The standard bootstrap method is one of the methods used for resampling. It is a method that uses samples to estimate the distribution of statistics based on independent observations, then developed to be used with other statistical inferences. Different versions of bootstrap have appeared, such as the smoothed bootstrap. It is use the linear interpolation histospline to smooth between the jump points of empirical distribution to produce the smoothed empirical distribution. In this paper the two methods will be discussed and compared using the prediction intervals.
Predictive analytics techniques are widely used in the application field, and the most common of these is fitting data with functions. The aim of function fittings is to predict the value of a response, by combing the regressors. Univariate probit and logit models are used for the same purposes when the response variable is binary. Both models used applied for the estimation of the functional relationship between response and regressors. The question of which model performs better comes to the mind. For this aim, a Monte Carlo simulation was performed to compare both the univariate probit and logit models under different conditions. In In this paper we considered the simulation of, employing latent variable approach with different sample sizes, cut points, and different correlations between response variable and regressors were taken into account. To make a comparison between univariate logit and probit models, Pearson residuals, deviations, Hosmer 186 Abeer H. Alsoruji et al. and Lemesshow, area under Receiver Operating Characteristic (ROC) curve, and Pseudo-R square statistics which are used for qualitative data analysis, were calculated and the results were interpreted.
Analyzing big data poses a great challenge for numerous researchers to explore the data structure. Dimension reduction methods can be used to reduce data dimensionality, taking it from occupying a high-dimensional space to existing in a lower-dimensional space while retaining as much information as possible. Principal Component Analysis is one of the most popular used to reduce the dimensional space. The bootstrap sample is obtained by randomly sampling n times with replacement from the original sample, the method provides easy tool to understand the interactive component and develop the process. There are not enough researches discussed the stability of PCA method using bootstrap method. In this paper, the bootstrap method is used to analyze the stability of PCA results and to estimate the number of PCA in efficient way. The method is used to estimate the number of PCA that needed to classify the data set, and the effectiveness of the discussed techniques is demonstrated through real data sets.
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