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1.
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
2.
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
3.
Statistical Methods & Applications - Semiparametric likelihoods for regression models with missing at random data (Chen in J Am Stat Assoc 99:1176–1189, 2004, Zhang and Rockette in J Stat... 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.
For regression on state and transition probabilities in multi-state models Andersen et al. (Biometrika 90:15–27, 2003) propose
a technique based on jackknife pseudo-values. In this article we analyze the pseudo-values suggested for competing risks models
and prove some conjectures regarding their asymptotics (Klein and Andersen, Biometrics 61:223–229, 2005). The key is a second
order von Mises expansion of the Aalen-Johansen estimator which yields an appropriate representation of the pseudo-values.
The method is illustrated with data from a clinical study on total joint replacement. In the application we consider for comparison
the estimates obtained with the Fine and Gray approach (J Am Stat Assoc 94:496–509, 1999) and also time-dependent solutions
of pseudo-value regression equations. 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.
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.
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
9.
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
10.
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
11.
Sasabuchi et al. (Biometrika 70(2):465–472, 1983) introduces a multivariate version of the well-known univariate isotonic
regression which plays a key role in the field of statistical inference under order restrictions. His proposed algorithm for
computing the multivariate isotonic regression, however, is guaranteed to converge only under special conditions (Sasabuchi
et al., J Stat Comput Simul 73(9):619–641, 2003). In this paper, a more general framework for multivariate isotonic regression
is given and an algorithm based on Dykstra’s method is used to compute the multivariate isotonic regression. Two numerical
examples are given to illustrate the algorithm and to compare the result with the one published by Fernando and Kulatunga
(Comput Stat Data Anal 52:702–712, 2007). 相似文献
12.
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
13.
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
14.
Yves F. Atchadé 《Statistics and Computing》2011,21(4):463-473
In empirical Bayes inference one is typically interested in sampling from the posterior distribution of a parameter with a
hyper-parameter set to its maximum likelihood estimate. This is often problematic particularly when the likelihood function
of the hyper-parameter is not available in closed form and the posterior distribution is intractable. Previous works have
dealt with this problem using a multi-step approach based on the EM algorithm and Markov Chain Monte Carlo (MCMC). We propose
a framework based on recent developments in adaptive MCMC, where this problem is addressed more efficiently using a single
Monte Carlo run. We discuss the convergence of the algorithm and its connection with the EM algorithm. We apply our algorithm
to the Bayesian Lasso of Park and Casella (J. Am. Stat. Assoc. 103:681–686, 2008) and on the empirical Bayes variable selection of George and Foster (J. Am. Stat. Assoc. 87:731–747, 2000). 相似文献
15.
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
16.
In this paper we discuss new adaptive proposal strategies for sequential Monte Carlo algorithms—also known as particle filters—relying
on criteria evaluating the quality of the proposed particles. The choice of the proposal distribution is a major concern and
can dramatically influence the quality of the estimates. Thus, we show how the long-used coefficient of variation (suggested
by Kong et al. in J. Am. Stat. Assoc. 89(278–288):590–599, 1994) of the weights can be used for estimating the chi-square distance between the target and instrumental distributions of the
auxiliary particle filter. As a by-product of this analysis we obtain an auxiliary adjustment multiplier weight type for which
this chi-square distance is minimal. Moreover, we establish an empirical estimate of linear complexity of the Kullback-Leibler
divergence between the involved distributions. Guided by these results, we discuss adaptive designing of the particle filter
proposal distribution and illustrate the methods on a numerical example.
This work was partly supported by the National Research Agency (ANR) under the program “ANR-05-BLAN-0299”. 相似文献
17.
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
18.
While most of the literature on measurement error focuses on additive measurement error, we consider in this paper the multiplicative
case. We apply the Simulation Extrapolation method (SIMEX)—a procedure which was originally proposed by Cook and Stefanski
(J. Am. Stat. Assoc. 89:1314–1328, 1994) in order to correct the bias due to additive measurement error—to the case where data are perturbed by multiplicative noise
and present several approaches to account for multiplicative noise in the SIMEX procedure. Furthermore, we analyze how well
these approaches reduce the bias caused by multiplicative perturbation. Using a binary probit model, we produce Monte Carlo
evidence on how the reduction of data quality can be minimized.
For helpful comments, we would like to thank Helmut Küchenhoff, Winfried Pohlmeier, and Gerd Ronning. Sandra Nolte gratefully
acknowledges financial support by the DFG. Elena Biewen and Martin Rosemann gratefully acknowledge the financial support by
the Federal Ministry of Education and Research (BMBF). The usual disclaimer applies. 相似文献
19.
In this paper we introduce a new probability model known as type 2 Marshall–Olkin bivariate Weibull distribution as an extension
of type 1 Marshall–Olkin bivariate Weibull distribution of Marshall–Olkin (J Am Stat Assoc 62:30–44, 1967). Various properties
of the new distribution are considered. Bivariate minification processes with the two types of Weibull distributions as marginals
are constructed and their properties are considered. It is shown that the processes are strictly stationary. The unknown parameters
of the type 1 process are estimated and their properties are discussed. Some numerical results of the estimates are also given. 相似文献
20.
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