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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.
Censored regression quantile (CRQ) methods provide a powerful and flexible approach to the analysis of censored survival data
when standard linear models are felt to be appropriate. In many cases however, greater flexibility is desired to go beyond
the usual multiple regression paradigm. One area of common interest is that of partially linear models: one (or more) of the
explanatory covariates are assumed to act on the response through a non-linear function. Here the CRQ approach of Portnoy
(J Am Stat Assoc 98:1001–1012, 2003) is extended to this partially linear setting. Basic consistency results are presented.
A simulation experiment and unemployment example justify the value of the partially linear approach over methods based on
the Cox proportional hazards model and on methods not permitting nonlinearity. 相似文献
3.
Shen PS 《Lifetime data analysis》2012,18(1):1-18
The cumulative incidence function provides intuitive summary information about competing risks data. Via a mixture decomposition
of this function, Chang and Wang (Statist. Sinca 19:391–408, 2009) study how covariates affect the cumulative incidence probability of a particular failure type at a chosen time point. Without
specifying the corresponding failure time distribution, they proposed two estimators and derived their large sample properties.
The first estimator utilized the technique of weighting to adjust for the censoring bias, and can be considered as an extension
of Fine’s method (J R Stat Soc Ser B 61: 817–830, 1999). The second used imputation and extends the idea of Wang (J R Stat Soc Ser B 65: 921–935, 2003) from a nonparametric setting to the current regression framework. In this article, when covariates take only discrete values,
we extend both approaches of Chang and Wang (Statist Sinca 19:391–408, 2009) by allowing left truncation. Large sample properties of the proposed estimators are derived, and their finite sample performance
is investigated through a simulation study. We also apply our methods to heart transplant survival data. 相似文献
4.
We develop a Bayesian analysis for the class of Birnbaum–Saunders nonlinear regression models introduced by Lemonte and Cordeiro
(Comput Stat Data Anal 53:4441–4452, 2009). This regression model, which is based on the Birnbaum–Saunders distribution (Birnbaum and Saunders in J Appl Probab 6:319–327,
1969a), has been used successfully to model fatigue failure times. We have considered a Bayesian analysis under a normal-gamma
prior. Due to the complexity of the model, Markov chain Monte Carlo methods are used to develop a Bayesian procedure for the
considered model. We describe tools for model determination, which include the conditional predictive ordinate, the logarithm
of the pseudo-marginal likelihood and the pseudo-Bayes factor. Additionally, case deletion influence diagnostics is developed
for the joint posterior distribution based on the Kullback–Leibler divergence. Two empirical applications are considered in
order to illustrate the developed procedures. 相似文献
5.
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
6.
Scale mixtures of normal distributions form a class of symmetric thick-tailed distributions that includes the normal one as
a special case. In this paper we consider local influence analysis for measurement error models (MEM) when the random error
and the unobserved value of the covariates jointly follow scale mixtures of normal distributions, providing an appealing robust
alternative to the usual Gaussian process in measurement error models. In order to avoid difficulties in estimating the parameter
of the mixing variable, we fixed it previously, as recommended by Lange et al. (J Am Stat Assoc 84:881–896, 1989) and Berkane
et al. (Comput Stat Data Anal 18:255–267, 1994). The local influence method is used to assess the robustness aspects of the
parameter estimates under some usual perturbation schemes. However, as the observed log-likelihood associated with this model
involves some integrals, Cook’s well–known approach may be hard to apply to obtain measures of local influence. Instead, we
develop local influence measures following the approach of Zhu and Lee (J R Stat Soc Ser B 63:121–126, 2001), which is based
on the EM algorithm. Results obtained from a real data set are reported, illustrating the usefulness of the proposed methodology,
its relative simplicity, adaptability and practical usage. 相似文献
7.
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
8.
This paper proposes a new probabilistic classification algorithm using a Markov random field approach. The joint distribution
of class labels is explicitly modelled using the distances between feature vectors. Intuitively, a class label should depend
more on class labels which are closer in the feature space, than those which are further away. Our approach builds on previous
work by Holmes and Adams (J. R. Stat. Soc. Ser. B 64:295–306, 2002; Biometrika 90:99–112, 2003) and Cucala et al. (J. Am. Stat. Assoc. 104:263–273, 2009). Our work shares many of the advantages of these approaches in providing a probabilistic basis for the statistical inference.
In comparison to previous work, we present a more efficient computational algorithm to overcome the intractability of the
Markov random field model. The results of our algorithm are encouraging in comparison to the k-nearest neighbour algorithm. 相似文献
9.
A marginal regression approach for correlated censored survival data has become a widely used statistical method. Examples
of this approach in survival analysis include from the early work by Wei et al. (J Am Stat Assoc 84:1065–1073, 1989) to more
recent work by Spiekerman and Lin (J Am Stat Assoc 93:1164–1175, 1998). This approach is particularly useful if a covariate’s
population average effect is of primary interest and the correlation structure is not of interest or cannot be appropriately
specified due to lack of sufficient information. In this paper, we consider a semiparametric marginal proportional hazard
mixture cure model for clustered survival data with a surviving or “cure” fraction. Unlike the clustered data in previous
work, the latent binary cure statuses of patients in one cluster tend to be correlated in addition to the possible correlated
failure times among the patients in the cluster who are not cured. The complexity of specifying appropriate correlation structures
for the data becomes even worse if the potential correlation between cure statuses and the failure times in the cluster has
to be considered, and thus a marginal regression approach is particularly attractive. We formulate a semiparametric marginal
proportional hazards mixture cure model. Estimates are obtained using an EM algorithm and expressions for the variance–covariance
are derived using sandwich estimators. Simulation studies are conducted to assess finite sample properties of the proposed
model. The marginal model is applied to a multi-institutional study of local recurrences of tonsil cancer patients who received
radiation therapy. It reveals new findings that are not available from previous analyses of this study that ignored the potential
correlation between patients within the same institution. 相似文献
10.
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
11.
Andrew C. Titman 《Lifetime data analysis》2009,15(4):519-533
We develop an improved approximation to the asymptotic null distribution of the goodness-of-fit tests for panel observed multi-state
Markov models (Aguirre-Hernandez and Farewell, Stat Med 21:1899–1911, 2002) and hidden Markov models (Titman and Sharples,
Stat Med 27:2177–2195, 2008). By considering the joint distribution of the grouped observed transition counts and the maximum
likelihood estimate of the parameter vector it is shown that the distribution can be expressed as a weighted sum of independent
c21{\chi^2_1} random variables, where the weights are dependent on the true parameters. The performance of this approximation for finite
sample sizes and where the weights are calculated using the maximum likelihood estimates of the parameters is considered through
simulation. In the scenarios considered, the approximation performs well and is a substantial improvement over the simple
χ
2 approximation. 相似文献
12.
This paper discusses the analysis of interval-censored failure time data, which has recently attracted a great amount of attention
(Li and Pu, Lifetime Data Anal 9:57–70, 2003; Sun, The statistical analysis of interval-censored data, 2006; Tian and Cai,
Biometrika 93(2):329–342, 2006; Zhang et al., Can J Stat 33:61–70, 2005). Interval-censored data mean that the survival time
of interest is observed only to belong to an interval and they occur in many fields including clinical trials, demographical
studies, medical follow-up studies, public health studies and tumorgenicity experiments. A major difficulty with the analysis
of interval-censored data is that one has to deal with a censoring mechanism that involves two related variables. For the
inference, we present a transformation approach that transforms general interval-censored data into current status data, for
which one only needs to deal with one censoring variable and the inference is thus much easy. We apply this general idea to
regression analysis of interval-censored data using the additive hazards model and numerical studies indicate that the method
performs well for practical situations. An illustrative example is provided. 相似文献
13.
This paper considers the problem of modeling migraine severity assessments and their dependence on weather and time characteristics.
We take on the viewpoint of a patient who is interested in an individual migraine management strategy. Since factors influencing
migraine can differ between patients in number and magnitude, we show how a patient’s headache calendar reporting the severity
measurements on an ordinal scale can be used to determine the dominating factors for this special patient. One also has to
account for dependencies among the measurements. For this the autoregressive ordinal probit (AOP) model of Müller and Czado
(J Comput Graph Stat 14: 320–338, 2005) is utilized and fitted to a single patient’s migraine data by a grouped move multigrid Monte Carlo (GM-MGMC) Gibbs sampler.
Initially, covariates are selected using proportional odds models. Model fit and model comparison are discussed. A comparison
with proportional odds specifications shows that the AOP models are preferred. 相似文献
14.
Variable selection is an important issue in all regression analysis and in this paper, we discuss this in the context of regression
analysis of recurrent event data. Recurrent event data often occur in long-term studies in which individuals may experience
the events of interest more than once and their analysis has recently attracted a great deal of attention (Andersen et al.,
Statistical models based on counting processes, 1993; Cook and Lawless, Biometrics 52:1311–1323, 1996, The analysis of recurrent
event data, 2007; Cook et al., Biometrics 52:557–571, 1996; Lawless and Nadeau, Technometrics 37:158-168, 1995; Lin et al.,
J R Stat Soc B 69:711–730, 2000). However, it seems that there are no established approaches to the variable selection with
respect to recurrent event data. For the problem, we adopt the idea behind the nonconcave penalized likelihood approach proposed
in Fan and Li (J Am Stat Assoc 96:1348–1360, 2001) and develop a nonconcave penalized estimating function approach. The proposed
approach selects variables and estimates regression coefficients simultaneously and an algorithm is presented for this process.
We show that the proposed approach performs as well as the oracle procedure in that it yields the estimates as if the correct
submodel was known. Simulation studies are conducted for assessing the performance of the proposed approach and suggest that
it works well for practical situations. The proposed methodology is illustrated by using the data from a chronic granulomatous
disease study. 相似文献
15.
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
16.
On locally optimal invariant unbiased tests for the variance components ratio in mixed linear models
Andrzej Michalski 《Statistical Papers》2009,50(4):855-868
In the paper the problem of testing of two-sided hypotheses for variance components in mixed linear models is considered.
When the uniformly most powerful invariant test does not exist (see e.g. Das and Sinha, in Proceedings of the second international
Tampere conference in statistics, 1987; Gnot and Michalski, in Statistics 25:213–223, 1994; Michalski and Zmyślony, in Statistics
27:297–310, 1996) then to conduct the optimal statistical inference on model parameters a construction of a test with locally
best properties is desirable, cf. Michalski (in Tatra Mountains Mathematical Publications 26:1–21, 2003). The main goal of
this article is the construction of the locally best invariant unbiased test for a single variance component (or for a ratio
of variance components). The result has been obtained utilizing Andersson’s and Wijsman’s approach connected with a representation
of density function of maximal invariant (Andersson, in Ann Stat 10:955–961, 1982; Wijsman, in Proceedings of fifth Berk Symp
Math Statist Prob 1:389–400, 1967; Wijsman, in Sankhyā A 48:1–42, 1986; Khuri et al., in Statistical tests for mixed linear models, 1998) and from generalized Neyman–Pearson Lemma
(Dantzig and Wald, in Ann Math Stat 22:87–93, 1951; Rao, in Linear statistical inference and its applications, 1973). One
selected real example of an unbalanced mixed linear model is given, for which the power functions of the LBIU test and Wald’s
test (the F-test in ANOVA model) are computed, and compared with the attainable upper bound of power obtained by using Neyman–Pearson
Lemma. 相似文献
17.
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
18.
This paper considers the analysis of multivariate survival data where the marginal distributions are specified by semiparametric
transformation models, a general class including the Cox model and the proportional odds model as special cases. First, consideration
is given to the situation where the joint distribution of all failure times within the same cluster is specified by the Clayton–Oakes
model (Clayton, Biometrika 65:141–151, l978; Oakes, J R Stat Soc B 44:412–422, 1982). A two-stage estimation procedure is adopted by first estimating the marginal parameters under the independence working
assumption, and then the association parameter is estimated from the maximization of the full likelihood function with the
estimators of the marginal parameters plugged in. The asymptotic properties of all estimators in the semiparametric model
are derived. For the second situation, the third and higher order dependency structures are left unspecified, and interest
focuses on the pairwise correlation between any two failure times. Thus, the pairwise association estimate can be obtained
in the second stage by maximizing the pairwise likelihood function. Large sample properties for the pairwise association are
also derived. Simulation studies show that the proposed approach is appropriate for practical use. To illustrate, a subset
of the data from the Diabetic Retinopathy Study is used. 相似文献
19.
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
20.
Quantile regression, including median regression, as a more completed statistical model than mean regression, is now well
known with its wide spread applications. Bayesian inference on quantile regression or Bayesian quantile regression has attracted
much interest recently. Most of the existing researches in Bayesian quantile regression focus on parametric quantile regression,
though there are discussions on different ways of modeling the model error by a parametric distribution named asymmetric Laplace
distribution or by a nonparametric alternative named scale mixture asymmetric Laplace distribution. This paper discusses Bayesian
inference for nonparametric quantile regression. This general approach fits quantile regression curves using piecewise polynomial
functions with an unknown number of knots at unknown locations, all treated as parameters to be inferred through reversible
jump Markov chain Monte Carlo (RJMCMC) of Green (Biometrika 82:711–732, 1995). Instead of drawing samples from the posterior, we use regression quantiles to create Markov chains for the estimation of
the quantile curves. We also use approximate Bayesian factor in the inference. This method extends the work in automatic Bayesian
mean curve fitting to quantile regression. Numerical results show that this Bayesian quantile smoothing technique is competitive
with quantile regression/smoothing splines of He and Ng (Comput. Stat. 14:315–337, 1999) and P-splines (penalized splines) of Eilers and de Menezes (Bioinformatics 21(7):1146–1153, 2005). 相似文献