مجله علوم آماری
سال هشتم شماره 1 (پیاپی 15، بهار و تابستان 1393)

In this paper، we deal with modeling crisp input-fuzzy output data by constructing a MARS-fuzzy regression model with crisp parameters estimation and fuzzy error terms for the fuzzy data set. The proposed method is a two-phase procedure which applies the MARS technique at phase one and an optimization problem at phase two to estimate the center and fuzziness of the response variable. A realistic application of the proposed method is also presented in a hydrology engineering problem. Empirical results demonstrate that the proposed approach is more efficient and more realistic than some traditional least-squares fuzzy regression models.

The instability of the least squares parameter estimates under collinearity، might also causes instability of the residuals. If so، a large residual from a least squares fit might not be indicative of an erratic data point، and conversely. In order to resolve the problem of collinearity in the regression model، biased estimators like the Liu estimator is suggested. In this paper، it is shown that when Liu mean shift regression is used to mitigate the effect of the collinearity، the influence of some observations can be drastically changed and also the appropriate statistic for testing outliers is derived. In order to illustrate the performance of the proposed method، a real example is presented.

The coefficient of variation is often used for comparing the dispersions of populations that have different measurement systems. In this study، the problem of testing the equality of coefficients of variation of several Normal populations is considered and a new test procedure based on Wald test and parametric bootstrap approach is developed. Since all the proposed tests for this problem are approximate، it is important to investigate how well each test controls the type I error rate. Therefore، via a simulation study، first the type I error rate of our new test is compared with some recently proposed tests. Then، the power of our proposed test is compared with others.

A semiparametric additive-multiplicative intensity function for recurrent events data under two competing risks have been supposed in this paper. The model contains unknown baseline hazard function that defined separately intensity function for different competing risks effects on subjects failure. The presented model is based on regression parameters for effective covariates and frailty variable which describe correlation between terminal event and recurrent events and personal difference of under study subjects. The model support right censored and informative censored survival data. For estimating unknown parameters، numerical methods have been used and baseline hazard parameters are approximated using Taylor series expansion. A simulation study and application of the model to the bone marrow transplantation data are performed to illustrate the performance of the proposed model.

In this paper we consider of location parameter estimation in the multivariate normal distribution with unknown covariance. Two restrictions on the mean vector parameter are imposed. First we assume that all elements of mean vector are nonnegative، at the second hand assumed only a subset of elements are nonnegative. We propose a class of shrinkage estimators which dominate the minimax estimator of mean vector under the quadratic loss function.

Bivariate Von Mises distribution، which behaves relatively similar to bivariate normal distributions، have been proposed for representing the simultaneously probabilistic variability of these angles. One of the remarkable properties of this distribution is having the univariate Von Mises as the conditional density. However، the marginal density takes various structures depend on its involved parameters and، in general، has no closed form. This issue encounters the statistical inference with particular problems. In this paper، this distribution and its properties is studied، then the procedure to sample via the acceptance-rejection algorithm is described. The problems encountered in choosing a proper candidate distribution، arising from the cyclic feature of both angles، is investigated and the properties of its conditional density is utilized to overcome this obstacle.