9,493 research outputs found
Simulation-based Estimation of Mean and Standard Deviation for Meta-analysis via Approximate Bayesian Computation (ABC)
Background: When conducting a meta-analysis of a continuous outcome,
estimated means and standard deviations from the selected studies are required
in order to obtain an overall estimate of the mean effect and its confidence
interval. If these quantities are not directly reported in the publications,
they need to must be estimated from other reported summary statistics, such as
the median, the minimum, the maximum, and quartiles. Methods: We propose a
simulation-based estimation approach using the Approximate Bayesian Computation
(ABC) technique for estimating mean and standard deviation based on various
sets of summary statistics found in published studies. We conduct a simulation
study to compare the proposed ABC method with the existing methods of Hozo et
al. (2005), Bland (2015), and Wan et al. (2014). Results: In the estimation of
the standard deviation, our ABC method performs best in skewed or heavy-tailed
distributions. The average relative error (ARE) approaches zero as sample size
increases. In the normal distribution, our ABC performs well. However, the Wan
et al. method is best since it is based on the normal distribution assumption.
When the distribution is skewed or heavy-tailed, the ARE of Wan et al. moves
away from zero even as sample size increases. In the estimation of the mean,
our ABC method is best since the AREs converge to zero. Conclusion: ABC is a
flexible method for estimating the study-specific mean and standard deviation
for meta-analysis, especially with underlying skewed or heavy-tailed
distributions. The ABC method can be applied using other reported summary
statistics such as the posterior mean and 95% credible interval when Bayesian
analysis has been employed
Order-statistics-based inferences for censored lifetime data and financial risk analysis
This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This thesis focuses on applying order-statistics-based inferences on lifetime analysis and financial risk measurement. The first problem is raised from fitting the Weibull distribution to progressively censored and accelerated life-test data. A new orderstatistics- based inference is proposed for both parameter and con dence interval estimation. The second problem can be summarised as adopting the inference used in the first problem for fitting the generalised Pareto distribution, especially when sample size is small. With some modifications, the proposed inference is compared with classical methods and several relatively new methods emerged from recent literature. The third problem studies a distribution free approach for forecasting financial volatility, which is essentially the standard deviation of financial returns. Classical models of this approach use the interval between two symmetric extreme quantiles of the return distribution as a proxy of volatility. Two new models are proposed, which use intervals of expected shortfalls and expectiles, instead of interval of quantiles. Different models are compared with empirical stock indices data.
Finally, attentions are drawn towards the heteroskedasticity quantile regression. The
proposed joint modelling approach, which makes use of the parametric link between
the quantile regression and the asymmetric Laplace distribution, can provide estimations
of the regression quantile and of the log linear heteroskedastic scale simultaneously.
Furthermore, the use of the expectation of the check function as a measure of
quantile deviation is discussed
Inference for Extremal Conditional Quantile Models, with an Application to Market and Birthweight Risks
Quantile regression is an increasingly important empirical tool in economics
and other sciences for analyzing the impact of a set of regressors on the
conditional distribution of an outcome. Extremal quantile regression, or
quantile regression applied to the tails, is of interest in many economic and
financial applications, such as conditional value-at-risk, production
efficiency, and adjustment bands in (S,s) models. In this paper we provide
feasible inference tools for extremal conditional quantile models that rely
upon extreme value approximations to the distribution of self-normalized
quantile regression statistics. The methods are simple to implement and can be
of independent interest even in the non-regression case. We illustrate the
results with two empirical examples analyzing extreme fluctuations of a stock
return and extremely low percentiles of live infants' birthweights in the range
between 250 and 1500 grams.Comment: 41 pages, 9 figure
Hierarchical models for semi-competing risks data with application to quality of end-of-life care for pancreatic cancer
Readmission following discharge from an initial hospitalization is a key
marker of quality of health care in the United States. For the most part,
readmission has been used to study quality of care for patients with acute
health conditions, such as pneumonia and heart failure, with analyses typically
based on a logistic-Normal generalized linear mixed model. Applying this model
to the study readmission among patients with increasingly prevalent advanced
health conditions such as pancreatic cancer is problematic, however, because it
ignores death as a competing risk. A more appropriate analysis is to imbed such
studies within the semi-competing risks framework. To our knowledge, however,
no comprehensive statistical methods have been developed for cluster-correlated
semi-competing risks data. In this paper we propose a novel hierarchical
modeling framework for the analysis of cluster-correlated semi-competing risks
data. The framework permits parametric or non-parametric specifications for a
range of model components, including baseline hazard functions and
distributions for key random effects, giving analysts substantial flexibility
as they consider their own analyses. Estimation and inference is performed
within the Bayesian paradigm since it facilitates the straightforward
characterization of (posterior) uncertainty for all model parameters including
hospital-specific random effects. The proposed framework is used to study the
risk of readmission among 5,298 Medicare beneficiaries diagnosed with
pancreatic cancer at 112 hospitals in the six New England states between
2000-2009, specifically to investigate the role of patient-level risk factors
and to characterize variation in risk across hospitals that is not explained by
differences in patient case-mix
Some Extended Classes of Distributions: Characterizations and Properties
Based on a simple relationship between two truncated moments and certain functions of the th order statistic, we characterize some extended classes of distributions recently proposed in the statistical literature, videlicet Beta-G, Gamma-G, Kumaraswamy-G and McDonald-G. Several properties of these extended classes and some special cases are discussed. We compare these classes in terms of goodness-of-fit criteria using some baseline distributions by means of two real data sets
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