9 research outputs found
Frequentist and Bayesian measures of confidence via multiscale bootstrap for testing three regions
A new computation method of frequentist -values and Bayesian posterior
probabilities based on the bootstrap probability is discussed for the
multivariate normal model with unknown expectation parameter vector. The null
hypothesis is represented as an arbitrary-shaped region. We introduce new
parametric models for the scaling-law of bootstrap probability so that the
multiscale bootstrap method, which was designed for one-sided test, can also
computes confidence measures of two-sided test, extending applicability to a
wider class of hypotheses. Parameter estimation is improved by the two-step
multiscale bootstrap and also by including higher-order terms. Model selection
is important not only as a motivating application of our method, but also as an
essential ingredient in the method. A compromise between frequentist and
Bayesian is attempted by showing that the Bayesian posterior probability with
an noninformative prior is interpreted as a frequentist -value of
``zero-sided'' test
The local power of the gradient test
The asymptotic expansion of the distribution of the gradient test statistic
is derived for a composite hypothesis under a sequence of Pitman alternative
hypotheses converging to the null hypothesis at rate , being the
sample size. Comparisons of the local powers of the gradient, likelihood ratio,
Wald and score tests reveal no uniform superiority property. The power
performance of all four criteria in one-parameter exponential family is
examined.Comment: To appear in the Annals of the Institute of Statistical Mathematics,
this http://www.ism.ac.jp/editsec/aism-e.htm
A note on the confidence properties of reference priors for the calibration model
Fieller-Creasy problem, Gibbs sampling, Jeffreys prior, inverse regression estimator, hpd regions, confidence interval, frequentist coverage, 62C10, 62F10, 62F15, 62F25,