Search results for "Uncertainty"
showing 10 items of 1010 documents
Visualizing parameters from loglinear models
2004
This paper presents a graphical display for the parameters resulting from loglinear models. Loglinear models provide a method for analyzing associations between two or several categorical variables and have become widely accepted as a tool for researchers during the last two decades. An important part of the output of any computer program focused on loglinear models is that devoted to estimation of parameters in the model. Traditionally, this output has been presented using tables that indicate the values of the coefficients, the associated standard errors and other related information. Evaluation of these tables can be rather tedious because of the number of values shown as well as their r…
Absolute Risk and Loss-of-Lifetime Estimates for Quantitative Risk Assessment
1998
Quantitative risk assessments in public health settings intend to describe the hazard of a specific exposure in a given population on the basis of epidemiological and/or experimental results. Two different risk quantities, the absolute lifetime excess risk and the loss-of-lifetime, which differ in their definition of hazard, are discussed and compared. For both measures estimation procedures are derived and the relationship between the various estimates which are currently in use are investigated. It is shown that the two most common estimators can be written as special cases of a more general concept. This leads to conclusions about the assumptions on which different estimation procedures …
A Note on Robust Intensity Estimation for Point Processes
1992
A robust intensity estimator based on independent marking is derived. A simulation study is made to convince that the new estimator works also in such cases where the usual estimators based on the distance methods do not work. Some truncated distributions are derived.
A Modification of Stone's Test for Trend for Binary Outcome
1998
STONE (1988) suggested the first isotonic regression estimator as a tool for drawing inferences on possibly increased cancer case counts among several subregions around a putative source. He assumed the case counts to be Poisson distributed and therefore introduced a rare disease assumption into his approach. However, when analyzing cross sectional data one would rather refer to prevalence estimates among these subregions around a point risk source (for example the origin of chemical fallout). Therefore we applied antitonic regression estimation in Binomial distributions to derive a test statistic and a p value to test for a possible trend in the observed prevalence data around the putative…
A Software Tool for the Exponential Power Distribution: The normalp Package
2005
In this paper we present the normalp package, a package for the statistical environment R that has a set of tools for dealing with the exponential power distribution. In this package there are functions to compute the density function, the distribution function and the quantiles from an exponential power distribution and to generate pseudo-random numbers from the same distribution. Moreover, methods concerning the estimation of the distribution parameters are described and implemented. It is also possible to estimate linear regression models when we assume the random errors distributed according to an exponential power distribution. A set of functions is designed to perform simulation studi…
Holt–Winters Forecasting: An Alternative Formulation Applied to UK Air Passenger Data
2007
Abstract This paper provides a formulation for the additive Holt–Winters forecasting procedure that simplifies both obtaining maximum likelihood estimates of all unknowns, smoothing parameters and initial conditions, and the computation of point forecasts and reliable predictive intervals. The stochastic component of the model is introduced by means of additive, uncorrelated, homoscedastic and Normal errors, and then the joint distribution of the data vector, a multivariate Normal distribution, is obtained. In the case where a data transformation was used to improve the fit of the model, cumulative forecasts are obtained here using a Monte-Carlo approximation. This paper describes the metho…
Maximum probability estimators in the case of exponential distribution
1975
In 1966–1969L. Weiss andJ. Wolfowitz developed the theory of „maximum probability” estimators (m.p.e.'s). M.p.e.'s have the property of minimizing the limiting value of the risk (see (2.10).) In the present paper, therfore, after a short description of the new method, a fundamental loss function is introduced, for which—in the so-called regular case—the optimality property of the maximum probability estimators yields the classical result ofR.A. Fisher on the asymptotic efficiency of the maximum likelihood estimator. Thereby it turns out that the m.p.e.'s possess still another important optimality property for this loss function. For the latter the parameters of the exponential distribution—…
Introducing libeemd: a program package for performing the ensemble empirical mode decomposition
2016
The ensemble empirical mode decomposition (EEMD) and its complete variant (CEEMDAN) are adaptive, noise-assisted data analysis methods that improve on the ordinary empirical mode decomposition (EMD). All these methods decompose possibly nonlinear and/or nonstationary time series data into a finite amount of components separated by instantaneous frequencies. This decomposition provides a powerful method to look into the different processes behind a given time series data, and provides a way to separate short time-scale events from a general trend. We present a free software implementation of EMD, EEMD and CEEMDAN and give an overview of the EMD methodology and the algorithms used in the deco…
Establishing some order amongst exact approximations of MCMCs
2016
Exact approximations of Markov chain Monte Carlo (MCMC) algorithms are a general emerging class of sampling algorithms. One of the main ideas behind exact approximations consists of replacing intractable quantities required to run standard MCMC algorithms, such as the target probability density in a Metropolis-Hastings algorithm, with estimators. Perhaps surprisingly, such approximations lead to powerful algorithms which are exact in the sense that they are guaranteed to have correct limiting distributions. In this paper we discover a general framework which allows one to compare, or order, performance measures of two implementations of such algorithms. In particular, we establish an order …
Horvitz-Thompson estimators for functional data: asymptotic confidence bands and optimal allocation for stratified sampling
2009
When dealing with very large datasets of functional data, survey sampling approaches are useful in order to obtain estimators of simple functional quantities, without being obliged to store all the data. We propose here a Horvitz--Thompson estimator of the mean trajectory. In the context of a superpopulation framework, we prove under mild regularity conditions that we obtain uniformly consistent estimators of the mean function and of its variance function. With additional assumptions on the sampling design we state a functional Central Limit Theorem and deduce asymptotic confidence bands. Stratified sampling is studied in detail, and we also obtain a functional version of the usual optimal …