In 2015, the United Nations (UN) set up 17 Sustainable Development Goals (SDGs) to be achieved by 2030 (General Assembly, 2015). The goals encompass indicators of various socioeconomic characteristics (General Assembly, 2015). To reach them, there is a need to reliably measure the indicators, especially at disaggregated levels. National Statistical Institutes (NSI) collect data on various socio-economic indicators by conducting censuses or sample surveys. Although a census provides data on the entire population, it is only carried out every 10 years in most countries and it requires enormous financial resources. Sample surveys on the other hand are commonly used because they are cheaper and require a shorter time to collect (Sarndal et al., 2003; Cochran, 2007). They are, therefore, essential sources of data on the country’s key socio-economic indicators, which are necessary for policy-making, allocating resources, and determining interventions necessary. Surveys are mostly designed for the national level and specific planned areas or domains. Therefore, the drawback is sample surveys are not adequate for data dis-aggregation due to small sample sizes (Rao and Molina, 2015). In this thesis, geographical divisions will be called areas, while other sub-divisions such as age-sex-ethnicity will be called domains in line with (Pfeffermann, 2013; Rao and Molina, 2015). One solution to obtain reliable estimates at disaggregated levels is to use small area estimation (SAE) techniques. SAE increases the precision of survey estimates by combining the survey data and another source of data, for example, a previous census, administrative data or other passively recorded data such as mobile phone data as used in Schmid et al. (2017). The results obtained using the survey data only are called direct estimates, while those obtained using SAE models will be called model-based estimates. The auxiliary data are covariates related to the response variable of interest (Rao and Molina, 2015). According to Rao and Molina (2015), an area or domain is regarded as small if the area or domain sample size is inadequate to estimate the desired accuracy. The field of SAE has grown substantially over the years mainly due to the demand from governments and private sectors. Currently, it is possible to estimate several linear and non-linear target statistics such as the mean and the Gini coefficient (Gini, 1912), respectively. This thesis contributes to the wide literature on SAE by presenting three important applications using Kenyan data sources. Chapter 1 is an application to estimate poverty and inequality in Kenya. The Empirical Best Predictor (EBP) of Molina and Rao (2010) and the M-quantile model of Chambers and Tzavidis (2006) are used to estimate poverty and inequality in Kenya. Four indicators are estimated, i.e. the mean, the Head Count Ratio, the Poverty Gap and the Gini coefficient. Three transformations are explored: the logarithmic, log-shift and the Box-Cox to mitigate the requirement for normality of model errors. The M-quantile model is used as a robust alternative to the EBP. The mean squared errors are estimated using bootstrap procedures. Chapter 2 is an application to estimate health insurance coverage in Kenyan counties using a binary M-quantile SAE model (Chambers et al., 2016) for women and men aged 15 to 49 years old. This has the advantage that we avoid specifying the distribution of the random effects and distributional robustness is automatically achieved. The MSE is estimated using an analytical approach based on Taylor series linearization. Chapter 3 presents the estimation of overweight prevalence at the county level in Kenya. In this application, the Fay-Herriot model (Fay and Herriot, 1979) is explored with arcsine square-root transformation. This is to stabilize the variance and meet the assumption of normality. To transform back to the original scale, we use a bias-corrected back transformation. For this model, the design variance is smoothed using Generalized Variance Functions as in (Pratesi, 2016, Chapter 11). The mean squared error is estimated using a bootstrap procedure. In summary, this thesis contributes to the vast literature on small area estimation from an applied perspective by; (a) Presenting for the first time regional disaggregated SAE results for selected indicators for Kenya. (b) Combining data sources to improve the estimation of the selected disaggregated socioeconomic indicators. (c) Exploring data-driven transformations to mitigate the assumption of normality in linear and linear mixed-effects models. (d) Presenting a robust approach to small area estimation based on the M-quantile model. (e) Estimating the mean squared error to access uncertainty using bootstrap procedures.