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1.
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
2.
Recurrent event data occur in many clinical and observational studies (Cook and Lawless, Analysis of recurrent event data,
2007) and in these situations, there may exist a terminal event such as death that is related to the recurrent event of interest
(Ghosh and Lin, Biometrics 56:554–562, 2000; Wang et al., J Am Stat Assoc 96:1057–1065, 2001; Huang and Wang, J Am Stat Assoc
99:1153–1165, 2004; Ye et al., Biometrics 63:78–87, 2007). In addition, sometimes there may exist more than one type of recurrent
events, that is, one faces multivariate recurrent event data with some dependent terminal event (Chen and Cook, Biostatistics
5:129–143, 2004). It is apparent that for the analysis of such data, one has to take into account the dependence both among
different types of recurrent events and between the recurrent and terminal events. In this paper, we propose a joint modeling
approach for regression analysis of the data and both finite and asymptotic properties of the resulting estimates of unknown
parameters are established. The methodology is applied to a set of bivariate recurrent event data arising from a study of
leukemia patients. 相似文献
3.
Angelika van der Linde 《AStA Advances in Statistical Analysis》2009,93(3):307-333
Recently, van der Linde (Comput. Stat. Data Anal. 53:517–533, 2008) proposed a variational algorithm to obtain approximate Bayesian inference in functional principal components analysis (FPCA),
where the functions were observed with Gaussian noise. Generalized FPCA under different noise models with sparse longitudinal
data was developed by Hall et al. (J. R. Stat. Soc. B 70:703–723, 2008), but no Bayesian approach is available yet. It is demonstrated that an adapted version of the variational algorithm can
be applied to obtain a Bayesian FPCA for canonical parameter functions, particularly log-intensity functions given Poisson
count data or logit-probability functions given binary observations. To this end a second order Taylor expansion of the log-likelihood,
that is, a working Gaussian distribution and hence another step of approximation, is used. Although the approach is conceptually
straightforward, difficulties can arise in practical applications depending on the accuracy of the approximation and the information
in the data. A modified algorithm is introduced generally for one-parameter exponential families and exemplified for binary
and count data. Conditions for its successful application are discussed and illustrated using simulated data sets. Also an
application with real data is presented. 相似文献
4.
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
5.
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
6.
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
7.
The Fisher information matrix for a mixture of two Laplace distributions is derived. Numerical tabulations of the matrix and
a computer program are provided for practical purposes. The work is motivated by two real–life examples discussed in Hsu (Appl
Stat 28:62–72, 1979) and Bhowmick et al. (Biostatistics 7:630–641, 2006).
相似文献
8.
Soo Hak Sung 《Statistical Papers》2012,53(1):73-82
In this paper, we obtain a complete convergence result for weighted sums of negatively dependent random variables under mild
conditions of weights. This result generalizes and improves the result of Zarei and Jabbari (Stat Papers doi:, 2009). Our result also extends the result of Taylor et al. (Stoch Anal Appl 20:643–656, 2002) on unweighted average to a
weighted average. 相似文献
9.
In this paper we introduce a new extension for the Birnbaum–Saunder distribution based on the family of the epsilon-skew-symmetric
distributions studied in Arellano-Valle et al. (J Stat Plan Inference 128(2):427–443, 2005). The extension allows generating
Birnbaun–Saunders type distributions able to deal with extreme or outlying observations (Dupuis and Mills, IEEE Trans Reliab
47:88–95, 1998). Basic properties such as moments and Fisher information matrix are also studied. Results of a real data application
are reported illustrating good fitting properties of the proposed model. 相似文献
10.
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
11.
The conditional specification technique introduced by Arnold et al. (Conditional specification of statistical models. Springer
series in statistics. Springer, New York, 1999) was used in Sarabia et al. (Astin Bull 34(1):85–98, 2004) to obtain bonus-malus
premiums. The Poisson distribution for which the parameter is a function of the classical structure parameter was used and
a new class of prior distributions appeared in a natural way. This model contains, as a particular case, the classical compound
Poisson model. In the present paper, the Bayesian robustness of this new model is examined and found to be much more robust
than in the classical model in Gómez et al. (Insur Math Econ 31:105–113, 2002). For the present study, the moment conditions
on the prior distribution are required. Examples, with real data, are given to illustrate our ideas under the net and exponential
premium principles. 相似文献
12.
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
13.
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
14.
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
15.
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
16.
In this paper, we study the MDPDE (minimizing a density power divergence estimator), proposed by Basu et al. (Biometrika 85:549–559,
1998), for mixing distributions whose component densities are members of some known parametric family. As with the ordinary
MDPDE, we also consider a penalized version of the estimator, and show that they are consistent in the sense of weak convergence.
A simulation result is provided to illustrate the robustness. Finally, we apply the penalized method to analyzing the red
blood cell SLC data presented in Roeder (J Am Stat Assoc 89:487–495, 1994).
This research was supported (in part) by KOSEF through Statistical Research Center for Complex Systems at Seoul National University. 相似文献
17.
Kajsa Kvist Per Kragh Andersen Jules Angst Lars Vedel Kessing 《Lifetime data analysis》2010,16(4):580-598
The effect of event-dependent sampling of processes consisting of recurrent events is investigated when analyzing whether
the risk of recurrence increases with event count. We study the situation where processes are selected for study if an event
occurs in a certain selection interval. Motivation comes from psychiatric epidemiology where repeated hospital admissions
are studied for patients with affective disease, as seen in Kessing et al. (Acta Psychiatr Scand 109:339–344, 2004b). For
the selected processes, either only disease course from selection and onwards is used in the analysis, or, both retrospective
and prospective disease course histories are used. We examine two methods to correct for the selection depending on which
data are used in the analysis. In the first case, the conditional distribution of the process given the pre-selection history
is determined. In the second case, an inverse-probability-of-selection weighting scheme is suggested. The ability of the methods
to correct for the bias due to selection is investigated with simulations. Furthermore, the methods are applied to affective
disease data from a register-based study (Kessing et al. Br J Psychiatry 185:372–377, 2004a) and from a long-term clinical
study (Kessing et al. Acta Psychiatr Scand 109:339–344, 2004b). 相似文献
18.
A partially adaptive estimator for the censored regression model based on a mixture of normal distributions 总被引:1,自引:0,他引:1
Steven B. Caudill 《Statistical Methods and Applications》2012,21(2):121-137
The goal of this paper is to introduce a partially adaptive estimator for the censored regression model based on an error
structure described by a mixture of two normal distributions. The model we introduce is easily estimated by maximum likelihood
using an EM algorithm adapted from the work of Bartolucci and Scaccia (Comput Stat Data Anal 48:821–834, 2005). A Monte Carlo study is conducted to compare the small sample properties of this estimator to the performance of some common
alternative estimators of censored regression models including the usual tobit model, the CLAD estimator of Powell (J Econom
25:303–325, 1984), and the STLS estimator of Powell (Econometrica 54:1435–1460, 1986). In terms of RMSE, our partially adaptive estimator performed well. The partially adaptive estimator is applied to data
on wife’s hours worked from Mroz (1987). In this application we find support for the partially adaptive estimator over the usual tobit model. 相似文献
19.
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
20.
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