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1.
Hu Yang 《统计学通讯:理论与方法》2013,42(15):4517-4527
ABSTRACTIn this article, we study the local influence for the elliptical linear regression model under equality constraints. We first obtain the parameter estimators of this model using the penalized log-likelihood function and iterative techniques. Then we obtain the diagnostics under the perturbations of constant variance, responses, and explanatory variables in the spirit of Cook (1986). Finally, a numerical example on the data set of the salinity of water is given to illustrate the theoretical results. 相似文献
2.
《统计学通讯:理论与方法》2013,42(5):799-813
The local influence approach of Cook [1]to regression diagnostic is developed and discussed, and compared with Cook's [2]deletion approach. The ability of the local influence approach to handle cases simultaneously, as well as some of its theoretical and practical difficulties, are reviewed. The perturbation ideas of the approach are applied to the linear model making distinction between the local perturbations on the assumptions of the model and the data. 相似文献
3.
Abstract A generalization of Chauvenet's test (see Bol'shev, L. N. 1969. On tests for rejecting outlying observations. Trudy In-ta prikladnoi Mat. Tblissi Gosudart. univ. 2:159–177. (In Russian); Voinov, V. G., Nikulin, M. N. 1996. Unbaised Estimators and Their Applications. Vol. 2. Kluwer Academic Publishers.) suitable to applied the problem of detecting r outliers in an univariate data set is proposed. In the exponential case, the Chauvenet's test can be used. Various modifications of this test were considered by Bol'shev, Ibrakimov and Khalfina (Ibrakimov, I. A., Khalfina 1978. Some asymptotic results concerning the Chauvenet test. Ter. Veroyatnost. i Primenen. 23(3):593–597.), Greenwood and Nikulin (Greenwood, Nikulin, P. E. 1996. A Guide to Chi-Squared Testing. New York: John Wiley and Sons, Inc.) depending on the choice of the estimation method used: MLE or MVUE. As procedures for testing one outlier in exponential model have been investigated by a number of authors including Chikkagoudar and Kunchur (Chikkagoudar, M. S., Kunchur, S. H. 1983. Distribution of test statistics for multiple outliers in exponential samples. Comm. Stat. Theory. and Meth. 12:2127–2142.), Lewis and Fieller (Lewis, T., Fiellerm N. R. J. 1979. A recursive algorithm for null distribution for outliers : I. Gamma samples. Technometrics 21:371–376.), Likes (Likes, J. 1966. Distribution of Dixon's statistics in the case of an exponential population. Metrika 11:46–54. (91, 96, 136, 198–200, 204, 209, 210).) and Kabe (Kabe, D. G. 1970. Testing outliers from an exponential population. Metrika 15:15–18.); only two types of statistics for testing multiple outliers exist. First is Dixon's while the second is based on the ratio of the sum of the observations suspected to be outliers to the sum of all observations of the sample. In fact, most of these authors have considered a general case of gamma model and the results for exponential model are given a special case. The object of the present communication is to focus on alternative models, namely slippage alternatives (see Barnett, Vic., Toby Lewis 1978. Outlier in Statistical Data. New York: John Wiley and Sons, Inc.) in exponential samples. We propose a statistic different from the well known Dixon's statistic Dr to test for multiple outliers. Distribution of the test based on this new statistic under slippage alternatives is obtained and hence the tables of critical values are given, for various n (size of the sample) and r (the number of outliers). The power of the new test is also calculated, it is compared to the power of the Dixon's statistic (Chikkagoudar, M. S., Kunchur, S. H. 1983. Distribution of test statistics for multiple outliers in exponential samples. Comm. Stat. Theory. and Meth. 12:2127–2142.). Notice that the new statistic based test power is greater the Dixon's statistic based test one. 相似文献
4.
C. M. Barros G. J. A. Amaral A. D. C. Nascimento A. H. M. A. Cysneiros 《统计学通讯:理论与方法》2017,46(14):6882-6898
A method for detecting outliers in axial data has been proposed by Best and Fisher (1986). For extending that work, we propose four new methods. Two of them are suitable for outlier detection and they depend on the classic geodesic distance and a modified version of this distance. The other two procedures, which are designed for influential observation detection, are based on the Kullback–Leibler and Cook’s distances. Some simulation experiments are performed to compare all considered methods. Detection and error rates are used as comparison criteria. Numerical results provide evidence in favor of the KL distance. 相似文献
5.
《统计学通讯:理论与方法》2012,41(2):343-360
AbstractThis paper presents the robust Bayesian inference based on the γ-divergence which is the same divergence as “type 0 divergence” in Jones et al. (2001) on the basis of Windham (1995). It is known that the minimum γ-divergence estimator works well to estimate the probability density for heavily contaminated data, and to estimate the variance parameters. In this paper, we propose a robust posterior distribution against outliers based on the γ-divergence and show the asymptotic properties of the proposed estimator. We also discuss some robustness properties of the proposed estimator and illustrate its performances in some simulation studies. 相似文献
6.
Singh et al. (1986) proposed an almost unbiased ridge estimator using Jackknife method that required transformation of the regression parameters. This article shows that the same method can be used to derive the Jackknifed ridge estimator of the original (untransformed) parameter without transformation. This method also leads in deriving easily the second-order Jackknifed ridge that may reduce the bias further. We further investigate the performance of these estimators along with a recent method by Batah et al. (2008) called modified Jackknifed ridge theoretically as well as numerically. 相似文献
7.
Gabriel Rodríguez 《统计学通讯:模拟与计算》2016,45(1):207-221
In recent articles, Fajardo et al. (2009) and Reisen and Fajardo (2012) propose an alternative semiparametric estimator of the fractional parameter in ARFIMA models which is robust to the presence of additive outliers. The results are very interesting, however, they use samples of 300 or 800 observations which are rarely found in macroeconomics. In order to perform a comparison, I estimate the fractional parameter using the procedure of Geweke and Porter-Hudak (1983) augmented with dummy variables associated with the (previously) detected outliers using the statistic τd suggested by Perron and Rodríguez (2003). Comparing with Fajardo et al. (2009) and Reisen and Fajardo (2012), I found better results for the mean and bias of the fractional parameter when T = 100 and the results in terms of the standard deviation and the MSE are very similar. However, for higher sample sizes such as 300 or 800, the robust procedure performs better. Empirical applications for seven monthly Latin-American inflation series with very small sample sizes contaminated by additive outliers are discussed. 相似文献
8.
Jigao Yan 《统计学通讯:理论与方法》2013,42(20):5074-5098
AbstractIn this paper, the complete convergence for maximal weighted sums of extended negatively dependent (END, for short) random variables is investigated. Some sufficient conditions for the complete convergence and some applications to a nonparametric model are provided. The results obtained in the paper generalize and improve the corresponding ones of Wang et al. (2014b) and Shen, Xue, and Wang (2017). 相似文献
9.
《统计学通讯:理论与方法》2013,42(12):2415-2440
Abstract In this article, nonparametric estimators of the regression function, and its derivatives, obtained by means of weighted local polynomial fitting are studied. Consider the fixed regression model where the error random variables are coming from a stationary stochastic process satisfying a mixing condition. Uniform strong consistency, along with rates, are established for these estimators. Furthermore, when the errors follow an AR(1) correlation structure, strong consistency properties are also derived for a modified version of the local polynomial estimators proposed by Vilar-Fernández and Francisco-Fernández (Vilar-Fernández, J. M., Francisco-Fernández, M. (2002). Local polynomial regression smoothers with AR-error structure. TEST 11(2):439–464). 相似文献
10.
By applying the recursion of Huffer (1988) repeatedly, we propose an algorithm for evaluating the null joint distribution of Dixon-type test statistics for testing discordancy of k upper outliers in exponential samples. By using the critical values of Dixon-type test statistics determined from the proposed algorithm and those of Cochran-type test statistics presented earlier by Lin and Balakrishnan (2009), we carry out an extensive Monte Carlo study to investigate the powers and the error probabilities for the effects of masking and swamping when the number of outliers k = 2 and 3. Based on our empirical findings, we recommend Rosner’s (1975) sequential test procedure based on Dixon-type test statistics for testing multiple outliers from an exponential distribution. 相似文献
11.
Kerry Patterson Hossein Hassani Saeed Heravi Anatoly Zhigljavsky 《Journal of applied statistics》2011,38(10):2183-2211
Real-time data on national accounts statistics typically undergo an extensive revision process, leading to multiple vintages on the same generic variable. The time between the publication of the initial and final data is a lengthy one and raises the question of how to model and forecast the final vintage of data – an issue that dates from seminal articles by Mankiw et al. [51], Mankiw and Shapiro [52] and Nordhaus [57]. To solve this problem, we develop the non-parametric method of multivariate singular spectrum analysis (MSSA) for multi-vintage data. MSSA is much more flexible than the standard methods of modelling that involve at least one of the restrictive assumptions of linearity, normality and stationarity. The benefits are illustrated with data on the UK index of industrial production: neither the preliminary vintages nor the competing models are as accurate as the forecasts using MSSA. 相似文献
12.
We study the limiting degree distribution of the vertex splitting model introduced in Ref.[3]. This is a model of randomly growing ordered trees, where in each time step the tree is separated into two components by splitting a vertex into two, and then inserting an edge between the two new vertices. Under some assumptions on the parameters, related to the growth of the maximal degree of the tree, we prove that the vertex degree densities converge almost surely to constants which satisfy a system of equations. Using this, we are also able to strengthen and prove some previously non-rigorous results mentioned in the literature. 相似文献
13.
In this article, we consider two different shared frailty regression models under the assumption of Gompertz as baseline distribution. Mostly assumption of gamma distribution is considered for frailty distribution. To compare the results with gamma frailty model, we consider the inverse Gaussian shared frailty model also. We compare these two models to a real life bivariate survival data set of acute leukemia remission times (Freireich et al., 1963). Analysis is performed using Markov Chain Monte Carlo methods. Model comparison is made using Bayesian model selection criterion and a well-fitted model is suggested for the acute leukemia data. 相似文献
14.
Uchenna Chinedu Nduka 《统计学通讯:模拟与计算》2018,47(1):206-228
This paper considers the estimation of parameters of AR(p) models for time series with t-distribution via EM-based algorithms. The paper develops asymptotic properties for the estimation to show that the estimators are efficient. Also testing theory for the estimators is considered. The robustness of the estimators and various tests to deviations from an assumed model is investigated. The study shows that the algorithms have equal estimation efficiency even if the error distribution is miss-specified or perturbed by outliers. Interestingly, the estimators from these algorithms performed better than that of the Modified Maximum Likelihood (MML) considered in Tiku et al. (2000). 相似文献
15.
《统计学通讯:理论与方法》2013,42(6):1021-1045
Salient features of a family of short-tailed symmetric distributions, introduced recently by Tiku and Vaughan [1], are enunciated. Assuming the error distribution to be one of this family, the methodology of modified likelihood is used to derive MML estimators of parameters in a linear regression model. The estimators are shown to be efficient, and robust to inliers. This paper is essentially the first to achieve robustness to inliers. The methodology is extended to long-tailed symmetric distributions and the resulting estimators are shown to be efficient, and robust to outliers. This paper should be read in conjunction with Islam et al. [2]who develop modified likelihood methodology for skew distributions in the context of linear regression. 相似文献
16.
ABSTRACTFollowing the work of Azzalini (1985 and 1986) on the skew-normal distribution, we propose an extension of the generalized extreme value (GEV) distribution, the SGEV. This new distribution allows for a better fit of maxima and can be interpreted as both the distribution of maxima when maxima are taken on dependent data and when maxima are taken over a random block size. We propose to estimate the parameters of the SGEV distribution via the probability-weighted moment method. A simulation study is presented to provide an application of the SGEV on block maxima procedure and return level estimation. The proposed method is also implemented on a real-life data. 相似文献
17.
This article focuses on the conditional density of a scalar response variable given a random variable taking values in a semimetric space. The local linear estimators of the conditional density and its derivative are considered. It is assumed that the observations form a stationary α-mixing sequence. Under some regularity conditions, the joint asymptotic normality of the estimators of the conditional density and its derivative is established. The result confirms the prospect in Rachdi et al. (2014) and can be applied in time-series analysis to make predictions and build confidence intervals. The finite-sample behavior of the estimator is investigated by simulations as well. 相似文献
18.
James R. Schott 《统计学通讯:理论与方法》2017,46(12):6112-6118
The allometric extension model is a multivariate regression model recently proposed by Tarpey and Ivey (2006). This model holds when the matrix of covariances between the variables in the response vector y and the variables in the vector of regressors x has a particular structure. In this paper, we consider tests of hypotheses for this structure when (y′, x′)′ has a multivariate normal distribution. In particular, we investigate the likelihood ratio test and a Wald test. 相似文献
19.
Lindeman et al. [12] provide a unique solution to the relative importance of correlated predictors in multiple regression by averaging squared semi-partial correlations obtained for each predictor across all p! orderings. In this paper, we propose a series of predictor sensitivity statistics that complement the variance decomposition procedure advanced by Lindeman et al. [12]. First, we detail the logic of averaging over orderings as a technique of variance partitioning. Second, we assess predictors by conditional dominance analysis, a qualitative procedure designed to overcome defects in the Lindeman et al. [12] variance decomposition solution. Third, we introduce a suite of indices to assess the sensitivity of a predictor to model specification, advancing a series of sensitivity-adjusted contribution statistics that allow for more definite quantification of predictor relevance. Fourth, we describe the analytic efficiency of our proposed technique against the Budescu conditional dominance solution to the uneven contribution of predictors across all p! orderings. 相似文献
20.
Rodrigo R. Pescim Edwin M. M. Ortega Gauss M. Cordeiro Morad Alizadeh 《Journal of applied statistics》2017,44(2):233-252
We introduce a log-linear regression model based on the odd log-logistic generalized half-normal distribution [7]. Some of its structural properties including explicit expressions for the density function, quantile and generating functions and ordinary moments are derived. We estimate the model parameters by the maximum likelihood method. For different parameter settings, proportion of censoring and sample size, some simulations are performed to investigate the behavior of the estimators. We derive the appropriate matrices for assessing local influence diagnostics on the parameter estimates under different perturbation schemes. We also define the martingale and modified deviance residuals to detect outliers and evaluate the model assumptions. In addition, we demonstrate that the extended regression model can be very useful in the analysis of real data and provide more realistic fits than other special regression models. The potentiality of the new regression model is illustrated by means of a real data set. 相似文献