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1.
Biao Zhang 《Metrika》1997,46(1):221-244
For estimating the distribution functionF of a population, the empirical or sample distribution functionF
n
has been studied extensively. Qin and Lawless (1994) have proposed an alternative estimator
for estimatingF in the presence of auxiliary information under a semiparametric model. They have also proved the point-wise asymptotic normality
of
. In this paper, we establish the weak convergence of
to a Gaussian process and show that the asymptotic variance function of
is uniformly smaller than that ofF
n
. As an application of
, we propose to employ the mean
and varianceŜ
n
2
of
to estimate the population mean and variance in the presence of auxiliary information. A simulation study is presented to
assess the finite sample performance of the proposed estimators
, andŜ
n
2
. 相似文献
2.
S. B. Provost 《Metrika》1988,35(1):191-196
The exact density of the statistic ln
, where
and
denote, respectively, the arithmetic and the geometric means of a random sample from a two-parameter gamma distribution,
is obtained in a computable form using the technique of the inverse Mellin transform. This statistic is related to the maximum
likelihood estimator of the shape parameter of a gamma distribution. 相似文献
3.
4.
Enrique Del Castillo 《Metrika》1996,43(1):189-201
The run length distribution of
charts with unknown process variance is analized using numerical integration. Both traditional
chart limits and a method due to Hillier are considered. It is shown that setting control limits based on the pooled standard
deviation, as opposed to the average sample standard deviation, provides better run length performance due to its smaller
mean square error. The effect of an unknown process variance is shown to increase the area under both tails of the run length
distribution. If Hillier’s method is used instead, only the right tail of the run length distribution is increased. Collani’s
model for the economic design of
charts is extended to the case of unknown process variance by writing his standardized objective function in terms of average
run lengths. 相似文献
5.
This paper deals with the estimation of survivor function
using optimally selected order statistics when the sample sizen is large. We use the estimates (μ*,σ*) based on the optimum set of order statistics
for largen and fixedk (≤n) such that the estimate
has optimum variance property. The asymptotic relative efficiency of such an estimator is compared with the one based on
the complete sample. The general theory of the problem and specific details with respect to a two-parameter Normal, Logistic,
Exponential and Pareto distributions is considered as an example. 相似文献
6.
Summary Minimizing
is discussed under the unbiasedness condition:
and the condition (A):f
i
(x) (i=1, ..., p) are linearly independent
, and
. 相似文献
7.
Eugene F. Schuster 《Metrika》1993,40(1):325-332
We consider the sample survey type problem of estimating the proportionp of a finite population of sizeN having a given attribute by the proportion
of successes in a random sample (with or without replacement) of sizer from the population. Our main result indicates that
is always at least a 91.0% confidence interval (C.I.) for the parameterp. We show that
is at least as large under the hypergeometric model of simple random sampling without replacement as it is under the corresponding
binomial model of random sampling with replacement. The significance of our main result is that it is a good, easily stated
accuracy rule, holding for allr, N, andp, which can easily be understood by the layman when assessing accuracy of the estimator
and discussing the relationship between accuracy and sample size. 相似文献
8.
Prof. Dr. W. Fieger 《Metrika》1977,24(1):7-22
Zusammenfassung Es sei A: R
n
R
n
eine Abbildung mit
für jedes
sei einn-dimensionaler Zufallsvektor. Wir beschreiben die Klasse aller TransformationenA, für die
unabhängige, nachN(0, 1) verteilte Komponenten hat, sofern nur die KomponentenX
1,...,X
n
des Zufallsvektors
ebenfalls unabhängig und identish Gaußisch verteilt sind mit Erwartungswert Null und Varianz 1. Weiter sind Bedingungen angegeben, die sicherstellen, daß
nachN(O, 2) verteilte KomponentenX
1,...,X
n
hat, sofern dieX
1,...,X
n
unabhängig und
und
identisch verteilt sind. Zwei vonBeer undLukacs behandelte Transformationen sind Spezialfälle der hier untersuchten Transformationen.
Summary Let A: R n R n be a transformation with the property for every . We consider a random vector and characterize the class of all transformationsA such that has independentN (0, 1) distributed componentsY 1,...,Y n if has the same distribution. Furthermore in the paper there are given conditions which ensure that hasN(O, 2 distributed components if and are identically distributed and the componentsX 1,...,X n are independent, identically distributed random variables. Two of the transformations tried byBeer andLukacs are special cases of our transformations.相似文献
9.
Herbert Vogt 《Metrika》1996,44(1):207-221
Let ζ
t
be the number of events which will be observed in the time interval [0;t] and define
as the average number of events per time unit if this limit exists. In the case of i.i.d. waiting-times between the events,E[ζ
t
] is the renewal function and it follows from well-known results of renewal theory thatA exists and is equal to 1/τ, if τ>0 is the expectation of the waiting-times.
This holds true also when τ = ∞.A may be estimate by ζ
t
/t or
where
is the mean of the firstn waiting-timesX
1,X
2, ...,X
n
. Both estimators converage with probability 1 to 1/τ if theX
i are i.i.d.; but the expectation of
may be infinite for alln and also if it is finite,
is in general a positively biased estimator ofA. For a stationary renewal process, ζ
t
/t is unbiased for eacht; if theX
i
are i.i.d. with densityf(x), then ζ
t
/t has this property only iff(x) is of the exponential type and only for this type the numbers of events in consecutive time intervals [0,t], [t, 2t], ... are i.i.d. random variables for arbitraryt > 0. 相似文献
10.
11.
U. Stadtmüller 《Metrika》1983,30(1):145-158
As an estimator
for an unknown probability density functionf, concentrated on a known intervalI, one can use a histogram smoothed by a suitable family of lattice distributions. For such an estimator a uniform weak consistency result and a central limit theorem with an error bound are given. Further for the global deviation of
fromf the asymptotic distribution is developed.Partially supported by the Natural Sciences and Engineering Research Council of Canada, grant A 2983, A4806, and A3988. 相似文献
12.
Lanxiang Chen 《Metrika》1989,36(1):149-159
A natural generalization of thep-dimensional normal distribution is provided by elliptically contoured distributions. In the case of the normal distribution
the likelihood ratio tests (LRT) of null-hypothesis of the form
相似文献
13.
14.
Michele Mulazzani 《Decisions in Economics and Finance》1993,16(1):87-97
Vengono studiate le proprietà delle intensità istantanee di interesse di leggi finanziarie scindibili non necessariamente omogeneef(x, s, t). Esse risultano dipendenti dal montante e dal tempo finale secondo il modello
. Ciò porta ad ottenere una naturale corrispondenza fra leggi finanziarie scindibili ed equazioni differenziali ordinarie. Si esaminano in dettaglio i casi particolari di leggi uniformi, leggi omogenee e leggi uniformi-omogenee, individuando la forma delle equazioni differenziali ad esse associate. Si estendono infine i risultati a leggi finanziarie del tipo
, che dipendono anche dalla variabile istante decisionale
.
Summary We study the properties of the interest rates of the so-called scindibili financial laws (not necessarily homogeneous)f(x, s, t). They explicity depend on the value off andt only, according to the form . This suggests a natural correspondence between such financial laws and ordinary differential equations.The particular cases of uniform laws, homogeneous laws and uniform-homogeneous laws are examined and the structure of the associated differential equations are obtained.The previous results are extended to the financial laws of type which also depend on a decisional time .相似文献 15.
K. F. Cheng 《Metrika》1982,29(1):215-225
For a specified distribution functionG with densityg, and unknown distribution functionF with densityf, the generalized failure rate function (x)=f(x)/gG
–1
F(x) may be estimated by replacingf andF byf
n and
, wheref
n is an empirical density function based on a sample of sizen from the distribution functionF, and
. Under regularity conditions we show
and, under additional restrictions
whereC is a subset ofR and n. Moreover, asymptotic normality is derived and the Berry-Esséen type bound is shown to be related to a theorem which concerns the sum of i.i.d. random variables. The order boundO(n–1/2+c
n
1/2
) is established under mild conditions, wherec
n is a sequence of positive constants related tof
n and tending to 0 asn.Research was supported in part by the Army, Navy and Air Force under Office of Naval Research contract No. N00014-76-C-0608. AMS 1970 subject classifications. Primary 62G05. Secondary 60F15. 相似文献
16.
17.
A consistent test for multivariate normality based on the empirical characteristic function 总被引:2,自引:1,他引:1
LetX
1,X
2, …,X
n be independent identically distributed random vectors in IR
d
,d ⩾ 1, with sample mean
and sample covariance matrixS
n. We present a practicable and consistent test for the composite hypothesisH
d: the law ofX
1 is a non-degenerate normal distribution, based on a weighted integral of the squared modulus of the difference between the
empirical characteristic function of the residualsS
n
−1/2
(X
j −
) and its pointwise limit exp (−1/2|t|2) underH
d. The limiting null distribution of the test statistic is obtained, and a table with critical values for various choices ofn andd based on extensive simulations is supplied. 相似文献
18.
Let be independent and identically distributed random variables with continuous distribution function. Denote by the corresponding order statistics. In the present paper, the concept of -neighbourhood runs, which is an extension of the usual run concept to the continuous case, is developed for the sequence of ordered random
variables 相似文献
19.
Let {v
n(θ)} be a sequence of statistics such that whenθ =θ
0,v
n(θ
0)
N
p(0,Σ), whereΣ is of rankp andθ εR
d. Suppose that underθ =θ
0, {Σ
n} is a sequence of consistent estimators ofΣ. Wald (1943) shows thatv
n
T
(θ
0)Σ
n
−1
v
n(θ
0)
x
2(p). It often happens thatv
n(θ
0)
N
p(0,Σ) holds butΣ is singular. Moore (1977) states that under certain assumptionsv
n
T
(θ
0)Σ
n
−
v
n(θ
0)
x
2(k), wherek = rank (Σ) andΣ
n
−
is a generalized inverse ofΣ
n. However, Moore’s result as stated is incorrect. It needs the additional assumption that rank (Σ
n) =k forn sufficiently large. In this article, we show that Moore’s result (as corrected) holds under somewhat different, but easier
to verify, assumptions.
Research partly supported by the U.S. Army Research Office through the Mathematical Sciences Institute at Cornell University. 相似文献
20.
In questo lavoro viene fornita una nuova caratterizzazione dell'ammissibilità attraverso un adeguato uso della nozione di ammissibilità parziale. Questa caratterizzazione consente di affrontare le questioni riguardanti la completezza della classe delle decisioni ammissibiliti sotto condizioni «maneggevoli». Fornisce inoltre un approccio unificante al problema della completezza che consente di derivare, come casi particolari, alcuni risultati già noti nella letteratura sull'argomento.
In this paper a new characterization of admissibility is given for general decision problems. It is based on an adequate use of the notion of partial admissibility.A general decision problem is usually synthetized by a triplet (, , ) where is the states (or parameters) space, the set of available decisions and is a family of real valued functions defined on and expressing numerically the consequences of choosing when the state is . The set is regarded as a subset of the space of all real valued functions on endowed with the topology of pointwise convergence.As for as admissibility is concerned all the pertinent information about decisions are contained in the corresponding functionsW .This allows to introduce a notion of partial admissibility through the neigh-bourhoods of this topology. Admissibile decisions are then shown to be limits of monotone non increasing sequences of partially admissible decisions.Moreover this topological characterization allows to prove the completeness of classes of admissible decisions under acceptable systems of conditions which contain as special cases, known results in literature. Lavoro svolto nell'ambito del Gruppo Nazionale per l'Analisi Funzionale e le sue Applicazioni del C.N.R. 相似文献 |