caa a22 4500 477062776 CHVBK 20180405111405.0 cr unu---uuuuu 170330e19960301xx s 000 0 eng 10.1007/BF00049285 doi (NATIONALLICENCE)springer-10.1007/BF00049285 Beran Rudolf Department of Statistics, University of California, 94720-3860, Berkeley, CA, U.S.A. aut Confidence sets centered at C p -estimators [Elektronische Daten] [Rudolf Beran] Suppose X n is an observation, or average of observations, on a discretized signal ξ n that is measured at n time points. The random vector X n has a N(ξ n , σ2 n I) distribution, the mean and variance being unknown. Under squared error loss, the unbiased estimator X n of ξ n can be improved by variable-selection. Consider the candidate estimator ξ n (A) whose i-th component equals the i-th component of X n whenever i/(n+1) lies in A and vanishes otherwise. Allow the set A to range over a large collection of possibilities. A C p -estimator is a candidate estimator that minimizes estimated quadratic loss over A. This paper constructs confidence sets that are centered at a C p -estimator, have correct asymptotic coverage probabiligy for ξ n , and are geometrically smaller than or equal to the competing confidence balls centered at X n . The asymptotics are locally uniform in the parameters (ξ n , σ2 n ). The results illustrate an approach to inference after variable-selection. The Institute of Statistical Mathematics, 1996 Variable-selection nationallicence coverage probability nationallicence geometrical loss nationallicence locally uniform asymptotics nationallicence Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 48/1(1996-03-01), 1-15 0020-3157 48:1<1 1996 48 10463 https://doi.org/10.1007/BF00049285 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00049285 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Beran Rudolf Department of Statistics, University of California, 94720-3860, Berkeley, CA, U.S.A aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 48/1(1996-03-01), 1-15 0020-3157 48:1<1 1996 48 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer