ABSTRACT
"Contains over 2500 equations and exhaustively covers not only nonparametrics but also parametric, semiparametric, frequentist, Bayesian, bootstrap, adaptive, univariate, and multivariate statistical methods, as well as practical uses of Markov chain models."
TABLE OF CONTENTS
chapter |11 pages
< is approximately (complex) normal for each Under station-
Y,, the variance of Eq. (4.2) is
chapter 2|2 pages
Modeling and Inference for Periodically Correlated Time Series
Robert B. Lund and Jslnrar V. Ba.1·mra
chapter |7 pages
... dand
... d ... -d". KLl'h-l cos(jwk) /j have slow decay with oscillations depending on the
chapter |1 pages
= is carried out using a Lagrange multiplier test. The
exp(iwt)f(w) dw. K(s, t) K(s, t) exp( t=-x
chapter |6 pages
Lxt+IK,(XI-
K"(-) /z- K"(X,-x) _ {M. ( )}2 (X, - z lying in a neighborhood of x. Here Mii) (x) denotes the ith derivative .... 'Mr)(x)V r, (n- (X;+k-
chapter |1 pages
= -f'"(k)-
f'"(k)=[ChT(u,v)](u,v= l, ChT(-h + I,k)J', a"(O) chT(u,v) N-l LXI-u+lxt-v+l·
chapter 7|11 pages
Nonlinear Estimation for Time Series Observed on Arrays
Robert H. Shumway, Sung-Etm Kim, and Robert R. Blandford
chapter 8|5 pages
Some Contributions to Multivariate Nonlinear Time Series and to Bilinear Models
T. Subba Rao and W. K. Wong
chapter 9|7 pages
Optimal Testing for Semi-Parametric AR Models-From Gaussian Lagrange Multipliers to Autoregression Rank Scores and Adaptive Tests
Marc Hallin and Bas J. M. Werker
chapter 10|3 pages
Statistical Analysis Based on Functionals of Nonparametric Spectral Density Estimators
Masanobti Taniguchi
chapter |1 pages
= ... ,X = ...
G(j) = {Gah(j); a= ... ,m, b ... ,r}'s trG(j)QG(j)' < oo. Then the process
chapter |5 pages
f + and( +
g is ( M qf, q'l q.f' f, gf, and ,ud)', is differentiable, /ii X ( li) by ( ·). h-d-+ j/i 1/
chapter 11|2 pages
Efficient Estimation in a Semiparametric Additive Regression Model with ARMA Errors
Anton Schick
chapter |7 pages
1, l) into
f, c G, (r,, fh, G,.) a fh(x) d>.(x) is continuous at 0 and there exists a
chapter |1 pages
= and assume that 8 is smooth in the following sense.
K, the tangent space, and a linear map D: K H, rdecreases to 0 pointwise and is 1r-integrable for large This version d:;k
chapter |1 pages
With£'= p' jp,
Q= is Qnk(x, dy) = Pnb(Y- Q(x, dy)( 1 -axe' o:x)) ). (Dk)(x,y) = -ax£'(y- o:x). Eb(c) +op(i).
chapter |16 pages
.f. Suppose.{ is
dth derivative_/") L(R). Assume that there exists D2 0 and 2 0, 0 d such
chapter 14|10 pages
Minimum Distance and Nonparametric Dispersion Functions
Omer Oztti'rk, Thomas P. Hettmansperger, and Jz'irg Hasler
chapter |3 pages
={X;-
JL(F)}ja-(F) and r is the expected value of e{F(e)- K0(e). ../ii( (F)_ foEFofo(t)t2 Q(F) = 4a-(F)
chapter |6 pages
'IE (0, 1).
(j, Z1(R)) - (j,Z(R))'s are defined by Eqns (2.20) and (2.16), ZJ R), i = 0, ± ±2, ... , of ZR) are inde- ti1R(G)- 8satisfying Eq. (2.24) and let m = [n1],
chapter |1 pages
= a > 0. Then, as
Jli<T(t(l- Proof The proof is, e.g., in Csorgo and Horvath (1993). P(j21og!!_ Proof Assertion (i) is the Erdos-Darling theorem, for the proof see, e.g., sLsi
chapter |5 pages
of Theorem 2.4. The proof follows the lines of the proof of
k-G+ Gjn-+ 0. of Theorem 2.6. The proof is omitted since the assertions can be
chapter 0|1 pages
, the support of 9. That
. Then, partition Binto Band Bot. partition B Band E , etc. In this way a tree-like structure {Bo,Bl,Boo,Bol,B ,Bool•· .. } by II. In order to complete the Be(o:o,o
chapter |2 pages
p "'.f(p) G G
'ell such that = 'T};- g(t) increases in t and g(t) arises as a r's connect to g, the q's connect to the underlying
chapter |11 pages
of the event for the ith individual in the interval
g(t) g(t) arises by integrating ((J(s))- g(t) defined by Eq. (9) is called an extended gamma g is again an
chapter 18|4 pages
Consistency Issues in Bayesian Nonparametrics
S. Ghosal, J. K. Ghosh, and R. V. Ramamoorthi
chapter |1 pages
Jf. The expected value under II, Err(P) is the prob-
P(B) P(B)II(dP). We will refer to the expec- Pin any of the above senses, then the Bayes estimate converges to Po in P(i) = 1}. Let Pbe in (j) } Jl(x) ensures two things: P in the sense, for any c
chapter |17 pages
P"' PT(T, and given P if XX.•• Xare iid P, then the poster-
a:,+ 2:ak" Jfo logj
chapter 19|14 pages
Breakdown Theory for Estimators Based on Bootstrap and Other Resampling Schemes
Gutti Jogesh Babu
chapter 20|3 pages
On Second-Order Properties of the Stationary Bootstrap Method for Studentized Statistics
S. N. Lahiri
chapter |2 pages
y'ii;(H(Xi,)-H(X,J)/iw
L;;:,,(at'V'L- at'Vi,a1,'Vh, of d x I vector of jax;' a:r)'. For a =D"H(X )/o!, a E (71..+)".
chapter |2 pages
> 0 such that for all
(np)- P(K (np) 1ogn. Then, by the definition of K and the formula for the f(t) r)/n] r/ + of Theorem 3.1. To prove the theorem, it is enough to show that
chapter 21|5 pages
Convergence to Equilibrium of Random Dynamical Systems Generated by liD Monotone Maps, with Applications to Economics
Rabi Bhattacharya and Mukul Majumdar
chapter |1 pages
oo, x] = tt(0) = 0 = (v o y-
(1-b)d(ft,v) d(T*"tt, T*"v) d(T*N (T*(Il-N) ft), T*N (T*(Il-N)v)) Ej2.
chapter |2 pages
p.d.f.f of a real-valued r.v. X is said to be a Polya frequency function of
(PFif, for all x PFif log ,xk(k>l) ..• Xbe a random sample without replacement
chapter |5 pages
> c > n
'n-'. F(x)]ja(x)}, n I, converges in distribu- f(x) of X J,,(x) f(x) a.s. on I, and also I, and x E J]----+ 0 a.s., where J is any compact subset of K(lx-
chapter 24|19 pages
Second-Order Information Loss Due to Nuisance Parameters: A Simple Measure
Bruce G. Lindsay and Richard Waterman
chapter 1966|1 pages
of multivariate multi-sample rank-order tests. Sankhya
of dispersion matrices. Sankhya, Series A, 30, 1-22. Co-
chapter |2 pages
of rank order tests for a genera/linear hypothesis. The Annals of
of location parameters in the multivariate one-
chapter |4 pages
of convergence in the central limit theorem for signed rank
of convergence to asymptotic normalityfor generalized linear
