Minimax Estimation of a Constrained Poisson Vector
نویسندگان
چکیده
منابع مشابه
Minimax regression estimation for Poisson coprocess
For a Poisson point process X , Itô’s famous chaos expansion implies that every square integrable regression function r with covariate X can be decomposed as a sum of multiple stochastic integrals called chaos. In this paper, we consider the case where r can be decomposed as a sum of δ chaos. In the spirit of Cadre and Truquet (2015), we introduce a semiparametric estimate of r based on i.i.d. ...
متن کاملMinimax Estimation of a Mean Vector
K E Y W O R D S AND PHRASES Minimax decision rule; squared error loss; Dirichlet process; compact sets; Bayes rules; isotonic regression. l . INTRODUCTION In an often cited paper, BOHLMANN (1976) has considered linear minimax estimators for the mean of a univariate distribution in a nonparametr ic setting under squared error loss. To be precise, BOHLMANN assumes that Fo(x ) is a family of C D F...
متن کاملOn minimax estimation of a sparse normal mean vector
Mallows has conjectured that among distributions which are Gaussian but for occasional contamination by additive noise, the one having least Fisher information has (two-sided) geometric contamination. A very similar problem arises in estimation of a non-negative vector parameter in Gaussian white noise when it is known also that most, i.e. (1 − ǫ), components are zero. We provide a partial asym...
متن کاملConstrained forms of statistical minimax :
A fundamental quantity in statistical decision theory is the notion of the minimax risk as5 sociated with an estimation problem. It is based on a saddlepoint problem, in which nature plays the 6 role of adversary in choosing the underlying problem instance, and the statistician seeks an estimator 7 with good properties uniformly over a class of problem instances. We argue that in many modern 8 ...
متن کاملMinimax Estimation of a Variance
The nonparametric problem of estimating a variance based on a sample of size n from a univariate distribution which has a known bounded range but is otherwise arbitrary is treated. For squared error loss, a certain linear function of the sample variance is seen to be minimax for each n from 2 through 13, except n = 4. For squared error loss weighted by the reciprocal of the variance, a constant...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 1992
ISSN: 0090-5364
DOI: 10.1214/aos/1176348658