Given data from a spherical Gaussian distribution with unknown mean vector θ, estimates of quadratic functionals are constructed by thresholding. Mean squared error bounds are derived via a comparison with those already available for a suitable noncentral χ variate. By way of illustration, the resulting inequalities are used to yield an optimal rate adaptivity result for estimation of integrate...

BACKGROUND Genetic determinants of blood pressure (BP) responses to the cold pressor test (CPT), a phenotype associated with risk of hypertension and cardiovascular disease has not been well studied. METHODS We examined the heritability of BP response to CPT in 1,994 subjects from 627 families in rural north China. BP was measured before and at 0, 1, 2, and 4 min after the participants immers...

In this paper, a new bivariate absolutely continuous probability distribution is introduced. The distribution, which called the unit-sinh-normal (BVUSHN) arises by applying transformation to Birnbaum–Saunders (BVBS). main properties of proposal are studied in detail. addition, from BVUSHN regression model also For both and respective associated model, parameter estimation conducted classical ap...

Study of the bivariate normal distribution raises the full range of issues involving objective Bayesian inference, including the different types of objective priors (e.g., Jeffreys, invariant, reference, matching), the different modes of inference (e.g., Bayesian, frequentist, fiducial) and the criteria involved in deciding on optimal objective priors (e.g., ease of computation, frequentist per...

We consider a class of semiparametric normal transformation models for right censored bivariate failure times. Nonparametric hazard rate models are transformed to a standard normal model and a joint normal distribution is assumed for the bivariate vector of transformed variates. A semiparametric maximum likelihood estimation procedure is developed for estimating the marginal survival distributi...

We provide a new characterization of the Bivariate normal-Wishart distribution. Let ~ x = fx 1 x 2 g have a non-singular Bivariate normal pdf f(~ x) = N(~ W) with unknown mean vector ~ and unknown precision matrix W. L e t f(~ x) = f(x 1)f(x 2 jx 1) where f(x 1) = N(m 1 1=v 1) and f(x 2 jx 1) = N(m 2j1 +b 12 x 1 1=v 2j1). Similarly, deene fv 2 v 1j2 b 21 m 2 m 1j2 g using the factorization f(~ ...