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1.
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
2.
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
3.
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
4.
I. Thomsen 《Metrika》1978,25(1):27-35
Summary The values of a variablex are assumed known for all elements in a finite population. Between this variable and another variableY, whose values are registered in a sample survey, there is the usual linear regression relationship. This paper considers problems of design and of estimation of the regression coefficienta and the interceptb. The followingGodambe type theorem is proved: There exists no minimum variance unbiased linear estimator ofa andb. We also derive that the usual estimators ofa andb have minimum variance if attention is restricted to the class of linear estimators unbiased in any given sample. 相似文献
5.
In this paper, the problem of estimating the precision matrix of a multivariate Pearson type II-model is considered. A new
class of estimators is proposed. Moreover, the risk functions of the usual and the proposed estimators are explicitly derived.
It is shown that the proposed estimator dominates the MLE and the unbiased estimator, under the quadratic loss function. A
simulation study is carried out and confirms these results. Improved estimator of tr (Σ
−1) is also obtained. 相似文献
6.
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
7.
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
8.
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
9.
Pearn et al. (Commun. Stat. Theory Methods, 27(4):985–1000, 1998) introduced the process accuracy index C
a
to measure the degree of process centering, the ability to cluster around the center. In this paper, we derive an explicit
form of the cumulative distribution function for the estimator [^(C)]a{\hat{C}_a } with the case of symmetric tolerances. Subsequently, the distributional and inferential properties of the estimated process
accuracy index C
a
are provided. Calculations of the critical values, P-values, and lower confidence bounds are developed for testing process accuracy. Further, a generalization of C
a
for the case with asymmetric tolerances is proposed to measure the process accuracy. Based on the results practitioners can
easily perform the testing of the process accuracy, and make reliable decisions on whether actions should be taken to improve
the process quality. An application is given to illustrate how we test the process accuracy using the actual data collected
from the factory. 相似文献
10.
MIDZUNO'S sampling procedure is considered where the first (n – 1) draws are carried out with simple random sampling without replacement and the nth draw with varying probabilities. It is shown that for this scheme, the best estimator in the HORVITZ–THOMPSON (1952) Tt–class of linear estimators exists and rejects the last draw. When MURTHY'S technique of unordering of an ordered estimator is employed, the rejected draw is restored and the unordered estimator is obtained. Surprisingly, this unordered estimator is the same as the unordered best estimator in the T1–class, derived for IKEDA–SEN'S sampling procedure. 相似文献
11.
Hira L. Koul 《Metrika》2002,55(1-2):75-90
Often in the robust analysis of regression and time series models there is a need for having a robust scale estimator of
a scale parameter of the errors. One often used scale estimator is the median of the absolute residuals s
1. It is of interest to know its limiting distribution and the consistency rate. Its limiting distribution generally depends
on the estimator of the regression and/or autoregressive parameter vector unless the errors are symmetrically distributed
around zero. To overcome this difficulty it is then natural to use the median of the absolute differences of pairwise residuals,
s
2, as a scale estimator. This paper derives the asymptotic distributions of these two estimators for a large class of nonlinear
regression and autoregressive models when the errors are independent and identically distributed. It is found that the asymptotic
distribution of a suitably standardizes s
2 is free of the initial estimator of the regression/autoregressive parameters. A similar conclusion also holds for s
1 in linear regression models through the origin and with centered designs, and in linear autoregressive models with zero mean
errors.
This paper also investigates the limiting distributions of these estimators in nonlinear regression models with long memory
moving average errors. An interesting finding is that if the errors are symmetric around zero, then not only is the limiting
distribution of a suitably standardized s
1 free of the regression estimator, but it is degenerate at zero. On the other hand a similarly standardized s
2 converges in distribution to a normal distribution, regardless of the errors being symmetric or not. One clear conclusion
is that under the symmetry of the long memory moving average errors, the rate of consistency for s
1 is faster than that of s
2. 相似文献
12.
The Baysian estimation of the mean vector θ of a p-variate normal distribution under linear exponential (LINEX) loss function is studied when as a special restricted model, it is suspected that for a p × r known matrix Z the hypothesis θ = Zβ, ${\beta\in\Re^r}The Baysian estimation of the mean vector θ of a p-variate normal distribution under linear exponential (LINEX) loss function is studied when as a special restricted
model, it is suspected that for a p × r known matrix Z the hypothesis θ = Zβ, b ? ?r{\beta\in\Re^r} may hold. In this area we show that the Bayes and empirical Bayes estimators dominate the unrestricted estimator (when nothing
is known about the mean vector θ). 相似文献
13.
Estimators of parameters in semi-parametric left truncated and right censored regression models are proposed. In contrast to the majority of existing estimators, the proposed estimators do not require the error term of the regression model to have a symmetric distribution. In addition the estimators use asymmetric “trimming” of observations. Consistency and asymptotic normality of the estimators are shown. Finite sample properties are considered in a small simulation study. For the left truncated case, an empirical application illustrates the usefulness of the estimator. 相似文献
14.
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
15.
Dr. A. Chaudhuri 《Metrika》1992,39(1):341-357
Summary General procedures are described to generate quantitative randomized response (RR) required to estimate the finite population
total of a sensitive variable. Permitting sample selection with arbitrary probabilities a formula for the mean square error
(MSE) of a linear estimator of total based on RR is noted indicating the simple modification over one that might be based
on direct response (DR) if the latter were available. A general formula for an unbiased estimator of the MSE is presented.
A simple approximation is proposed in case the RR ratio estimator is employed based on a simple random sample (SRS) taken
without replacement (WOR). Among sampling strategies employing unbiased but not necessarily linear estimators based on RR,
certain optimal ones are identified under two alternative models analogously to well-known counterparts based on DR, if available.
Unlike Warner’s (1965) treatment of categorical RR we consider quantitative RR here. 相似文献
16.
S. G. Prabhu Ajgaonkar 《Metrika》1972,18(1):15-20
Summary The variance function of a linear estimator can be expressed into a quadratic form. The present paper presents classes of
estimators of this quadratic form along the lines implicitly suggested byHorvitz andThompson [1952] while formulating the classes of linear estimators. Accordingly it is noted that there exist nine principal classes
of estimators out of which one principal class is examined in detail. Furthermore to illustrate the theory an example is considered
where the expression for a unique estimator variance of the best estimator in theT
1 class is derived. 相似文献
17.
In this paper, a compromised imputation procedure has been suggested. The estimator of mean obtained from compromised imputation
remains better than the estimators obtained from ratio method of imputation and mean method of imputation. An idea to form
“Warm Deck Method” of imputation has also been suggested.
Received: July 1998 相似文献
18.
Conditional nonparametric frontier models for convex and nonconvex technologies: a unifying approach 总被引:1,自引:1,他引:1
The explanation of productivity differentials is very important to identify the economic conditions that create inefficiency
and to improve managerial performance. In the literature two main approaches have been developed: one-stage approaches and
two-stage approaches. Daraio and Simar (2005, J Prod Anal 24(1):93–121) propose a fully nonparametric methodology based on
conditional FDH and conditional order-m frontiers without any convexity assumption on the technology. However, convexity has always been assumed in mainstream production
theory and general equilibrium. In addition, in many empirical applications, the convexity assumption can be reasonable and
sometimes natural. Lead by these considerations, in this paper we propose a unifying approach to introduce external-environmental
variables in nonparametric frontier models for convex and nonconvex technologies. Extending earlier contributions by Daraio
and Simar (2005, J Prod Anal 24(1):93–121) as well as Cazals et al. (2002, J Econometrics 106:1–25), we introduce a conditional
DEA estimator, i.e., an estimator of production frontier of DEA type conditioned to some external-environmental variables
which are neither inputs nor outputs under the control of the producer. A robust version of this conditional estimator is
proposed too. These various measures of efficiency provide also indicators of convexity which we illustrate using simulated
and real data.
Cinzia Daraio received Research support from the Italian Ministry of Education Research on Innovation Systems Project (iRis)
“The reorganization of the public system of research for the technological transfer: governance, tools and interventions”
and from the Italian Ministry of Educational Research Project (MIUR 40% 2004) “System spillovers on the competitiveness of
Italian economy: quantitative analysis for sectoral policies” which are acknowledged.
Léopold Simar received Research support from the “Interuniversity Attraction Pole”, Phase V (No. P5/24) from the Belgian Government
(Belgian Science Policy) is acknowledged. 相似文献
19.
Two families of kurtosis measures are defined as K
1(b)=E[ab
−|z|] and K
2(b)=E[a(1−|z|b)] where z denotes the standardized variable and a is a normalizing constant chosen such that the kurtosis is equal to 3 for normal distributions. K
2(b) is an extension of Stavig's robust kurtosis. As with Pearson's measure of kurtosis β2=E[z
4], both measures are expected values of continuous functions of z that are even, convex or linear and strictly monotonic in ℜ− and in ℜ+. In contrast to β2, our proposed kurtosis measures give more importance to the central part of the distribution instead of the tails. Tests
of normality based on these new measures are more sensitive with respect to the peak of the distribution. K
1(b) and K
2(b) satisfy Van Zwet's ordering and correlate highly with other kurtosis measures such as L-kurtosis and quantile kurtosis.
RID="*"
ID="*" The authors thank the referees for their insightful comments that significantly improved the clarity of the article. 相似文献
20.
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