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1.
In this paper we discuss robust estimation of the concentration parameter (κ) of the circular normal (CN) distribution. It is known that the MLE of the concentration parameter is not B-robust at the
family of all circular normal distributions with fixed mean direction (μ) and varying κ > 0. In this paper we propose a new estimator for κ and show that it is B-robust and SB-robust at the family {CN(μ, κ) : m ≤ κ ≤ M} where m and M are two arbitrary constants. 相似文献
2.
LetX andY be two random variables with finite expectationsE
X andE
Y, respectively. ThenX is said to be smaller thanY in the dilation order ifE[ϕ(X-E
X)]≤E[ϕ(Y-E
Y)] for any convex functionϕ for which the expectations exist. In this paper we obtain a new characterization of the dilation order. This characterization
enables us to give new interpretations to the dilation order, and using them we identify conditions which imply the dilation
order. A sample of applications of the new characterization is given.
Partially supported by MURST 40% Program on Non-Linear Systems and Applications.
Partially supported by “Gruppo Nazionale per l'Analisi Funzionale e sue Applicazioni”—CNR. 相似文献
3.
On MSE of EBLUP 总被引:1,自引:1,他引:0
Tomasz Ża̧dło 《Statistical Papers》2009,50(1):101-118
We consider Best Linear Unbiased Predictors (BLUPs) and Empirical Best Linear Unbiased Predictors (EBLUPs) under the general
mixed linear model. The BLUP was proposed by Henderson (Ann Math Stat 21:309–310, 1950). The formula of this BLUP includes
unknown elements of the variance-covariance matrix of random variables. If the elements in the formula of the BLUP proposed
by Henderson (Ann Math Stat 21:309–310, 1950) are replaced by some type of estimators, we obtain the two-stage predictor called
the EBLUP which is model-unbiased (Kackar and Harville in Commun Stat A 10:1249–1261, 1981). Kackar and Harville (J Am Stat
Assoc 79:853–862, 1984) show an approximation of the mean square error (the MSE) of the predictor and propose an estimator
of the MSE. The MSE and estimators of the MSE are also studied by Prasad and Rao (J Am Stat Assoc 85:163–171, 1990), Datta
and Lahiri (Stat Sin 10:613–627, 2000) and Das et al. (Ann Stat 32(2):818–840, 2004). In the paper we consider the BLUP proposed
by Royall (J Am Stat Assoc 71:657–473, 1976. Ża̧dło (On unbiasedness of some EBLU predictor. Physica-Verlag, Heidelberg, pp
2019–2026, 2004) shows that the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) may be treated as a generalisation
of the BLUP proposed by Henderson (Ann Math Stat 21:309–310, 1950) and proves model unbiasedness of the EBLUP based on the
formula of the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) under some assumptions. In this paper we derive
the formula of the approximate MSE of the EBLUP and its estimators. We prove that the approximation of the MSE is accurate
to terms o(D
−1) and that the estimator of the MSE is approximately unbiased in the sense that its bias is o(D
−1) under some assumptions, where D is the number of domains. The proof is based on the results obtained by Datta and Lahiri (Stat Sin 10:613–627, 2000). Using
our results we show some EBLUP based on the special case of the general linear model. We also present the formula of its MSE
and estimators of its MSE and their performance in Monte Carlo simulation study.
相似文献
4.
Konanur G. Janardan 《Statistical Papers》2005,46(4):587-597
A discrete distribution associated with a pure birth process starting with no individuals, with birth rates λ
n
=λ forn=0, 2, …,m−1 and λ
n
forn≥m is considered in this paper. The probability mass function is expressed in terms of an integral that is very convenient for
computing probabilities, moments, generating functions and others. Using this representation, the mean and the k-th factorial
moments of the distribution are obtained. Some nice characterizations of this distribution are also given. 相似文献
5.
Summary This paper deals with the sequential estimation ofq(ϑ1, ϑ2) when the underlying density function is of the formf(x)=q(ϑ1, ϑ2)h(x), where ϑ1 and ϑ2 are unknown truncation parameters. We study the sequential properties of the stopping rule and the sequential estimator ofq(ϑ1, ϑ2). In this study we assume that the sample is type II censored. 相似文献
6.
A. Stepanov 《Statistical Papers》2007,48(1):63-79
LetX
1,X
2, … be a sequence of i.i.d. random variables with some continuous distribution functionF. LetX(n) be then-th record value associated with this sequence and μ
n
−
, μ
n
+
be the variables that count the number of record values belonging to the random intervals(f−(X(n)), X(n)), (X(n), f+(X(n))), wheref−, f+ are two continuous functions satisfyingf−(x)<x, f+(x)>x. Properties of μ
n
−
, μ
n
+
are studied in the present paper. Some statistical applications connected with these variables are also provided. 相似文献
7.
Summary Let {X
n
} be a sequence of random variables conditionally independent and identically distributed given the random variable Θ. The
aim of this paper is to show that in many interesting situations the conditional distribution of Θ, given (X
1,…,X
n
), can be approximated by means of the bootstrap procedure proposed by Efron and applied to a statisticT
n
(X
1,…,X
n
) sufficient for predictive purposes. It will also be shown that, from the predictive point of view, this is consistent with
the results obtained following a common Bayesian approach. 相似文献
8.
In this paper, we study, by a Monte Carlo simulation, the effect of the order p of “Zhurbenko-Kolmogorov” taper on the asymptotic properties of semiparametric estimators. We show that p = [d + 1/2] + 1 gives the smallest variances and mean squared errors. These properties depend also on the truncation parameter
m. Moreover, we study the impact of the short-memory components on the bias and variances of these estimators. We finally carry
out an empirical application by using four monthly seasonally adjusted logarithm Consumer Price Index series.
相似文献
9.
Let X
1, X
2, ..., X
n be a random sample from a normal population with mean μ and variance σ
2. In many real life situations, specially in lifetime or reliability estimation, the parameter μ is known a priori to lie in an interval [a, ∞). This makes the usual maximum likelihood estimator (MLE) ̄ an inadmissible estimator of μ with respect to the squared error loss. This is due to the fact that it may take values outside the parameter space. Katz
(1961) and Gupta and Rohatgi (1980) proposed estimators which lie completely in the given interval. In this paper we derive
some new estimators for μ and present a comparative study of the risk performance of these estimators. Both the known and unknown variance cases have
been explored. The new estimators are shown to have superior risk performance over the existing ones over large portions of
the parameter space. 相似文献
10.
A basic concept for comparing spread among probability distributions is that of dispersive ordering. Let X and Y be two random variables with distribution functions F and G, respectively. Let F
−1 and G
−1 be their right continuous inverses (quantile functions). We say that Y is less dispersed than X (Y≤
disp
X) if G
−1(β)−G
−1(α)≤F
−1(β)−F
−1(α), for all 0<α≤β<1. This means that the difference between any two quantiles of G is smaller than the difference between the corresponding quantiles of F. A consequence of Y≤
disp
X is that |Y
1−Y
2| is stochastically smaller than |X
1−X
2| and this in turn implies var(Y)≤var(X) as well as E[|Y
1−Y
2|]≤E[|X
1−X
2|], where X
1, X
2 (Y
1, Y
2) are two independent copies of X(Y). In this review paper, we give several examples and applications of dispersive ordering in statistics. Examples include those
related to order statistics, spacings, convolution of non-identically distributed random variables and epoch times of non-homogeneous
Poisson processes.
This work was supported in part by KOSEF through Statistical Research Center for Complex Systems at Seoul National University.
Subhash Kochar is thankful to Dr. B. Khaledi for many helpful discussions. 相似文献
11.
We show that the definition of the θth sample quantile as the solution to a minimization problem introduced by Koenker and Bassett (Econometrica 46(1):33–50,
1978) can be easily extended to obtain an analogous definition for the θth sample quantity quantile widely investigated and applied in the Italian literature. The key point is the use of the first-moment
distribution of the variable instead of its distribution function. By means of this definition we introduce a linear regression
model for quantity quantiles and analyze some properties of the residuals. In Sect. 4 we show a brief application of the methodology
proposed.
This research was partially supported by Fondo d’Ateneo per la Ricerca anno 2005—Università degli Studi di Milano-Bicocca.
The paper is the result of the common work of the authors; in particular M. Zenga has written Sects. 1 and 5 while P. Radaelli
has written the remaining sections. 相似文献
12.
Two independent random samples are drawn from two multivariate normal populations with mean vectors μ1 and μ2 and a common
variance-covariance matrix Σ. Ahmed and Saleh (1990) considered preliminary test maximum likelihood estimator (PMLTE) for estimating μ1 based on the Hotelling's T
N
2, when it is suspected that μ1=μ2. In this paper, the PTMLE based on the Wald (W), Likelihood Ratio (LR) and Lagrangian Multiplier (LM) tests are considered. Using the quadratic risk function, the conditions of superiority of the proposed estimator for departure
parameter are derived. A max-min rule for the size of the preliminary test of significance is presented. It is demonstrated
that the PTMLE based on W test produces the highest minimum guaranteed efficiencies compared to UMLE among the three test procedures. 相似文献
13.
In this paper we describe active set type algorithms for minimization of a smooth function under general order constraints,
an important case being functions on the set of bimonotone r×s matrices. These algorithms can be used, for instance, to estimate a bimonotone regression function via least squares or (a
smooth approximation of) least absolute deviations. Another application is shrinkage estimation in image denoising or, more
generally, regression problems with two ordinal factors after representing the data in a suitable basis which is indexed by
pairs (i,j)∈{1,…,r}×{1,…,s}. Various numerical examples illustrate our methods. 相似文献
14.
In this paper, we study the asymptotic distributions of MLE and UMVUE of a parametric functionh(θ1, θ2) when sampling from a biparametric uniform distributionU(θ1, θ2). We obtain both limiting distributions as a convolution of exponential distributions, and we observe that the limiting distribution
of UMVUE is a shift of the limiting distribution of MLE. 相似文献
15.
Summary A standard improper prior for the parameters of a MANOVA model is shown to yield an inference that is incoherent in the sense
of Heath and Sudderth. The proof of incoherence is based on the fact that the formal Bayes estimate, sayδ
0
, of the covariance matrix based on the improper prior and a certain bounded loss function is uniformly inadmissible in that
there is another estimatorδ
l
and an ɛ>0 such that the risk functions satisfyR(δ
l
,Σ)⩽R δ
0
,Σ)−ε for all values of the covariance matrix Σ. The estimatorδ
I
is formal Bayes for an alternative improper prior which leads to a coherent inference.
Research supported by National Science Foundation grants DMS-89-22607 (for Eaton) and DMS-9123358 (for Sudderth). 相似文献
16.
17.
As GARCH models and stable Paretian distributions have been revisited in the recent past with the papers of Hansen and Lunde
(J Appl Econom 20: 873–889, 2005) and Bidarkota and McCulloch (Quant Finance 4: 256–265, 2004), respectively, in this paper
we discuss alternative conditional distributional models for the daily returns of the US, German and Portuguese main stock
market indexes, considering ARMA-GARCH models driven by Normal, Student’s t and stable Paretian distributed innovations. We find that a GARCH model with stable Paretian innovations fits returns clearly
better than the more popular Normal distribution and slightly better than the Student’s t distribution. However, the Student’s t outperforms the Normal and stable Paretian distributions when the out-of-sample density forecasts are considered. 相似文献
18.
In this paper, we discuss a general class of skew two-piece skew-normal distributions, denoted by GSTPSN(λ1, λ2, ρ). We derive its moment generating function and discuss some simple and interesting properties of this distribution. We then
discuss the modes of these distributions and present a useful representation theorem as well. Next, we focus on a different
generalization of the two-piece skew-normal distribution which is a symmetric family of distributions and discuss some of
its properties. Finally, three well-known examples are used to illustrate the practical usefulness of this family of distributions. 相似文献
19.
Estimation of population parameters is considered by several statisticians when additional information such as coefficient
of variation, kurtosis or skewness is known. Recently Wencheko and Wijekoon (Stat Papers 46:101–115, 2005) have derived minimum
mean square error estimators for the population mean in one parameter exponential families when coefficient of variation is
known. In this paper the results presented by Gleser and Healy (J Am Stat Assoc 71:977–981, 1976) and Arnholt and Hebert (, 2001) were generalized by considering T (X) as a minimal sufficient estimator of the parametric function g(θ) when the ratio t2=[ g(q) ]-2Var[ T(X ) ]{\tau^{2}=[ {g(\theta )} ]^{-2}{\rm Var}[ {T(\boldsymbol{X} )} ]} is independent of θ. Using these results the minimum mean square error estimator in a certain class for both population mean and variance can
be obtained. When T (X) is complete and minimal sufficient, the ratio τ2 is called “WIJLA” ratio, and a uniformly minimum mean square error estimator can be derived for the population mean and variance.
Finally by applying these results, the improved estimators for the population mean and variance of some distributions are
obtained. 相似文献
20.
S. Gurler 《Statistical Papers》2012,53(1):23-31
Sequential order statistics is an extension of ordinary order statistics. They model the successive failure times in sequential
k-out-of-n systems, where the failures of components possibly affect the residual lifetimes of the remaining ones. In this paper, we
consider the residual lifetime of the components after the kth failure in the sequential (n − k + 1)-out-of-n system. We extend some results on the joint distribution of the residual lifetimes of the remaining components in an ordinary
(n − k + 1)-out-of-n system presented in Bairamov and Arnold (Stat Probab Lett 78(8):945–952, 2008) to the case of the sequential (n − k + 1)-out-of-n system. 相似文献