ABSTRACT

This monograph of carefully collected articles reviews recent developments in theoretical and applied statistical science, highlights current noteworthy results and illustrates their applications; and points out possible new directions to pursue. With its enlightening account of statistical discoveries and its numerous figures and tables, Probabili

part |2 pages

PART I APPROXIMATION, O UNDS, AND NEQUALITIES

chapter |1 pages

Nonu niform Bomn ds in Pro ba

chapter |2 pages

H.Y . Clien

= 0) = = 1, ....n . W = Er=, = W E,"=, 2 + 1) = h(w) = . .}.

chapter |4 pages

Y. Chen

5 C" xp:[4(1 X-')Ejh(Z = 1,

chapter |1 pages

Y. C1w1

chapter |8 pages

Conclusion

chapter |5 pages

; the finict,ion

IX,,

chapter |17 pages

= < <

1 5 ,l 5 n,

chapter 3|2 pages

Applications of Compound Poisson Approximation .-I. U . Rurhotrr, 0. C:hr!j.scsaplaino~u, a ~ ~ d E:. Vu,qgclato~u

E. Vaggelatou 5 EOMOk7) + ElMl(L7) > 0 and for all bounded g N R. where ML(g) := + 1) &v(P,Q ) :=

chapter |3 pages

Ct2 ,

chapter |7 pages

< 2,1r~n,(4k 3)(1n

EI/17

chapter C|3 pages

l,rIM,C

:; S,

chapter 0|3 pages

E.

D. P.

chapter |5 pages

Colnpound Poisson Approximation for Sums of Depe12dent Raadorn Variables

..., are "weakly" dependent. S1lcl.1 problems

chapter 1|4 pages

)’. Markos V.

chapter Xi|2 pages

,, >

chapter X|2 pages

,t ,

, -- .;

chapter |7 pages

( I ( )

+ C:?l this = P(x::~-l

chapter |4 pages

RHS as

chapter |6 pages

Ukified Variance ounds and a

chapter |7 pages

= ,,,

chapter X|6 pages

P apatiatoi

chapter |4 pages

Probability Inequalities

< Let t > 0. Using Hoeffding's

chapter |1 pages

= 1, =

< p < 1. Then as a special

chapter 11|4 pages

1

. , X . , oJ'(1,. . ,n). . Following the

chapter |11 pages

PART PROBABILITY STOCHASTIC

chapter |10 pages

H. Peria and Lai

chapter |4 pages

H.c le la Pcrla and Tze L

a := < > 0 such that bm/I'(I- a > 6. Sincc lirn,,, l/I'(l > 1; > rjS) 5

chapter 11|7 pages

la Pena a

= m,

chapter |1 pages

Process

+ . =

chapter |2 pages

. S)

(fi, ,m ) (fi,. (6:m.

chapter |5 pages

for Boundary

. are independent, identically $?kl

chapter |3 pages

> 0, > a

chapter |2 pages

S.K orolyuk and K. Limnios

2 defined by the generator 1 ,5 2 which is uniformly ergodic in every class X 5 5 and PI &(z.

chapter |9 pages

S .K orolyuk K. Limnios

mJ2n= verage of SLOC > 0,g iven (9.2.3), in

chapter |7 pages

ueues with e termirrrist

chapter |16 pages

+ 1,

(2-tS (?],) l, = 0 > 1, n-1. > 1). By

chapter 1|2 pages

' a,s.siliou

chapter |13 pages

H.T sakiriclou +

+ + s + m%, + m,,-] + m,.)] -t o (m,. + m,., = n.

chapter X|13 pages

R ao, and h.

< cl,. (Oiie of the

chapter I|3 pages

,l).

chapter |17 pages

PPQ, thc

chapter |4 pages

Refinements of nctior~ls

. and let the arithmetic, geometric and

chapter |23 pages

MO,-

chapter |2 pages

First Bivariate Skew

chapter |3 pages

= and =

chapter |14 pages

n the Posterior ments for. and

chapter |3 pages

tions of

chapter |8 pages

nnI2/r( F

((1,+

chapter 1|5 pages

-cvhe~~

chapter |3 pages

= l,. . ,

> > 0, 1, , . , P,.

chapter |4 pages

If. Jlathai

0731, , E(O$,,a)b ove. Also ob-

chapter x|1 pages

("-")V,,, is of the form

= 2, = 1,

chapter |2 pages

SERIES, An,

NON-

chapter |7 pages

Coin tegration of Econon~ic

CT Rcgrcssiorr rnotlels and sim~dta.neouse quations nrodcls

chapter |1 pages

Yo.Y1,. .YT. B

Yt-l. 20.6 Nonstationary Models 1. This is the case when B Yt=Yt-l+Z,. Yo = &YtYi= =

chapter |1 pages

AYLh as no trend, the tiifk~.criciui?o; p

1, i l, . . , p. LT7e ca.

chapter l|10 pages

/ L

, are the solutions to

chapter |8 pages

T. Since the process {XT,,

clr and are real valued ant1 positive scql~criccsa pproitchi~~zegr o

chapter |9 pages

j(.)

> C; = 1/(1 = Ho =

chapter |8 pages

Note

= 0. = 0 C(L1) M f~ M = 0.

chapter |14 pages

[S :

P) is continiloi~sm d P P+ )-(2'/ap3 ~ = l,

part |2 pages

PART V INFERENCE APPLICATIONS

chapter 24|2 pages

Extensions of

Isoperirn e tric

chapter |2 pages

Error

chapter |8 pages

Allocation of

chapter |9 pages

ePositive

phrases Croup testing. IIH procedure, efficiency, ro-

chapter |14 pages

+ [j)

= .80, E{Y;) a

chapter |2 pages

P.G .

l)(f + .. , = 4.

chapter |2 pages

M.M athai P.

chapter |1 pages

P.G . -2loschopoulos

= (sI1 l~l+Y.

chapter |3 pages

on~in;~tloRne sults

(Irl',

chapter |5 pages

d;(r)

chapter |28 pages

if

1Cb =
By(0>

chapter 8|3 pages

De Vcstnx, R. D. mtl Kriegcr,

15. Marl&ou, M., Rasu,

chapter 31|7 pages

Multipolishing Large Two-

W. Tukey

chapter |2 pages

W. Tukey

chapter |7 pages

References

chapter |14 pages

n Distances an easures of

chapter |4 pages

ulae for Pro

chapter |9 pages

= -+

chapter |7 pages

(C,"Cl

chapter 34|2 pages

Estimation of Cycling Eflect on Reliability

R and let TTc be the z(.). = P{T,(

chapter |19 pages

meet on Rc1iel)ilit.y

chapter |1 pages

B.S ackrowitz

B,z ). < B1 B; > B2

chapter |6 pages

THCORE~I

A B,iyei tcst is = Xll+

chapter |8 pages

F. Neuts

chapter |35 pages

on Functional

chapter l|17 pages

,., 419, 427. 430.

M, 10-12, 121, 145