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1.
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
2.
Let X
1, X
2, ..., X
n
be a random sample from a normal distribution with unknown mean μ and known variance σ
2. In many practical situations, μ is known a priori to be restricted to a bounded interval, say [−m, m] for some m > 0. The sample mean , then, becomes an inadmissible estimator for μ. It is also not minimax with respect to the squared error loss function. Minimax and other estimators for this problem have
been studied by Casella and Strawderman (Ann Stat 9:870–878, 1981), Bickel (Ann Stat 9:1301–1309, 1981) and Gatsonis et al.
(Stat Prob Lett 6:21–30, 1987) etc. In this paper, we obtain some new estimators for μ. The case when the variance σ
2 is unknown is also studied and various estimators for μ are proposed. Risk performance of all estimators is numerically compared for both the cases when σ
2 may be known and unknown. 相似文献
3.
We consider the codifference and the normalized codifference function as dependence measures for stationary processes. Based on the empirical characteristic function, we propose estimators
of the codifference and the normalized codifference function. We show consistency of the proposed estimators, where the underlying model is the ARMA with symmetric α-stable innovations, 0 < α ≤ 2. In addition, we derive their limiting distribution. We present a simulation study showing the dependence of the estimator
on certain design parameters. Finally, we provide an empirical example using some stocks from Indonesia Stock Exchange. 相似文献
4.
We consider the problem of estimating the scale parameter θ of the shifted exponential distribution with unknown shift based on a set of observed records drawn from a sequential sample
of independent and identically distributed random variables. Under a large class of bowl-shaped loss functions, the best affine
equivariant estimator (BAEE) of θ is shown to be inadmissible. Two dominating procedures are proposed. A numerical study is performed to show the extent of
risk reduction that the improved estimators provide over the BAEE. 相似文献
5.
On Estimators of the Nearest Neighbour Distance Distribution Function for Stationary Point Processes
There are three approaches for the estimation of the distribution function D(r) of distance to the nearest neighbour of a stationary point process: the border method, the Hanisch method and the Kaplan-Meier approach. The corresponding estimators and some modifications are compared with respect to bias and mean squared error (mse). Simulations for Poisson, cluster and hard-core processes show that the classical border estimator has good properties; still better is the Hanisch estimator. Typically, mse depends on r, having small values for small and large r and a maximum in between. The mse is not reduced if the exact intensity λ (if known) or intensity estimators from larger windows are built in the estimators of D(r); in contrast, the intensity estimator should have the same precision as that of λ D(r). In the case of replicated estimation from more than one window the best way of pooling the subwindow estimates is averaging by weights which are proportional to squared point numbers. 相似文献
6.
Dr. J. Eichenauer-Herrmann 《Metrika》1992,39(1):199-208
Summary Admissibility of estimators under vague prior information on the distribution of the unknown parameter is studied which leads
to the notion of gamma-admissibility. A sufficient condition for an estimator of the formδ(x)=(ax+b)/(cx+d) to be gamma-admissible in the one-parameter exponential family under squared error loss is established. As an application
of this result two equalizer rules are shown to be unique gamma-minimax estimators by proving their gamma-admissibility. 相似文献
7.
Subsampling and the m out of n bootstrap have been suggested in the literature as methods for carrying out inference based on post-model selection estimators and shrinkage estimators. In this paper we consider a subsampling confidence interval (CI) that is based on an estimator that can be viewed either as a post-model selection estimator that employs a consistent model selection procedure or as a super-efficient estimator. We show that the subsampling CI (of nominal level 1−α for any α(0,1)) has asymptotic confidence size (defined to be the limit of finite-sample size) equal to zero in a very simple regular model. The same result holds for the m out of n bootstrap provided m2/n→0 and the observations are i.i.d. Similar zero-asymptotic-confidence-size results hold in more complicated models that are covered by the general results given in the paper and for super-efficient and shrinkage estimators that are not post-model selection estimators. Based on these results, subsampling and the m out of n bootstrap are not recommended for obtaining inference based on post-consistent model selection or shrinkage estimators. 相似文献
8.
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
9.
The problem of estimating a smooth distribution functionF at a pointτ based on randomly right censored data is treated under certain smoothness conditions onF. The asymptotic performance of a certain class of kernel estimators is compared to that of the Kaplan-Meier estimator ofF(τ). It is shown that the relative deficiency of the Kaplan-Meier estimator ofF(τ) with respect to the appropriately chosen kernel type estimator tends to infinity as the sample sizen increases to infinity. Strong uniform consistency and the weak convergence of the normalized process are also proved.
Research Surported in part by NIH grant 1R01GM28405. 相似文献
10.
We introduce an iterative procedure for estimating the unknown density of a random variable X from n independent copies of Y=X+ɛ, where ɛ is normally distributed measurement error independent of X. Mean integrated squared error convergence rates are studied over function classes arising from Fourier conditions. Minimax rates are derived for these classes. It is found that the sequence of estimators defined by the iterative procedure attains the optimal rates. In addition, it is shown that the sequence of estimators converges exponentially fast to an estimator within the class of deconvoluting kernel density estimators. The iterative scheme shows how, in practice, density estimation from indirect observations may be performed by simply correcting an appropriate ordinary density estimator. This allows to assess the effect that the perturbation due to contamination by ɛ has on the density to be estimated. We also suggest a method to select the smoothing parameter required by the iterative approach and, utilizing this method, perform a simulation study. 相似文献
11.
Understanding the effects of operational conditions and practices on productive efficiency can provide valuable economic and
managerial insights. The conventional approach is to use a two-stage method where the efficiency estimates are regressed on
contextual variables representing the operational conditions. The main problem of the two-stage approach is that it ignores
the correlations between inputs and contextual variables. To address this shortcoming, we build on the recently developed
regression interpretation of data envelopment analysis (DEA) to develop a new one-stage semi-nonparametric estimator that
combines the nonparametric DEA-style frontier with a regression model of the contextual variables. The new method is referred
to as stochastic semi-nonparametric envelopment of z variables data (StoNEZD). The StoNEZD estimator for the contextual variables is shown to be statistically consistent under
less restrictive assumptions than those required by the two-stage DEA estimator. Further, the StoNEZD estimator is shown to
be unbiased, asymptotically efficient, asymptotically normally distributed, and converge at the standard parametric rate of
order n
−1/2. Therefore, the conventional methods of statistical testing and confidence intervals apply for asymptotic inference. Finite
sample performance of the proposed estimators is examined through Monte Carlo simulations. 相似文献
12.
We consider a semiparametric method to estimate logistic regression models with missing both covariates and an outcome variable, and propose two new estimators. The first, which is based solely on the validation set, is an extension of the validation likelihood estimator of Breslow and Cain (Biometrika 75:11–20, 1988). The second is a joint conditional likelihood estimator based on the validation and non-validation data sets. Both estimators are semiparametric as they do not require any model assumptions regarding the missing data mechanism nor the specification of the conditional distribution of the missing covariates given the observed covariates. The asymptotic distribution theory is developed under the assumption that all covariate variables are categorical. The finite-sample properties of the proposed estimators are investigated through simulation studies showing that the joint conditional likelihood estimator is the most efficient. A cable TV survey data set from Taiwan is used to illustrate the practical use of the proposed methodology. 相似文献
13.
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
14.
Standard jackknife confidence intervals for a quantile Q
y
(β) are usually preferred to confidence intervals based on analytical variance estimators due to their operational simplicity.
However, the standard jackknife confidence intervals can give undesirable coverage probabilities for small samples sizes and
large or small values of β. In this paper confidence intervals for a population quantile based on several existing estimators of a quantile are derived.
These intervals are based on an approximation for the cumulative distribution function of a studentized quantile estimator.
Confidence intervals are empirically evaluated by using real data and some applications are illustrated. Results derived from
simulation studies show that proposed confidence intervals are narrower than confidence intervals based on the standard jackknife
technique, which assumes normal approximation. Proposed confidence intervals also achieve coverage probabilities above to
their nominal level. This study indicates that the proposed method can be an alternative to the asymptotic confidence intervals,
which can be unknown in practice, and the standard jackknife confidence intervals, which can have poor coverage probabilities
and give wider intervals. 相似文献
15.
Consider a family of distribution functions ${\{F(x, \theta),\,\theta \in \Theta\}}Consider a family of distribution functions {F(x, q), q ? Q}{\{F(x, \theta),\,\theta \in \Theta\}} . Suppose that there exists an estimator of the unknown parameter vector θ based on given data set. Then it is readily to obtain an estimator of any quantity given as an explicit function g(θ). Particularly, it is the case when the maximum likelihood estimator of θ is available. However, often some quantities of interest can not be expressed as an explicit function, rather it is determined
as an implicit function of θ. The present article studies this problem. Sufficient conditions are given for deriving estimators of these quantities. The
results are then applied to estimate change point of failure rate function, and change point of mean residual life function. 相似文献
16.
Suppose the observations (X
i,Y
i), i=1,…, n, are ϕ-mixing. The strong uniform convergence and convergence rate for the estimator of the regression function was studied
by serveral authors, e.g. G. Collomb (1984), L. Gy?rfi et al. (1989). But the optimal convergence rates are not reached unless
the Y
i are bounded or the E exp (a|Y
i|) are bounded for some a>0. Compared with the i.i.d. case the convergence of the Nadaraya-Watson estimator under ϕ-mixing variables needs strong moment
conditions. In this paper we study the strong uniform convergence and convergence rate for the improved kernel estimator of
the regression function which has been suggested by Cheng P. (1983). Compared with Theorem A in Y. P. Mack and B. Silverman
(1982) or Theorem 3.3.1 in L. Gy?rfi et al. (1989), we prove the convergence for this kind of estimators under weaker moment
conditions. The optimal convergence rate for the improved kernel estimator is attained under almost the same conditions of
Theorem 3.3.2 in L. Gy?rfi et al. (1989).
Received: September 1999 相似文献
17.
Minimax estimators andΓ-minimax estimators for a bounded normal mean under the lossl
p (θ, d)=|θ-d|p
Summary Let the random variableX be normal distributed with known varianceσ
2>0. It is supposed that the unknown meanθ is an element of a bounded intervalΘ. The problem of estimatingθ under the loss functionl
p
(θ, d)=|θ-d|
p
p≥2 is considered. In case the length of the intervalθ is sufficiently small the minimax estimator and theΓ(β, τ)-minimax estimator, whereΓ(β, τ) represents special vague prior information, are given. 相似文献
18.
Minimax estimation of a cumulative distribution function by converting to a parametric problem 总被引:2,自引:1,他引:2
Let X = (X
1,...,X
n
) be a sample from an unknown cumulative distribution function F defined on the real line
. The problem of estimating the cumulative distribution function F is considered using a decision theoretic approach. No assumptions are imposed on the unknown function F. A general method of finding a minimax estimator d(t;X) of F under the loss function of a general form is presented. The method of solution is based on converting the nonparametric problem
of searching for minimax estimators of a distribution function to the parametric problem of searching for minimax estimators
of the probability of success for a binomial distribution. The solution uses also the completeness property of the class of
monotone decision procedures in a monotone decision problem. Some special cases of the underlying problem are considered in
the situation when the loss function in the nonparametric problem is defined by a weighted squared, LINEX or a weighted absolute
error. 相似文献
19.
A frequently occurring problem is to find the maximum likelihood estimation (MLE) of p subject to p∈C (C⊂ P the probability vectors in R
k
). The problem has been discussed by many authors and they mainly focused when p is restricted by linear constraints or log-linear constraints. In this paper, we construct the relationship between the the
maximum likelihood estimation of p restricted by p∈C and EM algorithm and demonstrate that the maximum likelihood estimator can be computed through the EM algorithm (Dempster
et al. in J R Stat Soc Ser B 39:1–38, 1997). Several examples are analyzed by the proposed method. 相似文献
20.
This article considers the asymptotic estimation theory for the proportion in randomized response survey usinguncertain prior information (UPI) about the true proportion parameter which is assumed to be available on the basis of some sort of realistic conjecture. Three
estimators, namely, the unrestricted estimator, the shrinkage restricted estimator and an estimator based on a preliminary
test, are proposed. Their asymptotic mean squared errors are derived and compared. The relative dominance picture of the estimators
is presented. 相似文献