735 research outputs found

### On robust and efficient designs for risk estimation in epidemiologic studies

We consider the design problem for the estimation of several scalar measures suggested in the epidemiological literature for comparing the success rate in two samples. The designs considered so far in the literature are local in the sense that they depend on the unknown probabilities of success in the two groups and are not necessarily robust with respect to their misspecification. A maximin approach is proposed to obtain efficient and robust designs for the estimation of the relative risk, attributable risk and odds ratio, whenever a range for the success rates can be specified by the experimenter. It is demonstrated that the designs obtained by this method are usually more efficient than the uniform design, which allocates equal sample sizes to the two groups. --two by two table,odds ratio,relativ risk,attributable risk,optimal design,efficient design

### Multiplier bootstrap of tail copulas with applications

For the problem of estimating lower tail and upper tail copulas, we propose
two bootstrap procedures for approximating the distribution of the
corresponding empirical tail copulas. The first method uses a multiplier
bootstrap of the empirical tail copula process and requires estimation of the
partial derivatives of the tail copula. The second method avoids this
estimation problem and uses multipliers in the two-dimensional empirical
distribution function and in the estimates of the marginal distributions. For
both multiplier bootstrap procedures, we prove consistency. For these
investigations, we demonstrate that the common assumption of the existence of
continuous partial derivatives in the the literature on tail copula estimation
is so restrictive, such that the tail copula corresponding to tail independence
is the only tail copula with this property. Moreover, we are able to solve this
problem and prove weak convergence of the empirical tail copula process under
nonrestrictive smoothness assumptions that are satisfied for many commonly used
models. These results are applied in several statistical problems, including
minimum distance estimation and goodness-of-fit testing.Comment: Published in at http://dx.doi.org/10.3150/12-BEJ425 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

### Optimal designs for comparing curves

We consider the optimal design problem for a comparison of two regression
curves, which is used to establish the similarity between the dose response
relationships of two groups. An optimal pair of designs minimizes the width of
the confidence band for the difference between the two regression functions.
Optimal design theory (equivalence theorems, efficiency bounds) is developed
for this non standard design problem and for some commonly used dose response
models optimal designs are found explicitly. The results are illustrated in
several examples modeling dose response relationships. It is demonstrated that
the optimal pair of designs for the comparison of the regression curves is not
the pair of the optimal designs for the individual models. In particular it is
shown that the use of the optimal designs proposed in this paper instead of
commonly used "non-optimal" designs yields a reduction of the width of the
confidence band by more than 50%.Comment: 27 pages, 3 figure

### Detecting relevant changes in time series models

Most of the literature on change-point analysis by means of hypothesis
testing considers hypotheses of the form H0 : \theta_1 = \theta_2 vs. H1 :
\theta_1 != \theta_2, where \theta_1 and \theta_2 denote parameters of the
process before and after a change point. This paper takes a different
perspective and investigates the null hypotheses of no relevant changes, i.e.
H0 : ||\theta_1 - \theta_2|| ? \leq \Delta?, where || \cdot || is an
appropriate norm. This formulation of the testing problem is motivated by the
fact that in many applications a modification of the statistical analysis might
not be necessary, if the difference between the parameters before and after the
change-point is small. A general approach to problems of this type is developed
which is based on the CUSUM principle. For the asymptotic analysis weak
convergence of the sequential empirical process has to be established under the
alternative of non-stationarity, and it is shown that the resulting test
statistic is asymptotically normal distributed. Several applications of the
methodology are given including tests for relevant changes in the mean,
variance, parameter in a linear regression model and distribution function
among others. The finite sample properties of the new tests are investigated by
means of a simulation study and illustrated by analyzing a data example from
economics.Comment: Keywords: change-point analysis, CUSUM, relevant changes, precise
hypotheses, strong mixing, weak convergence under the alternative AMS Subject
Classification: 62M10, 62F05, 62G1

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