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1.
Maria Kozlowska Ryszard Walkowiak 《Annals of the Institute of Statistical Mathematics》1990,42(3):597-602
In this paper we consider experimental settings where treatments are being tested in b
1 rows and b
2 columns of sizes k
1i
and k
2j
, respectively, i=1,2,..., b
1, j=1,2,..., b
2. Some sufficient conditions for designs to be E-optimal in these classes are derived and some necessary and sufficient conditions for the E-optimality of some special classes of row and column designs are presented. Examples are also given to illustrate this theory. 相似文献
2.
Mike Jacroux 《Annals of the Institute of Statistical Mathematics》1985,37(1):557-566
Summary It is well known that in experimental settings wherev treatments are being tested inb blocks of sizek, a group divisible design having parametersλ
2=λ2+1 and whose correspondingC-matrix has maximal trace is both E and MV-optimal among all possible competing designs. In this paper, we show that under
certain conditions, the E and MV-optimal group divisible block designs mentioned in the previous sentence can be used to construct
E and MV-optimal row-column designs to handle experimental situations in which heterogeneity is to be eliminated in two directions
and wherev treatments are being tested inb columns andk rows. Examples are given to illustrate how the results obtained can be applied.
Research sponsored in part by National Science Foundation Grant No. DMS-8401943. 相似文献
3.
Summary In this paper we consider experimental situations in which ν treatments are to be tested inb blocks whereb
i
blocks containk
i
experimental units,i=1,...,p, k
1<k
2<...<k
p
. The idea of a group divisible (GD) design is extended to that of a group divisible design with unequal block sizes (GDUB
design) and then a number of results concerning the E- and MV-optimality of GD designs are generalized to the case of GDUB
designs. 相似文献
4.
Liu Huimei 《Annals of the Institute of Statistical Mathematics》2000,52(1):15-27
Let Xhave a multivariate, p-dimensional normal distribution (p 2) with unknown mean and known, nonsingular covariance . Consider testing H
0 : b
i 0, for some i = 1,..., k, and b
i 0, for some i = 1,..., k, versus H
1 : b
i < 0, for all i = 1,..., k, or b
i
< 0, for all i = 1,..., k, where b
1,..., b
k
, k 2, are known vectors that define the hypotheses and suppose that for each i = 1,..., k there is an j {1,..., k} (j will depend on i) such that b
i b
j 0. For any 0 < < 1/2. We construct a test that has the same size as the likelihood ratio test (LRT) and is uniformly more powerful than the LRT. The proposed test is an intersection-union test. We apply the result to compare linear regression functions. 相似文献
5.
In this study, we have found upper and lower bounds for the spectral norm of Cauchy–Toeplitz and Cauchy–Hankel matrices in the forms Tn=[1/(a+(i−j)b)]ni,j=1, Hn=[1/(a+(i+j)b)]ni,j=1. 相似文献
6.
John C. Clements 《Numerische Mathematik》1992,63(1):165-171
Summary AC
2 parametric rational cubic interpolantr(t)=x(t)
i+y(t)
j,t[t
1,t
n] to data S={(xj, yj)|j=1,...,n} is defined in terms of non-negative tension parameters
j
,j=1,...,n–1. LetP be the polygonal line defined by the directed line segments joining the points (x
j
,y
j
),t=1,...,n. Sufficient conditions are derived which ensure thatr(t) is a strictly convex function on strictly left/right winding polygonal line segmentsP. It is then proved that there always exist
j
,j=1,...,n–1 for whichr(t) preserves the local left/righ winding properties of any polygonal lineP. An example application is discussed.This research was supported in part by the natural Sciences and Engineering Research Council of Canada. 相似文献
7.
P. Vellaisamy 《Annals of the Institute of Statistical Mathematics》1992,44(3):551-562
Suppose a subset of populations is selected from the given k gamma G(
i,p
) (i = 1,2,...,k)populations, using Gupta's rule (1963, Ann. Inst. Statist. Math., 14, 199–216). The problem of estimating the average worth of the selected subset is first considered. The natural estimator is shown to be positively biased and the UMVUE is obtained using Robbins' UV method of estimation (1988, Statistical Decision Theory and Related Topics IV, Vol. 1 (eds. S. S. Gupta and J. O. Berger), 265–270, Springer, New York). A class of estimators that dominate the natural estimator for an arbitrary k is derived. Similar results are observed for the simultaneous estimation of the selected subset. 相似文献
8.
A packing array is a b × k array, A with entriesa
i,j
from a g-ary alphabet such that given any two columns,i and j, and for all ordered pairs of elements from a g-ary alphabet,(g
1, g
2), there is at most one row, r, such thata
r,i
= g
1 anda
r,j
= g
2. Further, there is a set of at leastn rows that pairwise differ in each column: they are disjoint. A central question is to determine, forgiven g, k and n, the maximum possible b. We examine the implications whenn is close to g. We give a brief analysis of the case n = g and showthat 2g rows is always achievable whenever more than g exist. We give an upper bound derivedfrom design packing numbers when n = g – 1. When g + 1 k then this bound is always at least as good as the modified Plotkin bound of [12]. When theassociated packing has as many points as blocks and has reasonably uniform replication numbers, we show thatthis bound is tight. In particular, finite geometries imply the existence of a family of optimal or near optimalpacking arrays. When no projective plane exists we present similarly strong results. This article completelydetermines the packing numbers, D(v, k, 1), when
. 相似文献
9.
Ewaryst Rafajłowicz Wojciech Myszka 《Annals of the Institute of Statistical Mathematics》1988,40(4):821-827
In the note Hoel's result (1965, Ann. Math. Statist., 36, 1097–1106) is generalized to a large family of experimental design optimality criterions. Sufficient conditions for optimality criterion are given, which ensure existence of the optimum experimental design measure which is a product of design measures on lower dimensional domains. 相似文献
10.
S. M. Ertel 《Mathematical Notes》1995,58(1):762-769
Forn pointsA
i
,i=1, 2, ...,n, in Euclidean space ℝ
m
, the distance matrix is defined as a matrix of the form D=(D
i
,j)
i
,j=1,...,n, where theD
i
,j are the distances between the pointsA
i
andA
j
. Two configurations of pointsA
i
,i=1, 2,...,n, are considered. These are the configurations of points all lying on a circle or on a line and of points at the vertices
of anm-dimensional cube. In the first case, the inverse matrix is obtained in explicit form. In the second case, it is shown that
the complete set of eigenvectors is composed of the columns of the Hadamard matrix of appropriate order. Using the fact that
distance matrices in Euclidean space are nondegenerate, several inequalities are derived for solving the system of linear
equations whose matrix is a given distance matrix.
Translated fromMatematicheskie Zametki, Vol. 58, No. 1, pp. 127–138, July, 1995. 相似文献
11.
Marco Buratti 《组合设计杂志》1999,7(6):406-425
Let X =((x1,1,x1,2,…,x1,k),(x2,1,x2,2,…,x2,k),…,(xt,1,xt,2,…,xt,k)) be a family of t multisets of size k defined on an additive group G. We say that X is a t-(G,k,μ) strong difference family (SDF) if the list of differences (xh,i-xh,j∣h=1,…,t;i≠ j) covers all of G exactly μ times. If a SDF consists of a single multiset X, we simply say that X is a (G,k,μ) difference multiset. After giving some constructions for SDF's, we show that they allow us to obtain a very useful method for constructing regular group divisible designs and regular (or 1-rotational) balanced incomplete block designs. In particular cases this construction method has been implicitly used by many authors, but strangely, a systematic treatment seems to be lacking. Among the main consequences of our research, we find new series of regular BIBD's and new series of 1-rotational (in many cases resovable) BIBD's. 相似文献
12.
William J. Martin 《组合设计杂志》1998,6(2):151-163
Let Vi (i = 1, 2) be a set of size vi. Let D be a collection of ordered pairs (b1, b2) where bi is a ki-element subset of Vi. We say that D is a mixed t-design if there exist constants λ (j,j2), (0 ≤ ji ≤ ki, j1 + j2 ≤ t) such that, for every choice of a j1-element subset S1 of V1 and every choice of a j2-element subset S2 of V2, there exist exactly λ(j1,j2) ordered pairs (b1, b2) in D satisfying S1 ⊆ b1 and S2 ⊆ b2. In W. J. Martin [Designs in product association schemes, submitted for publication], Delsarte's theory of designs in association schemes is extended to products of Q-polynomial association schemes. Mixed t-designs arise as a particularly interesting case. These include symmetric designs with a distinguished block and α-resolvable balanced incomplete block designs as examples. The theory in the above-mentioned paper yields results on mixed t-designs analogous to those known for ordinary t-designs, such as the Ray-Chaudhuri/Wilson bound. For example, the analogue of Fisher's inequality gives |D| ≥ v1 + v2 − 1 for mixed 2-designs with Bose's condition on resolvable designs as a special case. Partial results are obtained toward a classification of those mixed 2-designs D with |D| = v1 + v2 − 1. The central result of this article is Theorem 3.1, an analogue of the Assmus–Mattson theorem which allows us to construct mixed (t + 1 − s)-designs from any t-design with s distinct block intersection numbers. © 1998 John Wiley & Sons, Inc. J Combin Designs 6:151–163, 1998 相似文献
13.
Zoltán Füredi 《Combinatorica》1991,11(1):75-79
Let L
k
be the graph formed by the lowest three levels of the Boolean lattice B
k
, i.e.,V(L
k
)={0, 1,...,k, 12, 13,..., (k–1)k} and 0is connected toi for all 1ik, andij is connected toi andj (1i<jk).It is proved that if a graph G overn vertices has at leastk
3/2
n
3/2 edges, then it contains a copy of L
k
.Research supported in part by the Hungarian National Science Foundation under Grant No. 1812 相似文献
14.
G. R. Wood 《Journal of Optimization Theory and Applications》1988,58(2):331-350
A two-dimensional analogue of the well-known bisection method for root finding is presented in order to solve the following problem, related to the dispersion function of a set of random variables: given distribution functionsF
1,...,F
n and a probabilityp, find an interval [a,b] of minimum width such thatF
i(b)–F
i(a
–)p, fori=1,...,n.The author wishes to thank Dr. I. D. Coope, for helpful advice offered during the preparation of this paper, and the referee, whose comments contributed to a clearer presentation. 相似文献
15.
Pankaj K. Agarwal Sandeep Sen 《Journal of Algorithms in Cognition, Informatics and Logic》1996,20(3):581-601
Anm×nmatrix
=(ai, j), 1≤i≤mand 1≤j≤n, is called atotally monotonematrix if for alli1, i2, j1, j2, satisfying 1≤i1<i2≤m, 1≤j1<j2≤n.[formula]We present an[formula]time algorithm to select thekth smallest item from anm×ntotally monotone matrix for anyk≤mn. This is the first subquadratic algorithm for selecting an item from a totally monotone matrix. Our method also yields an algorithm of the same time complexity for ageneralized row-selection problemin monotone matrices. Given a setS={p1,…, pn} ofnpoints in convex position and a vectork={k1,…, kn}, we also present anO(n4/3logc n) algorithm to compute thekith nearest neighbor ofpifor everyi≤n; herecis an appropriate constant. This algorithm is considerably faster than the one based on a row-selection algorithm for monotone matrices. If the points ofSare arbitrary, then thekith nearest neighbor ofpi, for alli≤n, can be computed in timeO(n7/5 logc n), which also improves upon the previously best-known result. 相似文献
16.
Let B denote the set of values of b for which there exists a block design with b blocks and for k3, let Bk denote the subset of B determined by the designs with block size k. We present some information about B and the sets Bk. In particular, we discuss, for certain integers h, the question as to whether there exist integers k and k′ such that the equation b′=b+h has infinitely many solutions b,b′ satisfying bBk and b′Bk′. The study is restricted to the case λ=1. 相似文献
17.
In this note we consider band- or tridiagonal-matrices of orderk whose elements above, on, and below the diagonal are denoted byb
i
,a
i,c
i
. In the periodic case, i.e.b
i+m
=b
i
etc., we derive fork=nm andk=nm–1 formulas for the characteristic polynomial and the eigenvectors under the assumption that
i=1 In the latter case it is shown that the characteristic polynomial is divisible by them–1-th minor, as was already observed byRósa. We also give estimations for the number of real roots and an application to Fibonacci numbers. 相似文献
18.
Anm-consecutive-k-out-of-n:F system is a system ofn linearly arranged components which fails if and only if at leastm non-overlapping sequences ofk components fail, when there arek distinct components with failure probabilitiesq
i
fori=1,...,k and where the failure probability of thej-th component (j=rk+i (1 ≤i ≤k) isq
j
=q
i
, we call this system by anm-consecutive-k-out-of-n:F system with cycle (or period)k. In this paper we give a formula of the failure probability ofm-consecutive-k-out-of-n:F system with cyclek via the failure probability of consecutive-k-out-of-n:F system. 相似文献
19.
D. Fisher 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1989,40(1):39-50
Generalized load vectorsp and edge load vectorsF are denned in terms of the body force and surface on a shell. Necessary and sufficient conditions are derived forp andF, and therefore the body force and the surface force, to be conservative. It is shown for example thatp must satisfyp
i=P
ijk
q
j,1
q
k,2+Q
ij
1
q
j,2–Q
ij
2
q
j,1+R
i whereq is the generalized position vector andP
ijk, Qi,j
1 and Qij
2 are skew tensors.The case of hydrostatic pressure is examined in detail.This work was supported in part by NSF grant MSM 8618657. 相似文献
20.
E. W. Lambeck 《Designs, Codes and Cryptography》1991,1(3):261-266
Let be a distance regular graph with intersection array b
0, b
1,..., b
d–1; c
1,..., c
d. It is shown that in some cases (c
i–1, a
i–1, b
i–1) = (c
1, a
1, b
1)and (c
2i–1, a
2i–1, b
2i–1) imply k 2b
i + 1. As a corollary all distance regular graphs of diameter d = 3i – 1 with b
i = 1 and k > 2 are determined. 相似文献