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1.
Yong Bao 《Econometric Reviews》2018,37(4):309-324
A compact analytical representation of the asymptotic covariance matrix, in terms of model parameters directly, of the quasi maximum likelihood estimator (QMLE) is derived in autoregressive moving average (ARMA) models with possible nonzero means and non-Gaussian error terms. For model parameters excluding the error variance, it is found that the Huber (1967) sandwich form for the asymptotic covariance matrix degenerates into the inverse of the associated information matrix. In comparison to the existing result that involves the second moments of some auxiliary variables for the case of zero-mean ARMA models, the analytical asymptotic covariance in this article has an advantage in that it can be conveniently estimated by plugging in the estimated model parameters directly. 相似文献
2.
We propose a new ratio type estimator for estimating the finite population mean using two auxiliary variables in stratified two-phase sampling. Expressions for bias and mean squared error of the proposed estimator are derived up to the first order of approximation. The proposed estimator is more efficient than the usual stratified sample mean estimator, traditional stratified ratio estimator and some other stratified estimators including Bahl and Tuteja (1991), Chami et al. (2012), Chand (1975), Choudhury and Singh (2012), Hamad et al. (2013), Vishwakarma and Gangele (2014), Sanaullah et al. (2014), and Chanu and Singh (2014). 相似文献
3.
Ratio-Cum-Product Type Exponential Estimator of Finite Population Mean in Stratified Random Sampling
Rajesh Tailor 《统计学通讯:理论与方法》2014,43(2):343-354
This article addresses the problem of estimating the finite population mean in stratified random sampling using auxiliary information. Motivated by Singh (1967) and Bahl and Tuteja (1991) a ratio-cum-product type exponential estimator has been suggested and its bias and mean squared error have been derived under large sample approximation. Suggested estimator has been compared with usual unbiased estimator of population mean in stratified random sampling, combined ratio estimator, combined product estimator, ratio and product type exponential estimator of Singh et al. (2008). Conditions under which suggested estimator is more efficient than other considered estimators have been obtained. A numerical illustration is given in support of the theoretical findings. 相似文献
4.
Yasin Asar 《统计学通讯:模拟与计算》2017,46(4):2576-2586
The binary logistic regression is a widely used statistical method when the dependent variable is binary or dichotomous. In some of the situations of logistic regression, independent variables are collinear which leads to the problem of multicollinearity. It is known that multicollinearity affects the variance of maximum likelihood estimator (MLE) negatively. Thus, this article introduces new methods to estimate the shrinkage parameters of Liu-type logistic estimator proposed by Inan and Erdogan (2013) which is a generalization of the Liu-type estimator defined by Liu (2003) for the linear model. A Monte Carlo study is used to show the effectiveness of the proposed methods over MLE using the mean squared error (MSE) and mean absolute error (MAE) criteria. A real data application is illustrated to show the benefits of new methods. According to the results of the simulation and application proposed methods have better performance than MLE. 相似文献
5.
For two or more populations of which the covariance matrices have a common set of eigenvectors, but different sets of eigenvalues, the common principal components (CPC) model is appropriate. Pepler et al. (2015) proposed a regularized CPC covariance matrix estimator and showed that this estimator outperforms the unbiased and pooled estimators in situations, where the CPC model is applicable. This article extends their work to the context of discriminant analysis for two groups, by plugging the regularized CPC estimator into the ordinary quadratic discriminant function. Monte Carlo simulation results show that CPC discriminant analysis offers significant improvements in misclassification error rates in certain situations, and at worst performs similar to ordinary quadratic and linear discriminant analysis. Based on these results, CPC discriminant analysis is recommended for situations, where the sample size is small compared to the number of variables, in particular for cases where there is uncertainty about the population covariance matrix structures. 相似文献
6.
Based on the recursions in Huffer (1988) and Huffer and Lin (2001), we present a two-stage algorithm and two specialized methods for evaluating the probabilities involving linear combination of spacings of special forms. The two-stage algorithm combines the advantages of marking algorithm in Huffer and Lin (1997) and general algorithm in Huffer and Lin (2001). The proposed methods can analytically derive the exact expressions for some specific problems, and efficiently handle problems such as the distribution of the circular scan statistic and multiple coverage probabilities. 相似文献
7.
When a sufficient correlation between the study variable and the auxiliary variable exists, the ranks of the auxiliary variable are also correlated with the study variable, and thus, these ranks can be used as an effective tool in increasing the precision of an estimator. In this paper, we propose a new improved estimator of the finite population mean that incorporates the supplementary information in forms of: (i) the auxiliary variable and (ii) ranks of the auxiliary variable. Mathematical expressions for the bias and the mean-squared error of the proposed estimator are derived under the first order of approximation. The theoretical and empirical studies reveal that the proposed estimator always performs better than the usual mean, ratio, product, exponential-ratio and -product, classical regression estimators, and Rao (1991), Singh et al. (2009), Shabbir and Gupta (2010), Grover and Kaur (2011, 2014) estimators. 相似文献
8.
《统计学通讯:模拟与计算》2012,41(6):804-819
Poisson point processes play important role in various domains of Probability Theory and Mathematical Statistics. In this article, we investigate only two applications of Poisson point processes: a generated white noise problem and parameters estimation problem. This work continues the investigations started in paper Egorov and Kondybaev (2009). 相似文献
9.
Recently, Liu (2007) defined a new entropy which measures the distance between a prescribed and an empirical survival function. In this article, we use this measure called Differential Cumulative Entropy (DCE) for Weibull parameters estimation. We show that the DCE method provides biased estimations of the Weibull modulus, but utilizing unbiasing factors derived here we enhance the results. A simulation study shows the higher performance of the new method over commonly used maximum likelihood and linear regression methods in Weibull parameters estimation especially in small sample sizes. 相似文献
10.
《统计学通讯:理论与方法》2013,42(9):1725-1735
Abstract The study of multivariate distributions of order k, two of which are the multivariate negative binomial of order k and the multinomial of the same order, was introduced in Philippou et al. (Philippou, A. N., Antzoulakos, D. L., Tripsiannis, G. A. (1988). Multivariate distributions of order k. Statistics and Probability Letters 7(3):207–216.), and Philippou et al. (Philippou, A. N., Antzoulakos, D. L., Tripsiannis, G. A. (1990). Multivariate distributions of order k, part II. Statistics and Probability Letters 10(1):29–35.). Recently, an order k (or cluster) generalized negative binomial distribution and a multivariate negative binomial distribution were derived in Sen and Jain (Sen, K., Jain, R. (1996). Cluster generalized negative binomial distribution. In: Borthakur et al. A. C., Eds.; Probability Models and Statistics Medhi Festschrift, A. J., on the Occasion of his 70th Birthday. New Age International Publishers: New Delhi, 227–241.) and Sen and Jain (Sen, K., Jain, R. (1997). A multivariate generalized Polya-Eggenberger probability model-first passage approach. Communications in Statistics-Theory and Methods 26:871–884.), respectively. In this paper, all four distributions are generalized to a multivariate generalized negative binomial distribution of order k by means of an appropriate sampling scheme and a first passage event. This new distribution includes as special cases several known and new multivariate distributions of order k, and gives rise in the limit to multivariate generalized logarithmic, Poisson and Borel-Tanner distributions of the same order. Applications are indicated. 相似文献
11.
In this article, we have evaluated the performance of different forecasters and tested association between their performances for different pairs of variables. We have used three data sets of track records of professional U.S. economic forecasters participating in the Blue Chip consensus forecasting service (the data sets contain the root mean square errors (RMSE) of different forecasters for different years). To evaluate the performance of forecasters we have covered three well-known tests, namely the usual F test (cf. Fisher (1923)), Kruskal Wallis test (cf. Kruskal and Wallis (1952)), and Extension of Median test (cf. Daniel (1990)). To test the association between the forecaster's performances for different pairs of variables, we have considered Gini mean correlation coefficient rg1 (cf. Yitzhaki, S., and Olkin, I. (1991) and Yitzhaki (2003)), Modified rank correlation coefficient (cf. Zimmerman (1994)) and three modifications of Spearman rank correlation coefficient. We have observed that different forecasters do not necessarily offer same average performance. Moreover, an evidence of association between two criteria does not always lead us reaching at the same decision. The outcomes of the study may help the practitioners in selecting the best forecaster(s) for policymaking purposes. 相似文献
12.
Here, we apply the smoothing technique proposed by Chaubey et al. (2007) for the empirical survival function studied in Bagai and Prakasa Rao (1991) for a sequence of stationary non-negative associated random variables.The derivative of this estimator in turn is used to propose a nonparametric density estimator. The asymptotic properties of the resulting estimators are studied and contrasted with some other competing estimators. A simulation study is carried out comparing the recent estimator based on the Poisson weights (Chaubey et al., 2011) showing that the two estimators have comparable finite sample global as well as local behavior. 相似文献
13.
In this article, the frequency polygon studied by Scott (1985) is investigated as a nonparametric estimator for negatively associated samples. By the Bernstein type inequality, we give the uniformly strong consistency of the estimator and obtain the corresponding rate under some mild conditions. 相似文献
14.
Hadi Alizadeh Noughabi 《统计学通讯:模拟与计算》2017,46(7):5531-5540
The logistic distribution is one of the fundamental distribution and is widely used for describing model growth curves in survival analysis and biological studies. Applications of this distribution are presented in statistical literature. In this article, goodness of fit tests for the logistic distribution based on the empirical distribution function (EDF) are considered. In order to compute the test statistics, because the MLEs cannot be obtained explicitly, we use the approximate maximum likelihood estimates (AMLEs) suggested by Balakrishnan and Cohen (1990), which are simple explicit estimators. Power comparisons of the considered tests are carried out via simulations. Finally, two illustrative examples are presented and analyzed. 相似文献
15.
Leila Golparvar 《统计学通讯:模拟与计算》2017,46(1):404-422
The problem of selecting a population according to “selection and ranking” is an important statistical problem. The ideas in selecting the best populations with some demands having optimal criterion have been suggested originally by Bechhofer (1954) and Gupta (1956, 1965). In the area of ranking and selection, the large part of literature is connected with a single criterion. However, this may not satisfy the experimenter’s demand. We follow methodology of Huang and Lai (1999) and the main focus of this article is to select a best population under Type-II progressively censored data for the case of right tail exponential distributions with a bounded and unbounded supports for μi. We formulate the problem and develop a Bayesian setup with two kinds of bounded and unbounded prior for μi. We introduce an empirical Bayes procedure and study the large sample behavior of the proposed rule. It is shown that the proposed empirical Bayes selection rule is asymptotically optimal. 相似文献
16.
Nonlinear reproductive dispersion models with stochastic regressors (NRDMWSR) includes generalized linear models with stochastic regressors (Fahrmer and Kaufmann, 1985) as a special case. This article presents some mild regularity conditions. On the basis of those mild conditions, the existence, strong consistency, and asymptotic normality of maximum likelihood estimator (MLE) are obtained in NRDMWSR. 相似文献
17.
The traditional confidence interval associated with the ordinary least squares estimator of linear regression coefficient is sensitive to non-normality of the underlying distribution. In this article, we develop a novel kernel density estimator for the ordinary least squares estimator via utilizing well-defined inversion based kernel smoothing techniques in order to estimate the conditional probability density distribution of the dependent random variable. Simulation results show that given a small sample size, our method significantly increases the power as compared with Wald-type CIs. The proposed approach is illustrated via an application to a classic small data set originally from Graybill (1961). 相似文献
18.
In this article, we derive a new formula for extreme Student t quantiles. We use the fact that the Student t distribution arises as the limit of a variance-mixture of normals. For the normal distribution there is already a tail quantile formula derived by Reiss (1989). We generalize his procedure and transfer it to our scenario. Eventually, we compare the quantile estimates of our formula to those from Gafer and Kafadar (1984), who also derived a Student t quantile formula. Using R to generate a benchmark we find that our method is more accurate for very high quantiles. 相似文献
19.
Mosisa Aga 《统计学通讯:理论与方法》2013,42(4):663-673
This article provides an Edgeworth expansion for the distribution of the log-likelihood derivative LLD of the parameter of a time series generated by a linear regression model with Gaussian, stationary, and long-memory errors. Under some sets of conditions on the regression coefficients, the spectral density function, and the parameter values, an Edgeworth expansion of the density as well as the distribution function of a vector of centered and normalized derivatives of the plug-in log-likelihood PLL function of arbitrarily large order is established. This is done by extending the results of Lieberman et al. (2003), who provided an Edgeworth expansion for the Gaussian stationary long-memory case, to our present model, which is a linear regression process with stationary Gaussian long-memory errors. 相似文献
20.
Marco Barnabani 《统计学通讯:模拟与计算》2017,46(1):331-343
In general, the exact distribution of a convolution of independent gamma random variables is quite complicated and does not admit a closed form. Of all the distributions proposed, the gamma-series representation of Moschopoulos (1985) is relatively simple to implement but for particular combinations of scale and/or shape parameters the computation of the weights of the series can result in complications with too much time consuming to allow a large-scale application. Recently, a compact random parameter representation of the convolution has been proposed by Vellaisamy and Upadhye (2009) and it allows to give an exact interpretation to the weights of the series. They describe an infinite discrete probability distribution. This result suggested to approximate Moschopoulos’s expression looking for an approximating theoretical discrete distribution for the weights of the series. More precisely, we propose a general negative binomial distribution. The result is an “excellent” approximation, fast and simple to implement for any parameter combination. 相似文献