Model Assisted Statistics and Applications

This paper examines the extent of poverty in different districts (small domains) of the State of Odisha, India using direct, synthetic, composite, and model based small area estimation techniques. The district level poverty estimates are based on data collected during the 68 th round survey (2011–12) of the National Sample Survey Office (NSSO) and 2011 Population Census of India. It is shown that the model-based district level estimates are reasonably more reliable compared to other methods under comparison as confirmed by the diagnostic procedures.

In this paper, we have considered the exponentiated Pareto type I distribution. Various structural properties of the exponentiated Pareto type I distribution (such as quantile function, moments, incomplete moments, conditional moments, mean deviation about mean and median, stochastic ordering, Bonferroni and Lorenz curves, Renyi entropy and order statistics) are derived. We establish explicit expressions and recurrence relations for single and product moments of record values from exponentiated Pareto type I distribution. These recurrence relations enable computations of the means, variances and covariances of all record values for all sample sizes in a simple and effcient manner. By using these relations, we tabulate the first four moments and variances of record values. The maximum likelihood estimators of the unknown parameters cannot be obtained in explicit forms, and they have to be obtained by solving non-linear equations only. The asymptotic confidence intervals for the parameters are also obtained based on asymptotic variance covariance matrix. An application of the model to a real data sets is presented and compared with the fit attained by some other well-known two and three parameters distributions.

The aim of this research is to develop the novel procedure of Adaptive Neuro-Fuzzy Inference System (ANFIS) modeling for forecasting time series data. The procedure development applies statistical inference based on Lagrange Multiplier (LM) test for selecting input variables, determining the number of clusters, and generating the rule-bases. For selecting inputs, several lags which are indicated significantly different to zero are divided into 2 clusters (minimum number of clusters), and then the lags are selected as optimal inputs of ANFIS based on LM test procedure. The cluster numbers of optimal inputs are added using LM-test procedure such optimal clusters are obtained. Based on those results, a number of rule-bases are generated. The developed model is applied for forecasting cayenne production data in Central Java. The result of proposed procedure is that the optimal inputs consist of 2 lags (lag-1 and lag-3) which are divided into 2 clusters. In this case, the two rules are selected as optimal rules. Finally, the model can work well, and generates very satisfying result in forecasting cayenne production data. Based on the Root Mean Squares Error (RMSE) value, the ANFIS performance is better than performance of Autoregressive Integrated Moving Average (ARIMA) for forecasting cayenne production data in Central Java.

In order to estimate the proportion of people bearing a sensitive characteristic in a community, a sample is selected with unequal probabilities and randomized response data are obtained. Supposing data on a related variable are at hand in addition a model-design based estimation procedure modifying Chaudhuri and Saha’s (2004) is developed and studied. Four well-known Randomized Response (RR) methods are illustrated and a one-parameter logistic regression model is tried. Empirical Bayes estimation is examined and simulated results are presented to study the resulting efficacy.

When making predictions and inferences, data analysts are often faced with the challenge of selecting the best model among competing models as a result of large number of regressors that cumulate into large model space. Bayesian model averaging (BMA) is a technique designed to help account for uncertainty inherent in model selection process. In Bayesian analysis, issues of the choice of prior distribution have been quite delicate in data analysis and posterior model probabilities (PMP) in the context of model uncertainty under model selection process are typically sensititve to the specification of prior distribution. This research identified a set of eleven candidate default priors (Zellner’s g-priors) prominent in literature and applicable in Bayesian model averaging. A new robust g-prior specification for regression coefficients in Bayesian Model Averaging is investigated and its predictive performance assessed along with other g-prior structures in literature. The predictive abilities of these g-prior structures are assessed using log predictive scores (LPS) and log maximum likelihood (LML). The sensitivity of posterior results to the choice of these g-prior structures was demonstrated using simulated data and real-life data. The simulated data obtained from multivariate normal distribution were first used to demonstrate the predictive performance of the g-prior structures and later contaminated for the same purpose. Similarly for the same purpose, the real life data were normalized before using the data as obtained. Empirical findings reveal that under different conditions, the new g-prior structure exhibited robust, equally competitive and consistent predictive ability when compared with identified g-prior structures from the literature. The new g-prior offers a sound, fully Bayesian approach that features the virtues of prior input and predictive gains that minimise the risk of misspecification.

In this paper, a trivariate generalized non linear mixed model (TGLMM) using probit and complementary log-log transformations, is considered. These models are helpful in studying the complex relationship among the sensitivity (SN), specificity (SP) and disease prevalence (DP). For estimation of SN, SP, DP, positive (negative) predictive values (PPV and NPV) and positive (negative) likelihood ratios, Non-linear Mixed (NLMIXED) approach has been used. Model selection techniques are used to identify the best-fitting model for making statistical inference. The proposed trivariate non linear random effects models prove to be very useful in practice for meta-analysis of diagnostic accuracy studies.

In modern world, wine has become a part and pencil of life and culture. With the improvement of production techniques, wine making has been turned into as a form of art and a branch of science. Italian wine is very popular because of its variation in taste. The taste of wine depends on different types of cultivars. This paper attempts to classify the cultivars on the basis of different chemical constituents recorded as wine data. To accomplish this task, we used linear discriminant analysis (LDA), multinomial logistic regression (MLR), random forest (RF) and support vector machine (SVM) classification techniques. We have analyzed these in the absence of outliers and in the presence of different rate of outliers. In both of the cases, bootstrapping is used due to small data. We have used the accuracy, sensitivity and specificity as the measuring criteria of classification techniques. In absence of the outlier, LDA gives maximum classification accuracy, sensitivity and specificity. When the percentage of outlier is increases, the performance of RF tends to get better than LDA. Generally, we can suggest LDA when such type of data is obtained in the absence of outliers and RF in the presence of outliers.