In this article, Small Area Estimation under a Multivariate Linear model for repeated measures data is considered. The proposed model aims to get a model which borrows strength both across small areas and over time. The model accounts for repeated surveys, grouped response units and random effects variations. Estimation of model parameters is discussed within a likelihood based approach. Prediction of random effects, small area means across time points and per group units are derived. A parametric bootstrap method is proposed for estimating the mean-squared errors of the predicted small area means. Results are supported by a simulation study.
In this paper we consider the extended generalized multivariate analysis of variance (GMANOVA) with a linearly structured covariance matrix. The main theme is to find explicit estimators for the mean and for the linearly structured covariance matrix. We show how to decompose the residual space, the orthogonal complement to the mean space, into m + 1 orthogonal subspaces and how to derive explicit estimators of the covariance matrix from the sum of squared residuals obtained by projecting observations on those subspaces. Also an explicit estimator of the mean is derived and some properties of the proposed estimators are studied.
Detecting tax fraud is a top objective for practically all tax agencies in order to maximize revenues and maintain a high level of compliance. Data mining, machine learning, and other approaches such as traditional random auditing have been used in many studies to deal with tax fraud. The goal of this study is to use Artificial Neural Networks to identify factors of tax fraud in income tax data. The results show that Artificial Neural Networks perform well in identifying tax fraud with an accuracy of 92%, a precision of 85%, a recall score of 99%, and an AUC-ROC of 95%. All businesses, either cross-border or domestic, the period of the business, small businesses, and corporate businesses, are among the factors identified by the model to be more relevant to income tax fraud detection. This study is consistent with the previous closely related work in terms of features related to tax fraud where it covered all tax types together using different machine learning models. To the best of our knowledge, this study is the first to use Artificial Neural Networks to detect income tax fraud in Rwanda by comparing different parameters such as layers, batch size, and epochs and choosing the optimal ones that give better accuracy than others. For this study, a simple model with no hidden layers, softsign activation function performs better. The evidence from this study will help auditors in understanding the factors that contribute to income tax fraud which will reduce the audit time and cost, as well as recover money foregone in income tax fraud.
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