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1.
《Journal of Statistical Computation and Simulation》2012,82(7):815-826
Tests for the equality of variances are of interest in many areas such as quality control, agricultural production systems, experimental education, pharmacology, biology, as well as a preliminary to the analysis of variance, dose–response modelling or discriminant analysis. The literature is vast. Traditional non-parametric tests are due to Mood, Miller and Ansari–Bradley. A test which usually stands out in terms of power and robustness against non-normality is the W50 Brown and Forsythe [Robust tests for the equality of variances, J. Am. Stat. Assoc. 69 (1974), pp. 364–367] modification of the Levene test [Robust tests for equality of variances, in Contributions to Probability and Statistics, I. Olkin, ed., Stanford University Press, Stanford, 1960, pp. 278–292]. This paper deals with the two-sample scale problem and in particular with Levene type tests. We consider 10 Levene type tests: the W50, the M50 and L50 tests [G. Pan, On a Levene type test for equality of two variances, J. Stat. Comput. Simul. 63 (1999), pp. 59–71], the R-test [R.G. O'Brien, A general ANOVA method for robust tests of additive models for variances, J. Am. Stat. Assoc. 74 (1979), pp. 877–880], as well as the bootstrap and permutation versions of the W50, L50 and R tests. We consider also the F-test, the modified Fligner and Killeen [Distribution-free two-sample tests for scale, J. Am. Stat. Assoc. 71 (1976), pp. 210–213] test, an adaptive test due to Hall and Padmanabhan [Adaptive inference for the two-sample scale problem, Technometrics 23 (1997), pp. 351–361] and the two tests due to Shoemaker [Tests for differences in dispersion based on quantiles, Am. Stat. 49(2) (1995), pp. 179–182; Interquantile tests for dispersion in skewed distributions, Commun. Stat. Simul. Comput. 28 (1999), pp. 189–205]. The aim is to identify the effective methods for detecting scale differences. Our study is different with respect to the other ones since it is focused on resampling versions of the Levene type tests, and many tests considered here have not ever been proposed and/or compared. The computationally simplest test found robust is W50. Higher power, while preserving robustness, is achieved by considering the resampling version of Levene type tests like the permutation R-test (recommended for normal- and light-tailed distributions) and the bootstrap L50 test (recommended for heavy-tailed and skewed distributions). Among non-Levene type tests, the best one is the adaptive test due to Hall and Padmanabhan. 相似文献
2.
In this paper, we consider a constructive representation of skewed distributions, which proposed by Ferreira and Steel (J
Am Stat Assoc 101:823–829, 2006), and its basic properties is presented. We study the five versions of skew- normal distributions
in this general setting. An appropriate empirical model for a skewed distribution is introduced. In data analysis, we compare
this empirical model with the other four versions of skew-normal distributions, via some reasonable criteria. It is shown
that the proposed empirical model has a better fit for density estimation. 相似文献
3.
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
4.
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
5.
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
6.
Rosa Arboretti Giancristofaro Stefano Bonnini 《Statistical Methods and Applications》2009,18(2):221-236
In several sciences, especially when dealing with performance evaluation, complex testing problems may arise due in particular
to the presence of multidimensional categorical data. In such cases the application of nonparametric methods can represent
a reasonable approach. In this paper, we consider the problem of testing whether a “treatment” is stochastically larger than
a “control” when univariate and multivariate ordinal categorical data are present. We propose a solution based on the nonparametric
combination of dependent permutation tests (Pesarin in Multivariate permutation test with application to biostatistics. Wiley,
Chichester, 2001), on variable transformation, and on tests on moments. The solution requires the transformation of categorical
response variables into numeric variables and the breaking up of the original problem’s hypotheses into partial sub-hypotheses
regarding the moments of the transformed variables. This type of problem is considered to be almost impossible to analyze
within likelihood ratio tests, especially in the multivariate case (Wang in J Am Stat Assoc 91:1676–1683, 1996). A comparative
simulation study is also presented along with an application example. 相似文献
7.
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
8.
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
9.
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
10.
In this paper, we investigate different procedures for testing the equality of two mean survival times in paired lifetime
studies. We consider Owen’s M-test and Q-test, a likelihood ratio test, the paired t-test, the Wilcoxon signed rank test and a permutation test based on log-transformed survival times in the comparative study.
We also consider the paired t-test, the Wilcoxon signed rank test and a permutation test based on original survival times for the sake of comparison. The
size and power characteristics of these tests are studied by means of Monte Carlo simulations under a frailty Weibull model.
For less skewed marginal distributions, the Wilcoxon signed rank test based on original survival times is found to be desirable.
Otherwise, the M-test and the likelihood ratio test are the best choices in terms of power. In general, one can choose a test procedure based
on information about the correlation between the two survival times and the skewness of the marginal survival distributions. 相似文献
11.
《Journal of Statistical Computation and Simulation》2012,82(3):468-476
Lin et al. [Exact Bayesian variable sampling plans for the exponential distribution with progressive hybrid censoring, J. Stat. Comput. Simul. 81 (2011), pp. 873–882] claimed to have derived exact Bayesian sampling plans for exponential distributions with progressive hybrid censoring. We comment on the accuracy of the design parameters of their proposed sampling plans and the associated Bayes risks given in tables of Lin et al. [Exact Bayesian variable sampling plans for the exponential distribution with progressive hybrid censoring, J. Stat. Comput. Simul. 81 (2011), pp. 873–882]. Counter-examples to their claim are provided. 相似文献
12.
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
13.
Andrea Pallini 《Statistical Methods and Applications》1994,3(1):77-91
Summary We introduce variance reduction techniques as general tools for estimating probabilities from invariant permutation distributions.
The paper discusses importance sampling, antithetic sampling and control variates sampling as alternatives to uniform Monte
Carlo sampling for estimating exact critical values orP-values in a broad class of permutation tests. Results may be extended to permutation confidence intervals and linear rank
tests. An asymptotic theory is provided for each proposed variance reduction method.
Invited paper at the Conference held in Bologna, Italy, 27–28 May 1993, on ?Statistical Tests: Methodology and Econometric
Applications?. 相似文献
14.
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
15.
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
16.
Ramesh C. Gupta 《Statistical Papers》2011,52(1):125-138
In this paper, we consider a class of bivariate distributions by forming the odds of failure of a two component system. The
properties of this odds function and the association between the two variables are investigated by studying the local dependence
function and the association measure defined by Clayton (Biometrika 65:141–151, 1978) and Oakes (J Am Stat Assoc 84:487–493,
1989). We also study the effect of the association parameter on the failure rate of a series system and the regression mean
residual life function of a parallel system. Some stochastic comparisons with respect to the association parameter are also
studied. 相似文献
17.
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
18.
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
19.
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
20.
Thomas W. O'GORMAN 《Revue canadienne de statistique》1997,25(2):269-279
An adaptive test is proposed for the one-way layout. This test procedure uses the order statistics of the combined data to obtain estimates of percentiles, which are used to select an appropriate set of rank scores for the one-way test statistic. This test is designed to have reasonably high power over a range of distributions. The adaptive procedure proposed for a one-way layout is a generalization of an existing two-sample adaptive test procedure. In this Monte Carlo study, the power and significance level of the F-test, the Kruskal-Wallis test, the normal scores test, and the adaptive test were evaluated for the one-way layout. All tests maintained their significance level for data sets having at least 24 observations. The simulation results show that the adaptive test is more powerful than the other tests for skewed distributions if the total number of observations equals or exceeds 24. For data sets having at least 60 observations the adaptive test is also more powerful than the F-test for some symmetric distributions. 相似文献