Open Journal of Statistics
ISSN / EISSN : 2161718X / 21617198
Current Publisher: Scientific Research Publishing, Inc, (10.4236)
Total articles ≅ 615
Latest articles in this journal
Open Journal of Statistics, Volume 10, pp 52-63; doi:10.4236/ojs.2020.101004
Abstract:LINEX means linear exponential loss function which used in the analysis of statistical estimation and prediction problem which rises exponentially on one side of zero and almost linearly on the other side of zero. It is used in both overestimation and underestimation problems. Ali Shadrokh and Hassan Pazira  presented Shrinkage estimator in Gamma Type-II Censored Data under LINEX loss function. In that paper, they have explained how the LINEX loss function works however no practical or detail explanations were given in terms of changing the shape parameter and the error function. In this study we have explained how the LINEX loss function works through practical or detail explanations in terms of changing the shape parameter and the error function, also see how the loss function works with the data generated from gamma distribution through resampling methods to compare the performance of LINEX loss function considering the relative estimation error and usual estimation error through generating random numbers from gamma distribution like randomization method and by using bootstrapping samples. The very intention is to find out which resampling method performs well in using the LINEX loss function. Using Monte Carlo Simulations these estimators are compared. It is doing draw random number from the gamma distribution and finds the maximum likelihood estimate of θ is and using this estimator to explain the LINEX loss function ; , or , where c is the shape parameter and is any estimate of the parameter . The shape of this loss function is determined by the value of c. In the analysis we use the values of shape parameter c = -0.25, -0.50, -0.75, -1 and c = 0.25, 0.50, 0.75, 1. The same procedure is done by using bootstrapping method, and finally compared between this two methods. The relative estimation error should be used instead of the estimation error where the LINEX loss function works better in both of the cases. Between the two estimators, bootstrap method is better work because although the characteristics are same, bootstrap method is more dispersed than others.
Open Journal of Statistics, Volume 10, pp 31-51; doi:10.4236/ojs.2020.101003
Abstract:The purpose of this article is to present an alternative method for intervention analysis of time series data that is simpler to use than the traditional method of fitting an explanatory Autoregressive Integrated Moving Average (ARIMA) model. Time series regression analysis is commonly used to test the effect of an event on a time series. An econometric modeling method, which uses a heteroskedasticity and autocorrelation consistent (HAC) estimator of the covariance matrix instead of fitting an ARIMA model, is proposed as an alternative. The method of parametric bootstrap is used to compare the two approaches for intervention analysis. The results of this study suggest that the time series regression method and the HAC method give very similar results for intervention analysis, and hence the proposed HAC method should be used for intervention analysis, instead of the more complicated method of ARIMA modeling. The alternative method presented here is expected to be very helpful in gaming and hospitality research.
Open Journal of Statistics, Volume 10, pp 10-30; doi:10.4236/ojs.2020.101002
Abstract:When longitudinal data contains outliers, the classical least-squares approach is known to be not robust. To solve this issue, the exponential squared loss (ESL) function with a tuning parameter has been investigated for longitudinal data. However, to our knowledge, there is no paper to investigate the robust estimation procedure against outliers within the framework of mean-covariance regression analysis for longitudinal data using the ESL function. In this paper, we propose a robust estimation approach for the model parameters of the mean and generalized autoregressive parameters with longitudinal data based on the ESL function. The proposed estimators can be shown to be asymptotically normal under certain conditions. Moreover, we develop an iteratively reweighted least squares (IRLS) algorithm to calculate the parameter estimates, and the balance between the robustness and efficiency can be achieved by choosing appropriate data adaptive tuning parameters. Simulation studies and real data analysis are carried out to illustrate the finite sample performance of the proposed approach.
Open Journal of Statistics, Volume 10, pp 64-73; doi:10.4236/ojs.2020.101005
Abstract:The study is on the Binary logistic models of home ownership among civil servants in Wukari, Nigeria. The data used is of primary source using questionnaires. The multicollinear data, as well as the reduced data using the Principal component analysis and the stepwise regression methods to determine the factors that chiefly account for home ownership, were x-rayed. Four components were selected out of six namely grade level of respondent, cadre of institution of service of respondent, family size of respondent and age of respondent. The four components selected accounted for 87.78 percent of the variation and four variables were selected from them. The logit model for home ownership status is obtained from the selected variables. Test for the adequacy of the model was carried out using the count R2 which indicates how useful the explanatory variables are in predicting the response variables and can be referred to as measures of effect size. In testing the significance of each of the factors only Age of respondent is significant in determining variability in the home Ownership Model.
Open Journal of Statistics, Volume 10, pp 1-9; doi:10.4236/ojs.2020.101001
Abstract:In this study, we analyze brain activity data describing functional magnetic resonance imaging (MRI) imaging of 820 subjects with each subject being scanned at 4 different times. This multiple scanning gives us an opportunity to observe the consistency of imaging characteristics within the subjects as compared to the variability across the subjects. The most consistent characteristics are then used for the purpose of predicting subjects’ traits. We concentrate on four predictive methods (Regression, Logistic Regression, Linear Discriminant Analysis and Random Forest) in order to predict subjects’ traits such as gender and age based on the brain activities observed between brain regions. Those predictions are done based on the adjusted communication activity among the brain regions, as assessed from 4 scans of each subject. Due to a large number of such communications among the 116 brain regions, we performed a preliminary selection of the most promising pairs of brain regions. Logistic Regression performed best in classifying the subject gender based on communication activity among the brain regions. The accuracy rate was 85.6 percent for an AIC step-wise selected Logistic Regression model. On the other hand, the Logistic Regression model maintaining the entire set of ranked predictor was capable of getting an 87.7 percent accuracy rate. It is interesting to point out that the model with the AIC selected features was better classifying males, whereas the complete ranked model was better classifying females. The Random Forest technique performed best for prediction of age (grouped within five categories as provided by the original data) with 48.8 percent accuracy rate. Any set of predictors between 200 and 1600 was presenting similar rates of accuracy.
Open Journal of Statistics, Volume 9, pp 41-47; doi:10.4236/ojs.2019.91004
Abstract:Compound Poisson risk model has been simulated. It has started with exponential claim sizes. The simulations have checked for infinite ruin probabilities. An appropriate time window has been chosen to estimate and compare ruin probabilities. The infinite ruin probabilities of two-compound Poisson risk process have estimated and compared them with standard theoretical results.
Open Journal of Statistics, Volume 9, pp 470-483; doi:10.4236/ojs.2019.94032
Open Journal of Statistics, Volume 9, pp 445-457; doi:10.4236/ojs.2019.94030
Open Journal of Statistics, Volume 9, pp 484-493; doi:10.4236/ojs.2019.94033
Open Journal of Statistics, Volume 9, pp 436-444; doi:10.4236/ojs.2019.94029