Small area estimates have received much attention from both private and public sectors due to the growing demand for effective planning of health services, apportioning of government funds and policy and decision making. Surveys are generally designed to give representative estimates at national or district level, but estimates of variables of interest are often also needed at lower levels. These cannot be reliably obtained from the survey data as the sample sizes at these levels are too small. Census data are often available, but only give limited information with respect to the variables of interest. This problem is addressed by using small area estimation techniques, which combine the estimates from the survey and census data sets. The main purpose of this paper is obtaining confidence intervals based on the empirical best linear unbiased predictor (EBLUP) estimates. One of the criticism of the mean squared error (MSE) estimators is that it is not area-specific since it does not involve the direct estimator in its expression. However, most of the confidence intervals in the literature are constructed based on those MSEs. In this paper, we propose area specific confidence intervals for small area parameters under the Fay-Herriot model using area specific MSEs. We extend these confidence intervals to the difference between two small area means. The effectiveness of the proposed methods are also investigated via simulation studies and compared with the Cox (1975) and Prasad and Prasad and Rao (1990) methods. Our simulation results show that the proposed methods have higher coverage probabilities. Those methods are applied to the percentage of food expenditure measures in Ethiopia using the 2010/11 Household Consumption Expenditure (HCE) survey and the 2007 census data sets.

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Area level linear mixed models can be generally applied to produce small area indirect estimators when only aggregated data such as sample means are available. This paper tries to fill an important research gap in small area estimation literature, the problem of constructing confidence intervals (CIs) when the estimated variance of the random effect as well as the estimated mean squared error (MSE) is negative. More precisely, the coverage accuracy of the proposed CI is of the order O(m −3/2), where m is the number of sampled areas. The performance of the proposed method is illustrated with respect to coverage probability (CP) and average length (AL) using a simulation experiment. Simulation results demonstrate the superiority of the proposed method over existing naive CIs. In addition, the proposed CI based on the weighted estimator is comparable with the existing corrected CIs based on empirical best linear unbiased predictor (EBLUP) in the literature.

The 2019 novel coronavirus disease (COVID-19) has spread rapidly to many countries around the world from Wuhan, the capital of China’s Hubei province since December 2019. It has now a huge effect on the global economy. As of 13 September 2020, more than 28, 802, 775, and 920, 931 people are infected and dead, respectively. The mortality of COVID-19 infections is increasing as the number of infections increase. Many countries published control measures to contain its spread. Even though there are many drugs and vaccines under trial by pharmaceutical companies and research groups, no specific vaccine or drug has yet been found. Therefore, it is necessary to explain the behaviour of the case fatality rate (CFR) of COVID-19 using the most updated COVID-19 epidemiological data before 13 September 2020. The dynamics in the CFR were analyzed using the Markov-switching autoregressive (MSAR) models. Results showed that the two-regime and three-regime MSAR approach better captured the non-linear dynamics in the CFR time series data for each of the top heavily infected countries including the world. The results also showed that rises in CFRs are more volatile than drops. We believe that this information can be useful for the government to establish appropriate policies in a timely manner.