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1.
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
2.
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
3.
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
4.
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
5.
A. I. Dale 《Metrika》1977,24(1):169-173
Ver {V
n
} be a sequence of random elements in a separable Banach space. Conditions are obtained under which
. 相似文献
6.
Dr. Arne Sandström 《Metrika》1987,34(1):129-142
Let T(
) be a linear function of concomitants of order statistics, whereT (·) denotes a statistical functional depending on some distribution function (df)F and
is an estimator ofF. Under an auxiliary model approach we consider statistics of the form
, where
denotes a weighted empirical df and
a finite population df (t denotes a triangular array). The results can be used to estimate income inequality in finite populations and especially when
the survey is based on some design.
The paper was written when the author was working at the Statistical Research Unit, Statistics Sweden, Stockholm, Sweden
The research was supported by the Joint Committé of the Nordic Social Research Council. 相似文献
7.
L. Losonczi 《Metrika》1981,28(1):237-244
The functional equation
has been studied by several authors under various assumptions onf and onk, l. Here we solve this equation iff is measurable andk 3,l 2 are fixed integers. Using the solution we characterize the entropies of degree for all real . Our results generalize the results ofBehara/Nath [1973],Kannappan [1974] andMittal [1976]. 相似文献
8.
A necessary and sufficient condition for the almost everywhere convergence of the moving ergodic averages
is given. The result is then generalized to ergodic flows, and finally constrasted with earlier results ofPfaffelhuber andJain. 相似文献
9.
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
10.
11.
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
12.
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
13.
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
14.
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
15.
Dipl.-Math. M. Behl 《Metrika》1981,28(1):93-107
Summary For sampling inspection by variables in the one-sided case (item bad if variablex>a) under the usual assumption of normality with known variance 2 the operating characteristic is given by
, wherep denotes the fraction defective. If instead of a normal distribution ((·–a–)/) there is a distributionF((·–a–)/) whereF is sufficiently regular and normed like , one has the approximative operating characteristic
. It is shown that for arbitrarily fixed parametersn andc the function
takes the valueL
n,c
()
(p) at the pointp
F
(p)=1–F(––1(p)). Sufficient conditions for a simple behavior of the differencep
F
(p)–p are given. In the cases of rectangular and symmetrically truncated normal distribution these conditions are shown to be fulfilled. 相似文献
16.
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
17.
18.
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
19.
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.
Lavoro svolto nell'ambito del Gruppo Nazionale per l'Analisi Funzionale e le sue Applicazioni del C.N.R. 相似文献
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
20.
A bivariate normal distribution is considered whose mean lies in an equilateral triangle. We show by a convexity argument that the three point prior having mass 1/3 at each of the edges is least favourable if the length of a side of the equilateral triangle is less than or equal to
. Thus the corresponding Bayes estimator is minimax in that case. Numerical studies are given as well. 相似文献