3,395 research outputs found
A representative sampling plan for auditing health insurance claims
A stratified sampling plan to audit health insurance claims is offered. The
stratification is by dollar amount of the claim. The plan is representative in
the sense that with high probability for each stratum, the difference in the
average dollar amount of the claim in the sample and the average dollar amount
in the population, is ``small.'' Several notions of ``small'' are presented.
The plan then yields a relatively small total sample size with the property
that the overall average dollar amount in the sample is close to the average
dollar amount in the population. Three different estimators and corresponding
lower confidence bounds for over (under) payments are studied.Comment: Published at http://dx.doi.org/10.1214/074921707000000094 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
The Interval Property in Multiple Testing of Pairwise Differences
The usual step-down and step-up multiple testing procedures most often lack
an important intuitive, practical, and theoretical property called the interval
property. In short, the interval property is simply that for an individual
hypothesis, among the several to be tested, the acceptance sections of relevant
statistics are intervals. Lack of the interval property is a serious
shortcoming. This shortcoming is demonstrated for testing various pairwise
comparisons in multinomial models, multivariate normal models and in
nonparametric models. Residual based stepwise multiple testing procedures that
do have the interval property are offered in all these cases.Comment: Published in at http://dx.doi.org/10.1214/11-STS372 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Characterization of Bayes procedures for multiple endpoint problems and inadmissibility of the step-up procedure
The problem of multiple endpoint testing for k endpoints is treated as a 2^k
finite action problem. The loss function chosen is a vector loss function
consisting of two components. The two components lead to a vector risk. One
component of the vector risk is the false rejection rate (FRR), that is, the
expected number of false rejections. The other component is the false
acceptance rate (FAR), that is, the expected number of acceptances for which
the corresponding null hypothesis is false. This loss function is more
stringent than the positive linear combination loss function of Lehmann [Ann.
Math. Statist. 28 (1957) 1-25] and Cohen and Sackrowitz [Ann. Statist. (2005)
33 126-144] in the sense that the class of admissible rules is larger for this
vector risk formulation than for the linear combination risk function. In other
words, fewer procedures are inadmissible for the vector risk formulation. The
statistical model assumed is that the vector of variables Z is multivariate
normal with mean vector \mu and known intraclass covariance matrix \Sigma. The
endpoint hypotheses are H_i:\mu_i=0 vs K_i:\mu_i>0, i=1,...,k. A
characterization of all symmetric Bayes procedures and their limits is
obtained. The characterization leads to a complete class theorem. The complete
class theorem is used to provide a useful necessary condition for admissibility
of a procedure. The main result is that the step-up multiple endpoint procedure
is shown to be inadmissible.Comment: Published at http://dx.doi.org/10.1214/009053604000000986 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Decision theory results for one-sided multiple comparison procedures
A resurgence of interest in multiple hypothesis testing has occurred in the
last decade. Motivated by studies in genomics, microarrays, DNA sequencing,
drug screening, clinical trials, bioassays, education and psychology,
statisticians have been devoting considerable research energy in an effort to
properly analyze multiple endpoint data. In response to new applications, new
criteria and new methodology, many ad hoc procedures have emerged. The
classical requirement has been to use procedures which control the strong
familywise error rate (FWE) at some predetermined level \alpha. That is, the
probability of any false rejection of a true null hypothesis should be less
than or equal to \alpha. Finding desirable and powerful multiple test
procedures is difficult under this requirement. One of the more recent ideas is
concerned with controlling the false discovery rate (FDR), that is, the
expected proportion of rejected hypotheses which are, in fact, true. Many
multiple test procedures do control the FDR. A much earlier approach to
multiple testing was formulated by Lehmann [Ann. Math. Statist. 23 (1952)
541-552 and 28 (1957) 1-25]. Lehmann's approach is decision theoretic and he
treats the multiple endpoints problem as a 2^k finite action problem when there
are k endpoints. This approach is appealing since unlike the FWE and FDR
criteria, the finite action approach pays attention to false acceptances as
well as false rejections.Comment: Published at http://dx.doi.org/10.1214/009053604000000968 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
The effects of changes in patterns of communication on the behaviors of problem-solving groups.
Thesis (Ph.D.)--Boston UniversityThe study of organizations in their natural state and problem-solving groups in the laboratory has received increased attention in recent years. Communication in particular has been the research concern of many investigators. Problems of changes in communication processes have been virtually ignored in experimental studies as well as in field investigations. The existence of disparate notions unsupported by empirical evidence about the effects of such changes provides somewhat confusing and conflicting references for making predictions.
There is, however, a growing body of evidence coming from laboratory experimentation about the relationship between communication networks and the performances of problem-solving groups in them. As well as providing such evidence, certain of these studies also make possible the establishment of operationally distinguishable communication structures and the introduction of rigorously controlled changes in them. [TRUNCATED
Cottonfield Dance
https://digitalcommons.library.umaine.edu/mmb-ps/3233/thumbnail.jp
Point and Confidence Estimation of a Common Mean and Recovery of Interblock Information
Consider the problem of estimating a common mean of two independent normal distributions, each with unknown variances. Note that the problem of recovery of interblock information in balanced incomplete blocks designs is such a problem. Suppose a random sample of size m is drawn from the first population and a random sample of size n is drawn from the second population. We first show that the sample mean of the first population can be improved on (with an unbiased estimator having smaller variance), provided m ≧ 2 and n ≧ 3. The method of proof is applicable to the recovery of information problem. For that problem, it is shown that interblock information could be used provided b ≧ 4. Furthermore for the case b = t = 3, or in the common mean problem, where n = 2, it is shown that the prescribed estimator does not offer improvement. Some of the results for the common mean problem are extended to the case of K means. Results similar to some of those obtained for point estimation, are also obtained for confidence estimation
Inadmissibility of Large Classes of Sequential Tests
Assume observations are from a subclass of a one parameter exponential family whose dominating measure is nonatomic. Consider a one-sided sequential testing problem where null and alternative parameter sets have one common boundary point. Let the risk function be a linear combination of probability of error and expected sample size. Our main result is that a sequential test is inadmissible if its continuation region has unbounded width in terms of the natural sufficient statistic. We apply this result to prove that weight function tests, with weight functions that contain the common boundary point in their support, are inadmissible. Furthermore any obstructive test is inadmissible, where obstructive means that the stopping time for the test does not have a finite moment generating function for some parameter point. Specific tests of the above type are cited
A new multiple testing method in the dependent case
The most popular multiple testing procedures are stepwise procedures based on
-values for individual test statistics. Included among these are the false
discovery rate (FDR) controlling procedures of Benjamini--Hochberg [J. Roy.
Statist. Soc. Ser. B 57 (1995) 289--300] and their offsprings. Even for models
that entail dependent data, -values based on marginal distributions are
used. Unlike such methods, the new method takes dependency into account at all
stages. Furthermore, the -value procedures often lack an intuitive convexity
property, which is needed for admissibility. Still further, the new methodology
is computationally feasible. If the number of tests is large and the proportion
of true alternatives is less than say 25 percent, simulations demonstrate a
clear preference for the new methodology. Applications are detailed for models
such as testing treatments against control (or any intraclass correlation
model), testing for change points and testing means when correlation is
successive.Comment: Published in at http://dx.doi.org/10.1214/08-AOS616 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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