STATS 231 UC Davis

Review 1 O- AND O- NOTATION Review of oP and OP notation Wolfgang Polonik Department of Statistics University of California at Davis April 7, 2006 1 O- and o- notation an = o(1) little-oh-1 df an o as a . Let {an } be a sequence of real number

Review 1 L2 -PROJECTIONS Review of Conditional Expectations Wolfgang Polonik Department of Statistics University of California at Davis April 7, 2006 1 L2 -projections Let L2 denote the space of all random variables X (defined on a given probabi

Lecture notes; W. Polonik 1 RANK STATISTICS / RANK TESTS Lecture Notes, STA231C W. Polonik, Statistics, UC Davis 1 Rank Statistics / Rank Tests Let X1 , . . . , Xn iid F , with F continuous. If we assume that F has a pdf then this is denoted by f

STA231C, Spring 2006 Prof. W. Polonik HW # 2 1. Verify the recursive relationship n, m (u) = n1, m (u) + n, m1 (u n) with n,m (u) = # labeling of n+m distinct values into n X-values and m Y -values with exactly u pairs (X, Y ) satisfying X Y > 0

STA231C, Spring 2006 Prof. W. Polonik HW # 1 1. (Simple linear rank statistics) Let Rn = (R1 , . . . , Rn ) be a random permutation, i.e. P (Rn = rn ) = 1 n! for all rn Sn (= set of all n! permutations of {1, . . . , n}). Let a1 , . . . , an and

STA231C, Spring 2006 Prof. W. Polonik HW # 4 1. Let X1 , . . . , Xn , . . . iid F symmetric about 0, with EF (X 4 ) < , X n = 1 2 Sn = n1 n (Xi X n )2 , and dene i=1 (1) Tn 1 n n i=1 Xi , Xn = Sn and (2) Tn 1 = n n sign(Xi ). i=1 Let G(

STA231C, Spring 2006 Prof. W. Polonik HW # 3 1. Let X1 , . . . , Xn , . . . iid F with F continuous, and consider the U -statistic Wn = 2 1 i<j [ 1(Xi + Xj > 0) 2 ]. n(n1) (a) Find an expression for the variance of Wn by using Hoedings lemma. (Wha

STA 103 Practice Midterm II Solutions 1 (a) ^ ^ ^ ^ ^ ^ TRUE. Criterion is: choose estimator \"1 over \" 2 if mse( \"1 ) < mse( \" 2 ), otherwise choose \" 2 over \"1 . ^ For unbiased estimators, bias is equal to zero, so the criterion is equivalent to: c

Statistics 103 Winter 2008 Practice Midterm 1 The midterm is on Monday Jan 4, 3:10-4pm. Students whose last names start with A-H should go to 6 Wellman Hall. Others should go to 100 Hunt Hall. You can bring 1 page of handwritten notes. Please bring c