共查询到20条相似文献,搜索用时 15 毫秒
1.
Dr. Herbert Basler 《Metrika》1987,34(1):287-322
Summary The so-called Exact Test of R. A. Fisher for comparing two probabilitiesp
1 andp
2 in a Fourfold-Table with small cell frequencies is known as a UMPU-Test. But in practice the test is used in a nonrandomized,
often tabulated version.
Given a certain level of significanceα it is shown: the critical region of this nonrandomized test, referred to as “Fisher 1”, can be enlarged considerably. For
instance for all sample-size-sums up to 20 andα=0.01 the total number of points in the critical regions of “Fisher 1” is 552 whereas the analogous number of the new version
“Fisher 2” is 788. The size of tables for “Fisher 2” can be reduced considerably because the main parts of the critical regions
can be described by the aid of some Chi-square-test versions. In particular Yates’ continuity-correction turns out to be always
conservative in the above mentioned region relative to “Fisher 2” whereas this is not strictly true relative to “Fisher 1”.
相似文献
2.
Summary Dynamic exponential family regression provides a framework for nonlinear regression analysis with time dependent parametersβ
0,β
1, …,β
t, …, dimβ
t=p. In addition to the familiar conditionally Gaussian model, it covers e.g. models for categorical or counted responses. Parameters
can be estimated by extended Kalman filtering and smoothing. In this paper, further algorithms are presented. They are derived
from posterior mode estimation of the whole parameter vector (β′0, …,β′t) by Gauss-Newton resp. Fisher scoring iterations. Factorizing the information matrix into block-bidiagonal matrices, algorithms
can be given in a forward-backward recursive form where only inverses of “small”p×p-matrices occur. Approximate error covariance matrices are obtained by an inversion formula for the information matrix, which
is explicit up top×p-matrices.
Heinz Leo Kaufmann, my friend and coauthor for many years, died in a tragical rock climbing accident in August 1989. This
paper is dedicated to his memory. 相似文献
3.
Summary A general class of estimators for estimating the population mean of the character under study which make use of auxiliary
information is proposed. Under simple random sampling without replacement (SRSWOR), the expressions of Bias and Mean Square
Error (MSE), up to the first and the second degrees of approximation are derived. General conditions, up to the first order
approximation, are also obtained under which any member of this class performs more efficiently than the mean per unit estimator,
the ratio estimator and the product estimator. The class of estimators in its optimum case, under the first degree approximation,
is discussed. It is shown that it is not possible to obtain optimum values of parameters “a”, “b” and “p”, that are independent of each other. However, the optimum relation among them is given by (b−a)p=ρ C
y/C
x. Under this condition, the expression of MSE of the class is that of the linear regression estimator. 相似文献
4.
Based on the exponential and Poisson characteristics of the Poisson process, in this work we present some characterizations
of the Poisson process as a renewal process. More precisely, let γt be the residual life at time t of the renewal process A={A(t),t≥0 }, under suitable condition, we prove that if Var(γt)=E
2 (γt),∀t≥0, then A is a Poisson process. Secondly, we show that if Var (A(t)) is proportional to E (A(t)), then A is a Poisson process also, and Var (A(t))=E (A(t)).
Received: August 1999 相似文献
5.
This paper covers some of the past accomplishments of DEA (Data Envelopment Analysis) and some of its future prospects. It
starts with the “engineering-science” definitions of efficiency and uses the duality theory of linear programming to show
how, in DEA, they can be related to the Pareto–Koopmans definitions used in “welfare economics” as well as in the economic
theory of production. Some of the models that have now been developed for implementing these concepts are then described and
properties of these models and the associated measures of efficiency are examined for weaknesses and strengths along with
measures of distance that may be used to determine their optimal values. Relations between the models are also demonstrated
en route to delineating paths for future developments. These include extensions to different objectives such as “satisfactory”
versus “full” (or “strong”) efficiency. They also include extensions from “efficiency” to “effectiveness” evaluations of performances
as well as extensions to evaluate social-economic performances of countries and other entities where “inputs” and “outputs”
give way to other categories in which increases and decreases are located in the numerator or denominator of the ratio (=engineering-science)
definition of efficiency in a manner analogous to the way output (in the numerator) and input (in the denominator) are usually
positioned in the fractional programming form of DEA. Beginnings in each of these extensions are noted and the role of applications
in bringing further possibilities to the fore is highlighted.
相似文献
J. ZhuEmail: |
6.
Daniel J. Nordman 《Metrika》2008,68(3):351-363
Properties of a “blockwise”empirical likelihood for spatial regression with non-stochastic regressors are investigated for
spatial data on a lattice. The method enables nonparametric confidence regions for spatial trend parameters to be calibrated,
even though non-random regressors introduce non-stationary forms of spatial dependence into the “blockwise” construction. Additionally, the regression results are valid in a general
framework allowing for a variety of behavior in regressor variables as well as the underlying spatial error process. The same
regression method also applies when the regressors are stochastic. 相似文献
7.
M. C. Jones 《Metrika》2002,54(3):215-231
Relationships between F, skew t and beta distributions in the univariate case are in this paper extended in a natural way to the multivariate case. The result
is two new distributions: a multivariate t/skew t distribution (on ℜm) and a multivariate beta distribution (on (0,1)m). A special case of the former distribution is a new multivariate symmetric t distribution. The new distributions have a natural relationship to the standard multivariate F distribution (on (ℜ+)m) and many of their properties run in parallel. We look at: joint distributions, mathematically and graphically; marginal
and conditional distributions; moments; correlations; local dependence; and some limiting cases.
Received: March 2001 相似文献
8.
Holger Dette 《Metrika》1993,40(1):37-50
The optimal design problem for the estimation of several linear combinationsc′
l
ϑ (l=1, …,m) is considered in the usual linear regression modely=f′(x)ϑ (f(x) ∈ ℝ
k
,ϑ ∈ ℝ
k
). An optimal design minimizes a (weighted)p-norm of the variances of the least squares estimates for the different linear combinationsc′
l
ϑ. A generalized Elfving theorem is used to derive the relation of the new optimality criterion to theE-optimal design problem. It is shown that theE-optimal design for the parameterϑ minimizes such a (weighted)p-norm whenever the vectorc=(c′
1, …, c′k)′ is an inball vector of a symmetric convex and compact “Elfving set” in. 相似文献
9.
Prof. Dr. T. Royen 《Metrika》1990,37(1):145-154
Summary It is proved that for any fixed argument the sequence (P
k) of the distribution functions of the ranges ofk i.i.d. univariate random variables is log-concave if the random variables have a log-concave density. If the support of the
distribution is an infinite interval and the density is monotonous then the theorem holds also with “log-convex” instead of
“log-concave”. The resulting inequalities can be used by a quick algorithm for closed maximum range test procedures for all
pairwise comparisons (Royen 1988, 1989a, 1989b). Under the above assumptions the application of this algorithm can be extended
e.g. to pairwise comparisons of variances. 相似文献
10.
Summary LetX andY be two random vectors with values in ℝ
k
and ℝ∝, respectively. IfZ=(X
T,Y
T)
T
is multivariate normal thenX givenY=y andY givenX=x are (multivariate) normal; the converse is wrong. In this paper simple additional conditions are stated such that the converse
is true, too. Furthermore, the case is treated that the random vectorZ=(X
1
T
, …,X
t
T
)
T
is splitted intot≥3 partsX
1, …,X
t. 相似文献
11.
Building on new insights into the genesis ofPareto-Distributions,(“Kopp” effect etc.) as publishedearlier in “Quality and
Quantity”, the author gives at least oneauthentic/definitive Pareto-Formula. A practical example of the synthetic generation
of Pareto Distributions by means of spreadsheets. A working D.I.Y-method for fine-fitting Pareto-curvesto scattergrams with
spreadsheets using interalia an indirect method of the least squares of residuals is fully demonstrated. A comparative test-fit
to a cumulative Pareto- Distribution example, where a simulative curve-formula evolved by Prof. B. Arnold/Ucla is used for
demonstration. Easy to absorb and to retain graphical tableaux are employed to visualize the chain of descent and interconnections
between normal distributions, log-normal distributions and Pareto- Distributions. A quasi-dichotomy of the Pareto-formulae
is presented in tableau-form. One innovative formula for Pareto-distribution is given as:
F(x)= k*e― [((ln(Integral(In(x)))) ‐ (ln(Integral(ln(μ)))))2 / 2*(ln(Integral(ln(σ))))2}
Readers e-mailed constructive opinions &/or inputs are encouraged and welcomed.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
12.
Bernhard Klar 《Metrika》1999,49(1):53-69
This paper presents a new widely applicable omnibus test for discrete distributions which is based on the difference between
the integrated distribution function Ψ(t)=∫t
∞ (1−F(x))dx and its empirical counterpart. A bootstrap version of the test for common lattice models has accurate error rates even for
small samples and exhibits high power with respect to competitive procedures over a large range of alternatives.
Received: July 1998 相似文献
13.
For the invariant decision problem of estimating a continuous distribution function F with two entropy loss functions, it is proved that the best invariant estimators d
0 exist and are the same as the best invariant estimator of a continuous distribution function under the squared error loss
function L (F, d)=∫|F (t) −d (t) |2
dF (t). They are minimax for any sample size n≥1. 相似文献
14.
A distributionF is said to be “more IFR” than another distributionG ifG
−1
F is convex. WhenF(0) =G(0) = 0, the problem of testingH
0 :F(x) =G (θx) for someθ > 0 andx ⩾ 0, against the alternativeH
A:F is more IFR thanG, is considered in this paper. Both cases, whenG is completely specified (one-sample case) and when it is not specified but a random sample form it is available (two-sample
case) are considered. The proposed tests are based onU-statistics. The asymptotic relative efficiency of the tests are compared with several other tests and the test statistics
remain asymptotically normal under certain dependency assumptions.
Research supported in part by a grant from the US Air Force Office of Scientific Research. 相似文献
15.
F. Brodeau 《Metrika》1999,49(2):85-105
This paper is devoted to the study of the least squares estimator of f for the classical, fixed design, nonlinear model X (t
i)=f(t
i)+ε(t
i), i=1,2,…,n, where the (ε(t
i))i=1,…,n are independent second order r.v.. The estimation of f is based upon a given parametric form. In Brodeau (1993) this subject has been studied in the homoscedastic case. This time
we assume that the ε(t
i) have non constant and unknown variances σ2(t
i). Our main goal is to develop two statistical tests, one for testing that f belongs to a given class of functions possibly discontinuous in their first derivative, and another for comparing two such
classes. The fundamental tool is an approximation of the elements of these classes by more regular functions, which leads
to asymptotic properties of estimators based on the least squares estimator of the unknown parameters. We point out that Neubauer
and Zwanzig (1995) have obtained interesting results for connected subjects by using the same technique of approximation.
Received: February 1996 相似文献
16.
Norbert Henze 《Metrika》1997,45(1):121-130
Smooth goodness of fit tests were introduced by Neyman (1937). They can be regarded as a compromise between globally consistent
(“omnibus”) tests of fit and procedures having high power in the direction of a specific alternative. It is commonly believed
that components of smooth tests like, e.g., skewness and kurtosis measures in the context of testing for normality, have special
diagnostic properties in case of rejection of a hypothesisH
0 in the sense that they constitute direct measures of the kind of departure fromH
0. Recent years, however, have witnessed a complete change of attitude towards the diagnostic capabilities of skewness and
kurtosis measures in connection with normality testing. In this paper, we argue that any component of any smooth test of fit
is strictly non-diagnostic when used conventionally. However, a proper rescaling of components does indeed achieve the desired
“directed diagnosis”. 相似文献
17.
Dr. P. N. Rathie 《Metrika》1972,18(1):216-219
Equivalence of the generalized entropyH
β (P, Φ
t
) defined in this paper andKapur’s entropy of orderα and typeβ, ie.H
α
β
(P), is established. The results given recently byCampbell follow as special cases.
International Conference on System Sciences, Honolulu, January 1968. 相似文献
18.
Parisian options are path-dependent options whose payoff depends on whether the underlying asset’s price remains continuously
at or above a given barrier over a given time interval. Costabile’s (Decis Econ Finance 25(2):111–125, 2002b) algorithm for
pricing Parisian options based on a combinatorial approach in binomial tree has a time complexity of O( n3){O\left( {n^{3}}\right)}. We improve that algorithm to yield one with a time complexity of only O(n2){O\left({n^{2}}\right)}. 相似文献
19.
Abstract
It is market practice to quote interest rate derivatives traded “over the counter” in terms of their implied volatility. For
this reason, the term structure of at-the-money cap volatilities as well as the volatility surface of at-the-money swaptions
are directly observed. This paper analyzes the case of caps. Any analysis of these markets would most likely report two main
facts. The first is that the level of the volatility is inversely related to the level of the interest rates. The second is
that the term structure is either a decreasing or a humped function of maturity. For a reference, see Rebonato (2003) and
Brigo and Mercurio (2001). Rebonato (2003) suggests that the structure of implied volatility is humped in periods of normal
market conditions and decreasing when markets are “excited”. Interpreting and explaining such phenomena is indeed an interesting
and important issue.
Mathematics Subject Classification (2000): 91B70
Journal of Economic Literature Classification: E43, C13 相似文献
20.
Consider the heteroscedastic regression model Y
(j)(x
in
, t
in
) = t
in
β + g(x
in
) + σ
in
e
(j)(x
in
), 1 ≤ j ≤ m, 1 ≤ i ≤ n, where sin2=f(uin){\sigma_{in}^{2}=f(u_{in})}, (x
in
, t
in
, u
in
) are fixed design points, β is an unknown parameter, g(·) and f(·) are unknown functions, and the errors {e
(j)(x
in
)} are mean zero NA random variables. The moment consistency for least-squares estimators and weighted least-squares estimators
of β is studied. In addition, the moment consistency for estimators of g(·) and f(·) is investigated. 相似文献