Bootstrap models for interval estimation of longevity characteristics of sequential systems from small samples

This article firstly defines hierarchical data missing pattern, which is a generalization of monotone data missing pattern. Then multivariate Behrens–Fisher problem with hierarchical missing data is considered to illustrate that how ideas in dealing with monotone missing data can be extended to deal with hierarchical missing pattern. A pivotal quantity similar to the Hotelling T 2 is presented, and the moment matching method is used to derive its approximate distribution which is for testing and interval estimation. The precision of the approximation is illustrated through Monte Carlo data simulation. The results indicate that the approximate method is very satisfactory even for moderately small samples.

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Interval Estimation with Small Samples for Median Lethal Dose or Median Effective Dose

Design and Analysis of Animal Studies in Pharmaceutical Development ◽

10.1201/9781482269918-4 ◽

1998 ◽

pp. 55-90

Keyword(s):

Effective Dose ◽

Lethal Dose ◽

Interval Estimation ◽

Small Samples ◽

Median Lethal Dose

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Statistical Inference for the Inverted Scale Family under General Progressive Type-II Censoring

Symmetry ◽

10.3390/sym12050731 ◽

2020 ◽

Vol 12 (5) ◽

pp. 731

Author(s):

Jing Gao ◽

Kehan Bai ◽

Wenhao Gui

Keyword(s):

Monte Carlo ◽

Maximum Likelihood ◽

Monte Carlo Simulations ◽

Maximum Likelihood Estimator ◽

Confidence Intervals ◽

Interval Estimation ◽

Bayesian Estimator ◽

Small Samples ◽

Likelihood Estimator ◽

Scale Family

Two estimation problems are studied based on the general progressively censored samples, and the distributions from the inverted scale family (ISF) are considered as prospective life distributions. One is the exact interval estimation for the unknown parameter θ , which is achieved by constructing the pivotal quantity. Through Monte Carlo simulations, the average 90 % and 95 % confidence intervals are obtained, and the validity of the above interval estimation is illustrated with a numerical example. The other is the estimation of R = P ( Y < X ) in the case of ISF. The maximum likelihood estimator (MLE) as well as approximate maximum likelihood estimator (AMLE) is obtained, together with the corresponding R-symmetric asymptotic confidence intervals. With Bootstrap methods, we also propose two R-asymmetric confidence intervals, which have a good performance for small samples. Furthermore, assuming the scale parameters follow independent gamma priors, the Bayesian estimator as well as the HPD credible interval of R is thus acquired. Finally, we make an evaluation on the effectiveness of the proposed estimations through Monte Carlo simulations and provide an illustrative example of two real datasets.

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Applying the Anderson-Darling Test to Suicide Clusters

Crisis ◽

10.1027/0227-5910/a000197 ◽

2013 ◽

Vol 34 (6) ◽

pp. 434-437 ◽

Cited By ~ 5

Author(s):

Donald W. MacKenzie

Keyword(s):

Poisson Process ◽

Goodness Of Fit ◽

Small Samples ◽

Massachusetts Institute Of Technology ◽

Homogeneous Poisson Process ◽

Cornell University ◽

The Difference ◽

Suicide Clusters ◽

Institute Of Technology ◽

Anderson Darling

Background: Suicide clusters at Cornell University and the Massachusetts Institute of Technology (MIT) prompted popular and expert speculation of suicide contagion. However, some clustering is to be expected in any random process. Aim: This work tested whether suicide clusters at these two universities differed significantly from those expected under a homogeneous Poisson process, in which suicides occur randomly and independently of one another. Method: Suicide dates were collected for MIT and Cornell for 1990–2012. The Anderson-Darling statistic was used to test the goodness-of-fit of the intervals between suicides to distribution expected under the Poisson process. Results: Suicides at MIT were consistent with the homogeneous Poisson process, while those at Cornell showed clustering inconsistent with such a process (p = .05). Conclusions: The Anderson-Darling test provides a statistically powerful means to identify suicide clustering in small samples. Practitioners can use this method to test for clustering in relevant communities. The difference in clustering behavior between the two institutions suggests that more institutions should be studied to determine the prevalence of suicide clustering in universities and its causes.

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The German Version of the Satisfaction With Life Scale (SWLS)

European Journal of Psychological Assessment ◽

10.1027/1015-5759/a000058 ◽

2011 ◽

Vol 27 (2) ◽

pp. 127-132 ◽

Cited By ~ 180

Author(s):

Heide Glaesmer ◽

Gesine Grande ◽

Elmar Braehler ◽

Marcus Roth

Keyword(s):

Convergent Validity ◽

Satisfaction With Life ◽

Age Groups ◽

Population Based ◽

Factorial Invariance ◽

Satisfaction With Life Scale ◽

Small Samples ◽

Cross Sectional ◽

Confirmatory Factor Analyses ◽

Life Scale

The Satisfaction with Life Scale (SWLS) is the most commonly used measure for life satisfaction. Although there are numerous studies confirming factorial validity, most studies on dimensionality are based on small samples. A controversial debate continues on the factorial invariance across different subgroups. The present study aimed to test psychometric properties, factorial structure, factorial invariance across age and gender, and to deliver population-based norms for the German general population from a large cross-sectional sample of 2519 subjects. Confirmatory factor analyses supported that the scale is one-factorial, even though indications of inhomogeneity of the scale have been detected. Both findings show invariance across the seven age groups and both genders. As indicators of the convergent validity, a positive correlation with social support and negative correlation with depressiveness was shown. Population-based norms are provided to support the application in the context of individual diagnostics.

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