In this paper, the estimation for finite population total of a study variable will be considered, and the local linear regression will be used. The study variable is available for the sample and is supplemented by two auxiliary variables, which are available for every element in the finite population. Also, the resampling methods will be combined with the local linear regression method to estimate the total. The comparisons between different methods will be performed based on the mean squared error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). A simulation study is carried out to assess the effects.

The class of bivariate integer-valued time series models, described via copula theory, is gaining popularity in the literature because of applications in health sciences, engineering, financial management and more. Each time series follows a Markov chain with the serial dependence captured using copula-based distribution functions from the Poisson and the zero-inflated Poisson margins. The copula theory is again used to capture the dependence between the two series. However, the efficiency and adaptability of the copula are being challenged because of the discrete nature of data and also in the case of zero-inflation of count time series. Likelihood-based inference is used to estimate the model parameters for simulated and real data with the bivariate integral of copula functions. While such copula functions offer great flexibility in capturing dependence, there remain challenges related to identifying the best copula type for a given application.  This paper presents a survey of the literature on bivariate copula for discrete data with an emphasis on the zero-inflated nature of the modelling. We demonstrate additional experiments on to confirm that the copula has potential as greater research area.

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The nonparametric regression estimator for the finite population total under twostage sampling is introduced using a new technique. In stage one, a sample of clusters is selected and in stage two, sub samples of elements within each selected cluster are obtained. The auxiliary variable is available for all elements in the population and the nonparametric model describes the relationship between the study variable and the auxiliary variable. The kernel and local linear regression is used in the estimation of total without using the expressions of the inclusion probabilities and three scenarios are proposed to estimate the finite population total. The comparison between the two nonparametric methods is performed based on the mean squared error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). Also, a comparison between the three scenarios is done. These comparisons are performed using a simulation study.