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We observe an infinitely dimensional Gaussian random vector x = ξ + v
where
ξ is a sequence of standard Gaussian variables and v ∈ l2 is an
unknown
mean. We consider the hypothesis testing problem H0 : v = 0versus
alternatives for the sets
.
The sets Vε are lq-ellipsoids
of semi-axes ai = i-s R/ε with lp-ellipsoid
of semi-axes bi = i-r pε/ε removed or
similar Besov bodies Bq,t;s (R/ε) with Besov
bodies Bp,h;r (pε/ε) removed. Here
or
are the parameters which define the
sets Vε
for given radii...
Let U₀ be a random vector taking its values in a measurable space and having an unknown distribution P and let U₁,...,Uₙ and be independent, simple random samples from P of size n and m, respectively. Further, let be real-valued functions defined on the same space. Assuming that only the first sample is observed, we find a minimax predictor d⁰(n,U₁,...,Uₙ) of the vector with respect to a quadratic errors loss function.
A problem of minimax prediction for the multinomial and multivariate hypergeometric distribution is considered. A class of minimax predictors is determined for estimating linear combinations of the unknown parameter and the random variable having the multinomial or the multivariate hypergeometric distribution.
A class of minimax predictors of random variables with multinomial or multivariate hypergeometric distribution is determined in the case when the sample size is assumed to be a random variable with an unknown distribution. It is also proved that the usual predictors, which are minimax when the sample size is fixed, are not minimax, but they remain admissible when the sample size is an ancillary statistic with unknown distribution.
The problem of predicting integrals of stochastic processes is
considered. Linear estimators have been constructed by means of
samples at N discrete times for processes having a fixed
Hölderian regularity s > 0 in quadratic mean. It is known
that the rate of convergence of the mean squared error is of
order N-(2s+1). In the class of analytic processes
Hp, p ≥ 1, we show that among all estimators,
the linear ones are optimal. Moreover, using optimal coefficient
estimators derived through...
A minimax theorem is proved which contains a recent result of Pinelis and a version of the classical minimax theorem of Ky Fan as special cases. Some applications to the theory of convex metric spaces (farthest points, rendez-vous value) are presented.
Disparities of discrete distributions are introduced as a natural and useful extension of the information-theoretic divergences. The minimum disparity point estimators are studied in regular discrete models with i.i.d. observations and their asymptotic efficiency of the first order, in the sense of Rao, is proved. These estimators are applied to continuous models with i.i.d. observations when the observation space is quantized by fixed points, or at random, by the sample quantiles of fixed orders....
We study a minimum distance estimator in -norm for a class ofnonlinear hyperbolic stochastic partial differential equations, driven by atwo-parameter white noise. The consistency and asymptotic normality of thisestimator are established under some regularity conditions on thecoefficients. Our results are applied to the two-parameterOrnstein-Uhlenbeck process.
Currently displaying 101 –
120 of
253