JOURNAL OF STATISTICAL SCIENCES
Year:2019 | Volume:13 | Issue:1 |Papers Count:14

Often, in high dimensional problems, where the number of variables is large the number of observations, penalized estimators based on shrinkage methods have better efficiency than the OLS estimator from the prediction error viewpoint. In these estimators, the tuning or shrinkage parameter plays a deterministic role in variable selection. The bridge estimator is an estimator which simplifies to ridge or LASSO estimators varying the tuning parameter. In these paper, the shrinkage bridge estimator is derived under a linear constraint on regression coefficients and its consistency is proved. Furthermore, its efficiency is evaluated in a simulation study and a real example.

One of the applicable tools, in order to develop the economy's politics, is Iranian's cooperation in increasing their level of public knowledge and the humanization of economic. Economical index, rate, price, and percentage are not informative only. From this point of view, one of the scientific ways to study the economic data is "Statistical Modeling" through the applicable concept of "Copula Function". In this paper, through the copula functions and the applicable concept of dependence, called "Directional dependence", the dependence structure between variations in family's income and the expenses allocated to buy cultural and miscellaneous goods would be widely studied. Simulation results show that by decreasing the level of income, Iranian families tend to decrease their cultural costs rather than unnecessary miscellaneous costs.

Before analyzing a time series data, it is better to verify the dependency of the data, because if the data be independent, the fitting of the time series model is not efficient. In recent years, the power divergence statistics used for the goodness of fit test. In this paper, we introduce an independence test of time series via power divergence which depends on the parameter λ . We obtain asymptotic distribution of the test statistic. Also using a simulation study, we estimate the error type I and test power for some λ and n. Our simulation study shows that for extremely large sample sizes, the estimated error type I converges to the nominal α , for any λ . Furthermore, the modified chi-square, modified likelihood ratio, and Freeman-Tukey test have the most power.

In this paper, under certain conditions, the usual stochastic, convex and dispersive orders between the smallest claim amounts with independent Weibull claims are discussed. Also, under conditions on some well-known common copula, some stochastic comparisons of smallest claim amounts with dependent heterogeneous claims have been obtained.

Uncertainty is an inherent characteristic of biological and geospatial data which is almost made by measurement error in the observed values of the quantity of interest. Ignoring measurement error can lead to biased estimates and inflated variances and so an inappropriate inference. In this paper, the Gaussian spatial model is fitted based on covariate measurement error. For this purpose, we adopt the Bayesian approach and utilize the Markov chain Monte Carlo algorithms and data augmentations to carry out calculations. The methodology is illustrated using simulated data.

In the last decade, Poisson regression has been used for modeling count response variables. Poisson regression is not a suitable choice when count data bears superfluity of zero numbers. In this article, two models zero-inflated Poisson regression and bivariate zero-inflated Poisson regression with random effect are used to modeling count responses with a superfluity of zero numbers. Usually, distribution of the random effect is considered normal, but we intend to employ more flexible skew-normal distribution for the distribution of the random effect. Finally, the purpose model is applied to data which as obtained from the Shahid Chamran University of Ahvaz concerning the number of failed courses and fail grade point average semesters. we used a simulation method to verify parameter estimations.

The study of regression diagnostic, including identification of the influential observations and outliers, is of particular importance. The sensitivity of least squares estimators to the outliers and influential observations lead to extending the regression diagnostic in order to provide criteria to assess the anomalous observations. Detecting influential observations and outliers in the presence of collinearity is a complicated task, in the sense that collinearity may cover some of the unusual data. One of the considerable methods to identify outliers is the mean shift outliers method. In this article, we extend the mean shift outliers method to the ridge estimates under linear stochastic restrictions, which is used to reduce the effect of collinearity, and to provide the test statistic to identify the outliers in these estimators. Finally, we show the ability of our proposed method using a practical example of real data.

The complex systems containing of n elements are considered, each having two dependent components. The main goal of this paper is to investigate the mean residual life of such systems with some intact components at time t. Toward this end, the bivariate binomial model and also two different generalizations are described. Finally, some graphical and numerical analyses are provided for mean residual life of such systems under Farlie-Gumbel-Morgenstern model.

In this study, the multi-parameter exponential family of distribution has been used to approximate the distribution of indefinite quadratic forms in normal random vectors. Moments of quadratic forms can be obtained in any orders in terms of representation of the quadratic forms as weighted sum of non-central chi-square random variables. By Stein's identity in exponential family, we estimated parameters of probability density function. The method handled in some examples and we indicated this method suitable for approximating the quadratic form distribution.

Usually in survey sampling when the sensitive questions are asked directly, the respondents do not provide true answers. The randomized response techniques have been introduced to protect the privacy responses. In this article we focus on Simons randomized response technique for qualitative variables. Using the combination of the two different Simmons’ models, a new combined randomized response technique is introduced to increase protection of privacy. Using simulation in R package, efficiency of the proposed model is compared to the Simmons’ and Alavi and Tajodini's (1394) models. Finally, the proposed model has been employed for estimating the proportion of student cheating in Shahid Chamran University.

Recalling the definition of shape as a point on hyper-sphere, proposed by Kendall, the regression model is studied in this paper. In order to simplify the modeling, the triangulation via two landmarks is proposed. The triangulation not only simplifies the regression modelling of the shapes but also provides straightforward computation procedure to reconstruct geometrical structure of the objects. Novelty of the proposed method in this paper is on using the predictor variable, based upon the shape, which suitably describes the geometrical variability of the response. The comparison and evaluation of the proposed methods with the full Procrustes matching through the mean square error criteria are done. Application of two models for the configurations of rat skulls is investigated.

In this paper, a general method for goodness of fit test for the location-scale family of distributions under Type-II progressive censoring is presented and its properties are investigated. Then, using Monte Carlo simulation studies, the power of this test is compared with the powers of some existing tests for testing the Gumbel distribution. Finally the proposed test is used for fitting a distribution to a real data set.

Testing the Hypothesis of independence of a p-variate vector subvectors, as a pretest for many others related tests, is always as a matter of interest. When the sample size n is much larger than the dimension p, the likelihood ratio test (LRT) with chisquare approximation, has an acceptable performance. However, for moderately high-dimensional data by which n is not much larger than p, the chisquare approximation for null distribution of the LRT statistic is no more usable. As a general case, here, a simultaneous subvectors independence testing procedure in all k p-variate normal distributions is considered. To test this hypothesis, a normal approximation for the null distribution of the LRT statistic was proposed. A simulation study was performed to show that the proposed normal approximation outperforms the chisquare approximation. Finally, the proposed testing procedure was applied on prostate cancer data.

This paper is investigating the mixture autoregressive model with constant mixing weights in state space form and generalization to ARMA mixture model. Using a sequential Monte Carlo method, the forecasting, filtering and smoothing distributions are approximated and parameters f the model is estimated via the EM algorithm. The results show the dimension of parameter vector in state space representation reduces. The results of the simulation study show that the proposed filtering algorithm has a steady state close to the real values of the state vector. Moreover, according to simulation results, the mean vectors of filtering and smoothing distribution converges to state vector quickly.