共查询到20条相似文献,搜索用时 31 毫秒
1.
Klaus Ziegler 《Metrika》2001,53(2):141-170
In the nonparametric regression model with random design and based on i.i.d. pairs of observations (X
i, Y
i), where the regression function m is given by m(x)=?(Y
i|X
i=x), estimation of the location θ (mode) of a unique maximum of m by the location of a maximum of the Nadaraya-Watson kernel estimator for the curve m is considered. In order to obtain asymptotic confidence intervals for θ, the suitably normalized distribution of is bootstrapped in two ways: we present a paired bootstrap (PB) where resampling is done from the empirical distribution
of the pairs of observations and a smoothed paired bootstrap (SPB) where the bootstrap variables are generated from a smooth
bivariate density based on the pairs of observations. While the PB requires only relatively small computational effort when
carried out in practice, it is shown to work only in the case of vanishing asymptotic bias, i.e. of “undersmoothing” when
compared to optimal smoothing for mode estimation. On the other hand, the SPB, although causing more intricate computations,
is able to capture the correct amount of bias if the pilot estimator for m oversmoothes.
Received: May 2000 相似文献
2.
Bernhard Klar 《Metrika》1999,49(1):53-69
This paper presents a new widely applicable omnibus test for discrete distributions which is based on the difference between
the integrated distribution function Ψ(t)=∫t
∞ (1−F(x))dx and its empirical counterpart. A bootstrap version of the test for common lattice models has accurate error rates even for
small samples and exhibits high power with respect to competitive procedures over a large range of alternatives.
Received: July 1998 相似文献
3.
We study the construction of confidence intervals for efficiency levels of individual firms in stochastic frontier models
with panel data. The focus is on bootstrapping and related methods. We start with a survey of various versions of the bootstrap.
We also propose a simple parametric alternative in which one acts as if the␣identity of the best firm is known. Monte Carlo
simulations indicate that the parametric method works better than the␣percentile bootstrap, but not as well as bootstrap methods
that make bias corrections. All of these methods are valid␣only for large time-series sample size (T), and correspondingly none of the methods yields very accurate confidence intervals except when T is large enough that the identity of the best firm is clear. We also present empirical results for two well-known data sets.
相似文献
4.
5.
A distributionF is said to be “more IFR” than another distributionG ifG
−1
F is convex. WhenF(0) =G(0) = 0, the problem of testingH
0 :F(x) =G (θx) for someθ > 0 andx ⩾ 0, against the alternativeH
A:F is more IFR thanG, is considered in this paper. Both cases, whenG is completely specified (one-sample case) and when it is not specified but a random sample form it is available (two-sample
case) are considered. The proposed tests are based onU-statistics. The asymptotic relative efficiency of the tests are compared with several other tests and the test statistics
remain asymptotically normal under certain dependency assumptions.
Research supported in part by a grant from the US Air Force Office of Scientific Research. 相似文献
6.
Prof. Dr. W. Stute 《Metrika》1992,39(1):257-267
LetX
1, ...,X
n
be an i.i.d. sample from some parametric family {θ :θ (Θ} of densities. In the random censorship model one observesZ
i
=min (X
i
,Y
i
) andδ
i
=1{
x
i
≤Y
i}, whereY
i
is a censoring variable being independent ofX
i
. In this paper we investigate the strong consistency ofθ
n
maximizing the modified likelihood function based on (Z
i
,δ
i
, 1≤i≤n. The main result constitutes an extension of Wald’s theorem for complete data to censored data.
Work partially supported by the “Deutsche Forschungsgemeinschaft”. 相似文献
7.
Let (W
n
,n ≥ 0) denote the sequence of weak records from a distribution with support S = { α0,α1,...,α
N
}. In this paper, we consider regression functions of the form ψ
n
(x) = E(h(W
n
) |W
n+1 = x), where h(·) is some strictly increasing function. We show that a single function ψ
n
(·) determines F uniquely up to F(α0). Then we derive an inversion formula which enables us to obtain F from knowledge of ψ
n
(·), ψ
n-1(·), h(·) and F(α0). 相似文献
8.
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
9.
In this article, the unit root test for the AR(1) model with dependent residuals is considered. We adopt a bootstrap procedure
to bootstrap the residuals with bootstrap sample size m less than the size n of the original sample. Under the assumptions that m → ∞ and m/n → 0, the convergence in probability of the bootstrap distribution function is established.
Research supported by National Natural Science Foundation of China (No. 10471126) 相似文献
10.
Some notions ofL
p
(μ)-completeness resp. totally L
p
(μ)-completeness (1≦p≦∞) are characterized for families of probability distributions dominated by aσ-finite measureμ and their conservation with respect to direct products is proved. Furthermore, it is shown that totallyL
∞(μ)-completeness does not implyL
1(μ)-completeness and that there are families of probability distributions in the i.i.d. case induced by the order statistic,
which are L1(μ)-complete but not totallyL
∞(μ)-complete. 相似文献
11.
LetX
1,X
2, ...,X
n
(n≥3) be a random sample on a random variableX with distribution functionF having a unique continuous inverseF
−1 over (a,b), −∞≤a<b≤∞ the support ofF. LetX
1:n
<X
2:n
<...<X
n:n
be the corresponding order statistics. Letg be a nonconstant continuous function over (a,b). Then for some functionG over (a, b) and for some positive integersr ands, 1<r+1<s≤n
相似文献
12.
Gábor Szűcs 《Metrika》2008,67(1):63-81
Statistical procedures based on the estimated empirical process are well known for testing goodness of fit to parametric distribution
families. These methods usually are not distribution free, so that the asymptotic critical values of test statistics depend
on unknown parameters. This difficulty may be overcome by the utilization of parametric bootstrap procedures. The aim of this
paper is to prove a weak approximation theorem for the bootstrapped estimated empirical process under very general conditions,
which allow both the most important continuous and discrete distribution families, along with most parameter estimation methods. The emphasis is on families of discrete distributions,
and simulation results for families of negative binomial distributions are also presented. 相似文献
13.
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
14.
Estimates of technical inefficiency based on fixed effects estimation of the stochastic frontier model with panel data are
biased upward. Previous work has attempted to correct this bias using the bootstrap, but in simulations the bootstrap corrects
only part of the bias. The usual panel jackknife is based on the assumption that the bias is of order T
−1 and is similar to the bootstrap. We show that when there is a tie or a near tie for the best firm, the bias is of order T
−1/2, not T
−1, and this calls for a different form of the jackknife. The generalized panel jackknife is quite successful in removing the
bias. However, the resulting estimates have a large variance. 相似文献
15.
The paper proposes a framework for modelling cointegration in fractionally integrated processes, and considers methods for testing the existence of cointegrating relationships using the parametric bootstrap. In these procedures, ARFIMA models are fitted to the data, and the estimates used to simulate the null hypothesis of non-cointegration in a vector autoregressive modelling framework. The simulations are used to estimate p-values for alternative regression-based test statistics, including the F goodness-of-fit statistic, the Durbin–Watson statistic and estimates of the residual d. The bootstrap distributions are economical to compute, being conditioned on the actual sample values of all but the dependent variable in the regression. The procedures are easily adapted to test stronger null hypotheses, such as statistical independence. The tests are not in general asymptotically pivotal, but implemented by the bootstrap, are shown to be consistent against alternatives with both stationary and nonstationary cointegrating residuals. As an example, the tests are applied to the series for UK consumption and disposable income. The power properties of the tests are studied by simulations of artificial cointegrating relationships based on the sample data. The F test performs better in these experiments than the residual-based tests, although the Durbin–Watson in turn dominates the test based on the residual d. 相似文献
16.
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
17.
Rainer Göb 《Metrika》1997,45(1):131-169
Consider lots of discrete items 1, 2, …,N with quality characteristicsx
1,x
2, …,x
N
. Leta be a target value for item quality. Lot quality is identified with the average square deviation
from target per item in the lot (lot average square deviation from target). Under economic considerations this is an appropriate
lot quality indicator if the loss respectively the profit incurred from an item is a quadratic function ofx
i
−a. The present paper investigates tests of significance on the lot average square deviationz under the following assumptions: The lot is a subsequence of a process of production, storage, transport; the random quality
characteristics of items resulting from this process are i.i.d. with normal distributionN(μ, σ
2); the target valuea coincides with the process meanμ. 相似文献
18.
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
19.
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
20.
LetX
1,…,X
m
andY
1,…,Y
n
be two independent samples from continuous distributionsF andG respectively. Using a Hoeffding (1951) type theorem, we obtain the distributions of the vector S=(S
(1),…,S
(n)), whereS
(j)=# (X
i
’s≤Y
(j)) andY
(j) is thej-th order statistic ofY sample, under three truncation models: (a)G is a left truncation ofF orG is a right truncation ofF, (b)F is a right truncation ofH andG is a left truncation ofH, whereH is some continuous distribution function, (c)G is a two tail truncation ofF. Exploiting the relation between S and the vectorR of the ranks of the order statistics of theY-sample in the pooled sample, we can obtain exact distributions of many rank tests. We use these to compare powers of the
Hajek test (Hajek 1967), the Sidak Vondracek test (1957) and the Mann-Whitney-Wilcoxon test.
We derive some order relations between the values of the probagility-functions under each model. Hence find that the tests
based onS
(1) andS
(n) are the UMP rank tests for the alternative (a). We also find LMP rank tests under the alternatives (b) and (c). 相似文献
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