable (r.v.) and consider the problem of estimation of upper prediction limit (UPL) that includes at leastlout ofmfuture observations from a Weibull distribution at each ofrlocations, based on the proposed approximation and the well-known Box-Cox normal approximation. A comparative study based on Monte Carlo simulations revealed that the normal approximation-based UPLs for Weibull distribution outperform those based on the existing generalized variable (GV) approach. The normal approximation-based UPLs have markedly larger coverage probabilities than GV approach, particularly for small unknown shape parameter where the distribution is highly skewed, and for small sample sizes which are commonly encountered in industrial applications. Results are illustrated with a real dataset for practitioners.

scholarly journals Reaction times and other skewed distributions: problems with the mean and the median

2018 ◽  
Author(s):  
Guillaume A. Rousselet ◽  
Rand R. Wilcox
Keyword(s):  
Reaction Times ◽  
Small Sample ◽  
Careful Examination ◽  
Central Tendency ◽  
Skewed Distributions ◽  
Experimental Conditions ◽  
Sample Mean ◽  
Sample Median ◽  
The Mean ◽  
Small Sample Sizes

ABSTRACTTo summarise skewed (asymmetric) distributions, such as reaction times, typically the mean or the median are used as measures of central tendency. Using the mean might seem surprising, given that it provides a poor measure of central tendency for skewed distributions, whereas the median provides a better indication of the location of the bulk of the observations. However, the sample median is biased: with small sample sizes, it tends to overestimate the population median. This is not the case for the mean. Based on this observation, Miller (1988) concluded that “sample medians must not be used to compare reaction times across experimental conditions when there are unequal numbers of trials in the conditions.” Here we replicate and extend Miller (1988), and demonstrate that his conclusion was ill-advised for several reasons. First, the median’s bias can be corrected using a percentile bootstrap bias correction. Second, a careful examination of the sampling distributions reveals that the sample median is median unbiased, whereas the mean is median biased when dealing with skewed distributions. That is, on average the sample mean estimates the population mean, but typically this is not the case. In addition, simulations of false and true positives in various situations show that no method dominates. Crucially, neither the mean nor the median are sufficient or even necessary to compare skewed distributions. Different questions require different methods and it would be unwise to use the mean or the median in all situations. Better tools are available to get a deeper understanding of how distributions differ: we illustrate a powerful alternative that relies on quantile estimation. All the code and data to reproduce the figures and analyses in the article are available online.

scholarly journals Confidence Regions for Multivariate Quantiles

Water ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 996 ◽  
Author(s):  
Maximilian Coblenz ◽  
Rainer Dyckerhoff ◽  
Oliver Grothe
Keyword(s):  
Simulation Study ◽  
Level Sets ◽  
Confidence Regions ◽  
Small Sample ◽  
Sample Sizes ◽  
Coverage Probabilities ◽  
Sample Application ◽  
Small Sample Sizes ◽  
Reliable Methods ◽  
Insight Into

Multivariate quantiles are of increasing importance in applications of hydrology. This calls for reliable methods to evaluate the precision of the estimated quantile sets. Therefore, we focus on two recently developed approaches to estimate confidence regions for level sets and extend them to provide confidence regions for multivariate quantiles based on copulas. In a simulation study, we check coverage probabilities of the employed approaches. In particular, we focus on small sample sizes. One approach shows reasonable coverage probabilities and the second one obtains mixed results. Not only the bounded copula domain but also the additional estimation of the quantile level pose some problems. A small sample application gives further insight into the employed techniques.

scholarly journals Analysis of power of the classical and robust normality tests against bimodal distribution

2009 ◽  
Vol 57 (6) ◽  
pp. 253-260
Author(s):  
Luboš Střelec
Keyword(s):  
Simulation Study ◽  
Bimodal Distribution ◽  
Small Sample ◽  
The Other ◽  
Sample Sizes ◽  
Test Statistic ◽  
Lilliefors Test ◽  
The Mean ◽  
Anderson Darling ◽  
Small Sample Sizes

The aim of this paper is to compare the power of selected normality tests to detect a bimodal distribution. We use some classical normality tests (the Shapiro-Wilk test, the Lilliefors test, the Anderson-Darling test, the classical Jarque-Bera test and the Jarque-Bera-Urzua test), some robust normality tests (the robust Jarque-Bera test and the Medcouple test) and the modified Jarque-Bera tests, where the median instead of the mean is used in the classical Jarque-Bera test statistic. The results of simulation study show that the Anderson-Darling and the Shapiro-Wilk tests outperform the others, especially in small sample sizes. On the other hand the classical Jarque-Bera, the Jarque-Bera-Urzua and robust Jarque-Bera tests are biased, especially in small sample sizes again. Finally, the modification of the Jarque-Bera test leads to increase of power against bimodal distribution.

scholarly journals Sample Size Requirements for Calibrated Approximate Credible Intervals for Proportions in Clinical Trials

2021 ◽  
Vol 18 (2) ◽  
pp. 595
Author(s):  
Fulvio De Santis ◽  
Stefania Gubbiotti
Keyword(s):  
Clinical Trials ◽  
Posterior Probability ◽  
Interval Estimation ◽  
Small Sample ◽  
Sample Sizes ◽  
Posterior Density ◽  
Unknown Parameters ◽  
Credible Intervals ◽  
Small Sample Sizes ◽  
Highest Posterior Density

In Bayesian analysis of clinical trials data, credible intervals are widely used for inference on unknown parameters of interest, such as treatment effects or differences in treatments effects. Highest Posterior Density (HPD) sets are often used because they guarantee the shortest length. In most of standard problems, closed-form expressions for exact HPD intervals do not exist, but they are available for intervals based on the normal approximation of the posterior distribution. For small sample sizes, approximate intervals may be not calibrated in terms of posterior probability, but for increasing sample sizes their posterior probability tends to the correct credible level and they become closer and closer to exact sets. The article proposes a predictive analysis to select appropriate sample sizes needed to have approximate intervals calibrated at a pre-specified level. Examples are given for interval estimation of proportions and log-odds.

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