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1.
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
2.
David D. Hanagal 《Statistical Papers》2009,50(1):29-49
We propose bivariate Weibull regression model with frailty in which dependence is generated by a gamma or positive stable
or power variance function distribution. We assume that the bivariate survival data follows bivariate Weibull of Hanagal (Econ
Qual Control 19:83–90, 2004; Econ Qual Control 20:143–150, 2005a; Stat Pap 47:137–148, 2006a; Stat Methods, 2006b). There
are some interesting situations like survival times in genetic epidemiology, dental implants of patients and twin births (both
monozygotic and dizygotic) where genetic behavior (which is unknown and random) of patients follows known frailty distribution.
These are the situations which motivate to study this particular model.
David D. Hanagal is on leave from Department of Statistics, University of Pune, Pune 411007, India. 相似文献
3.
Arijit Chaudhuri Tasos C. Christofides Amitava Saha 《Statistical Methods and Applications》2009,18(3):389-418
In estimating the proportion of people bearing a sensitive attribute A, say, in a given community, following Warner’s (J Am Stat Assoc 60:63–69, 1965) pioneering work, certain randomized response
(RR) techniques are available for application. These are intended to ensure efficient and unbiased estimation protecting a
respondent’s privacy when it touches a person’s socially stigmatizing feature like rash driving, tax evasion, induced abortion,
testing HIV positive, etc. Lanke (Int Stat Rev 44:197–203, 1976), Leysieffer and Warner (J Am Stat Assoc 71:649–656, 1976),
Anderson (Int Stat Rev 44:213–217, 1976, Scand J Stat 4:11–19, 1977) and Nayak (Commun Stat Theor Method 23:3303–3321, 1994)
among others have discussed how maintenance of efficiency is in conflict with protection of privacy. In their RR-related activities
the sample selection is traditionally by simple random sampling (SRS) with replacement (WR). In this paper, an extension of
an essential similarity in case of general unequal probability sample selection even without replacement is reported. Large
scale surveys overwhelmingly employ complex designs other than SRSWR. So extension of RR techniques to complex designs is
essential and hence this paper principally refers to them. New jeopardy measures to protect revelation of secrecy presented
here are needed as modifications of those in the literature covering SRSWR alone. Observing that multiple responses are feasible
in addressing such a dichotomous situation especially with Kuk’s (Biometrika 77:436–438, 1990) and Christofides’ (Metrika
57:195–200, 2003) RR devices, an average of the response-specific jeopardizing measures is proposed. This measure which is
device dependent, could be regarded as a technical characteristic of the device and it should be made known to the participants
before they agree to use the randomization device.
The views expressed are the authors’, not of the organizations they work for. Prof Chaudhuri’s research is partially supported
by CSIR Grant No. 21(0539)/02/EMR-II. 相似文献
4.
Randomized response techniques are widely employed in surveys dealing with sensitive questions to ensure interviewee anonymity
and reduce nonrespondents rates and biased responses. Since Warner’s (J Am Stat Assoc 60:63–69, 1965) pioneering work, many
ingenious devices have been suggested to increase respondent’s privacy protection and to better estimate the proportion of
people, π
A
, bearing a sensitive attribute. In spite of the massive use of auxiliary information in the estimation of non-sensitive parameters,
very few attempts have been made to improve randomization strategy performance when auxiliary variables are available. Moving
from Zaizai’s (Model Assist Stat Appl 1:125–130, 2006) recent work, in this paper we provide a class of estimators for π
A
, for a generic randomization scheme, when the mean of a supplementary non-sensitive variable is known. The minimum attainable
variance bound of the class is obtained and the best estimator is also identified. We prove that the best estimator acts as
a regression-type estimator which is at least as efficient as the corresponding estimator evaluated without allowing for the
auxiliary variable. The general results are then applied to Warner and Simmons’ model. 相似文献
5.
Martin Slawski 《Statistics and Computing》2012,22(1):153-168
In view of its ongoing importance for a variety of practical applications, feature selection via ℓ
1-regularization methods like the lasso has been subject to extensive theoretical as well empirical investigations. Despite
its popularity, mere ℓ
1-regularization has been criticized for being inadequate or ineffective, notably in situations in which additional structural
knowledge about the predictors should be taken into account. This has stimulated the development of either systematically
different regularization methods or double regularization approaches which combine ℓ
1-regularization with a second kind of regularization designed to capture additional problem-specific structure. One instance
thereof is the ‘structured elastic net’, a generalization of the proposal in Zou and Hastie (J. R. Stat. Soc. Ser. B 67:301–320,
2005), studied in Slawski et al. (Ann. Appl. Stat. 4(2):1056–1080, 2010) for the class of generalized linear models. 相似文献
6.
The multivariate skew-t distribution (J Multivar Anal 79:93–113, 2001; J R Stat Soc, Ser B 65:367–389, 2003; Statistics 37:359–363,
2003) includes the Student t, skew-Cauchy and Cauchy distributions as special cases and the normal and skew–normal ones as limiting cases. In this paper,
we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis of repeated measures, pretest/post-test
data, under multivariate null intercept measurement error model (J Biopharm Stat 13(4):763–771, 2003) where the random errors
and the unobserved value of the covariate (latent variable) follows a Student t and skew-t distribution, respectively. The results and methods are numerically illustrated with an example in the field of
dentistry. 相似文献
7.
Marco Marozzi 《Statistical Papers》2012,53(1):61-72
A class of tests due to Shoemaker (Commun Stat Simul Comput 28: 189–205, 1999) for differences in scale which is valid for
a variety of both skewed and symmetric distributions when location is known or unknown is considered. The class is based on
the interquantile range and requires that the population variances are finite. In this paper, we firstly propose a permutation
version of it that does not require the condition of finite variances and is remarkably more powerful than the original one.
Secondly we solve the question of what quantile choose by proposing a combined interquantile test based on our permutation
version of Shoemaker tests. Shoemaker showed that the more extreme interquantile range tests are more powerful than the less
extreme ones, unless the underlying distributions are very highly skewed. Since in practice you may not know if the underlying
distributions are very highly skewed or not, the question arises. The combined interquantile test solves this question, is
robust and more powerful than the stand alone tests. Thirdly we conducted a much more detailed simulation study than that
of Shoemaker (1999) that compared his tests to the F and the squared rank tests showing that his tests are better. Since the F and the squared rank test are not good for differences in scale, his results suffer of such a drawback, and for this reason
instead of considering the squared rank test we consider, following the suggestions of several authors, tests due to Brown–Forsythe
(J Am Stat Assoc 69:364–367, 1974), Pan (J Stat Comput Simul 63:59–71, 1999), O’Brien (J Am Stat Assoc 74:877–880, 1979) and
Conover et al. (Technometrics 23:351–361, 1981). 相似文献
8.
The second-order least-squares estimator (SLSE) was proposed by Wang (Statistica Sinica 13:1201–1210, 2003) for measurement
error models. It was extended and applied to linear and nonlinear regression models by Abarin and Wang (Far East J Theor Stat
20:179–196, 2006) and Wang and Leblanc (Ann Inst Stat Math 60:883–900, 2008). The SLSE is asymptotically more efficient than
the ordinary least-squares estimator if the error distribution has a nonzero third moment. However, it lacks robustness against
outliers in the data. In this paper, we propose a robust second-order least squares estimator (RSLSE) against X-outliers. The RSLSE is highly efficient with high breakdown point and is asymptotically normally distributed. We compare
the RSLSE with other estimators through a simulation study. Our results show that the RSLSE performs very well. 相似文献
9.
Gabriela Beganu 《Statistical Methods and Applications》2007,16(3):347-356
It is known that the Henderson Method III (Biometrics 9:226–252, 1953) is of special interest for the mixed linear models
because the estimators of the variance components are unaffected by the parameters of the fixed factor (or factors). This
article deals with generalizations and minor extensions of the results obtained for the univariate linear models. A MANOVA
mixed model is presented in a convenient form and the covariance components estimators are given on finite dimensional linear
spaces. The results use both the usual parametric representations and the coordinate-free approach of Kruskal (Ann Math Statist
39:70–75, 1968) and Eaton (Ann Math Statist 41:528–538, 1970). The normal equations are generalized and it is given a necessary
and sufficient condition for the existence of quadratic unbiased estimators for covariance components in the considered model. 相似文献
10.
Alessio Farcomeni 《Statistical Methods and Applications》2006,15(1):43-73
In a breakthrough paper, Benjamini and Hochberg (J Roy Stat Soc Ser B 57:289–300, 1995) proposed a new error measure for multiple testing, the FDR; and developed a distribution-free procedure to control it under independence among the test statistics. In this paper we argue by extensive simulation and theoretical considerations that the assumption of independence is not needed. Along the lines of (Ann Stat 32:1035–1061, 2004b), we moreover provide a more powerful method, that exploits an estimator of the number of false nulls among the tests. We propose a whole family of iterative estimators that prove robust under dependence and independence between the test statistics. These estimators can be used to improve also classical multiple testing procedures, and in general to estimate the weight of a known component in a mixture distribution. Innovations are illustrated by simulations. 相似文献
11.
The selection of copulas is an important aspect of dependence modeling issues. In many practical applications, only a limited
number of copulas is tested and the copula with the best result for a goodness-of-fit test is chosen, which, however, does
not always lead to the best possible fit. In this paper we develop a practical and logical method for improving the goodness-of-fit
of a particular Archimedean copula by means of transforms. In order to do this, we introduce concordance invariant transforms which can also be tail dependence preserving, based on an analysis on the λ-function,
l = \fracjj¢{\lambda=\frac{\varphi}{\varphi'}}, where j{\varphi} is the Archimedean generator. The methodology is applied to the data set studied in Cook and Johnson (J R Stat Soc B 43:210–218,
1981) and Genest and Rivest (J Am Stat Assoc 88:1043–1043, 1993), where we improve the fit of the Frank copula and obtain
statistically significant results. 相似文献
12.
In this paper, A variance decomposition approach to quantify the effects of endogenous and exogenous variables for nonlinear
time series models is developed. This decomposition is taken temporally with respect to the source of variation. The methodology
uses Monte Carlo methods to affect the variance decomposition using the ANOVA-like procedures proposed in Archer et al. (J.
Stat. Comput. Simul. 58:99–120, 1997), Sobol’ (Math. Model. 2:112–118, 1990). The results of this paper can be used in investment problems, biomathematics and control theory, where nonlinear time series
with multiple inputs are encountered. 相似文献
13.
In this paper we present a review of population-based simulation for static inference problems. Such methods can be described as generating a collection of random variables {X
n
}
n=1,…,N
in parallel in order to simulate from some target density π (or potentially sequence of target densities). Population-based simulation is important as many challenging sampling problems
in applied statistics cannot be dealt with successfully by conventional Markov chain Monte Carlo (MCMC) methods. We summarize
population-based MCMC (Geyer, Computing Science and Statistics: The 23rd Symposium on the Interface, pp. 156–163, 1991; Liang and Wong, J. Am. Stat. Assoc. 96, 653–666, 2001) and sequential Monte Carlo samplers (SMC) (Del Moral, Doucet and Jasra, J. Roy. Stat. Soc. Ser. B 68, 411–436, 2006a), providing a comparison of the approaches. We give numerical examples from Bayesian mixture modelling (Richardson and Green,
J. Roy. Stat. Soc. Ser. B 59, 731–792, 1997). 相似文献
14.
Amitava Saha 《Statistical Papers》2010,51(2):349-355
Singh et al. (Stat Trans 6(4):515–522, 2003) proposed a modified unrelated question procedure and they also demonstrated that
the modified procedure is capable of producing a more efficient estimator of the population parameter π
A
, namely, the proportion of persons in a community bearing a sensitive character A when π
A
< 0.50. The development of Singh et al. (Stat Trans 6(4):515–522, 2003) is based on simple random samples with replacement
and on the assumption that π
B
, namely, the proportion of individuals bearing an unrelated innocuous character B is known. Due to these limitations, Singh et al.’s (Stat Trans 6(4):515–522, 2003) procedure cannot be used in practical
surveys where usually the sample units are chosen with varying selection probabilities. In this article, following Singh et
al. (Stat Trans 6(4):515–522, 2003) we propose an alternative RR procedure assuming that the population units are sampled
with unequal selection probabilities and that the value of π
B
is unknown. A numerical example comparing the performance of the proposed RR procedure under alternative sampling designs
is also reported. 相似文献
15.
Wellner JA 《Lifetime data analysis》2007,13(4):481-496
We review limit theory and inequalities for the Kaplan–Meier Kaplan and Meier (J Am Stat Assoc 53:457–481, 1958) product limit
estimator of a survival function on the whole line . Along the way we provide bounds for the constant in an interesting inequality due to Biotouzé et al. (Ann Inst H Poincaré
Probab Stat 35:735–763, 1999), and provide some numerical evidence in support of one of their conjectures.
Supported in part by NSF grant DMS-0503822 and by NI-AID grant 2R01 AI291968-04. 相似文献
16.
This note provides the asymptotic distribution of a Perron-type innovational outlier unit root test developed by Popp (J Stat
Comput Sim 78:1145–1161, 2008) in case of a shift in the intercept for non-trending data. In Popp (J Stat Comput Sim 78:1145–1161,
2008), only critical values for finite samples based on Monte Carlo techniques are tabulated. Using similar arguments as in
Zivot and Andrews (J Bus Econ Stat 10:251–270, 1992), weak convergence is shown for the test statistics. 相似文献
17.
Giuseppe Storti 《Statistical Methods and Applications》2008,17(2):251-274
The class of Multivariate BiLinear GARCH (MBL-GARCH) models is proposed and its statistical properties are investigated. The
model can be regarded as a generalization to a multivariate setting of the univariate BL-GARCH model proposed by Storti and
Vitale (Stat Methods Appl 12:19–40, 2003a; Comput Stat 18:387–400, 2003b). It is shown how MBL-GARCH models allow to account
for asymmetric effects in both conditional variances and correlations. An EM algorithm for the maximum likelihood estimation
of the model parameters is derived. Furthermore, in order to test for the appropriateness of the conditional variance and
covariance specifications, a set of robust conditional moments test statistics are defined. Finally, the effectiveness of
MBL-GARCH models in a risk management setting is assessed by means of an application to the estimation of the optimal hedge
ratio in futures hedging. 相似文献
18.
In this paper, we introduce an alternative stochastic restricted Liu estimator for the vector of parameters in a linear regression
model when additional stochastic linear restrictions on the parameter vector are assumed to hold. The new estimator is a generalization
of the ordinary mixed estimator (OME) (Durbin in J Am Stat Assoc 48:799–808, 1953; Theil and Goldberger in Int Econ Rev 2:65–78,
1961; Theil in J Am Stat Assoc 58:401–414, 1963) and Liu estimator proposed by Liu (Commun Stat Theory Methods 22:393–402,
1993). Necessary and sufficient conditions for the superiority of the new stochastic restricted Liu estimator over the OME,
the Liu estimator and the estimator proposed by Hubert and Wijekoon (Stat Pap 47:471–479, 2006) in the mean squared error
matrix (MSEM) sense are derived. Furthermore, a numerical example based on the widely analysed dataset on Portland cement
(Woods et al. in Ind Eng Chem 24:1207–1241, 1932) and a Monte Carlo evaluation of the estimators are also given to illustrate
some of the theoretical results. 相似文献
19.
We introduce a new family of skew-normal distributions that contains the skew-normal distributions introduced by Azzalini
(Scand J Stat 12:171–178, 1985), Arellano-Valle et al. (Commun Stat Theory Methods 33(7):1465–1480, 2004), Gupta and Gupta
(Test 13(2):501–524, 2008) and Sharafi and Behboodian (Stat Papers, 49:769–778, 2008). We denote this distribution by GBSN
n
(λ1, λ2). We present some properties of GBSN
n
(λ1, λ2) and derive the moment generating function. Finally, we use two numerical examples to illustrate the practical usefulness
of this distribution. 相似文献
20.
This article generalizes the Monte Carlo Markov Chain (MCMC) algorithm, based on the Gibbs weighted Chinese restaurant (gWCR)
process algorithm, for a class of kernel mixture of time series models over the Dirichlet process. This class of models is
an extension of Lo’s (Ann. Stat. 12:351–357, 1984) kernel mixture model for independent observations. The kernel represents a known distribution of time series conditional
on past time series and both present and past latent variables. The latent variables are independent samples from a Dirichlet
process, which is a random discrete (almost surely) distribution. This class of models includes an infinite mixture of autoregressive
processes and an infinite mixture of generalized autoregressive conditional heteroskedasticity (GARCH) processes. 相似文献