Multiple imputation with chained equations (MICE) is a widespread approach to account for missing data in empirical research. Combining MICE with bootstrapping, that is, repeatedly resampling with replacement from the data to estimate variances and confidence intervals of statistics of interest, is not straightforward. The current document provides an overview of how to use bootstrapping with imputed data in Stata. Two main approaches (impute first and then bootstrap or vice-versa) are discussed and shortly compared. Code is provided for Stata.

Bootstrapping is a flexible, powerful and well-established statistical approach to quantify the uncertainty of virtually any point estimate. While multiple versions of bootstrap confidence intervals are already available in Stata, dbs implements the double (iterated) bootstrap. Instead of relying on parametric assumptions such as the non-parametric resampling bootstrap confidence interval does, it is more flexible and derives critical values directly from that data. To do so, multiple methods are available (analytic approach, double resampling, jackknife estimation). In a comparative simulation study it is empirically demonstrated that the strengths of the double bootstrap are particularly evident for small samples (n < 100) when heteroscedasticity is present. While all other approaches result in undercoverage, only the double bootstrap reaches the target coverage level and hence avoids incorrect statistical conclusions. The computational burden is not even necessarily larger than for other bootstrap approaches.

Spatial regression models have garnered significant attention across several disciplines, including functional magnetic resonance imaging analysis, econometrics, home price analysis, and many other domains. The phenomenon of sparsity is often found in nature, when a limited number of factors contribute significantly to the overall variation. Spatial regression models frequently use sparsity to indicate less complex computational and more superficial covariance structures. The spatial error model is a significant spatial regression model that focuses on the geographical dependence present in the error terms rather than the response variable. This study proposes an effective approach for estimating the vector of regression coefficients in the spatial error model, taking into consideration of the prior knowledge that some coefficients are insignificant and there is multicollinearity among the regressors. It also introduces pretest and shrinkage ridge estimators for spatial error regression models, evaluating their performance compared to traditional maximum likelihood estimators. It also assesses their efficacy using real-world data and bootstrapping techniques for comparison purposes.

In developed countries, especially the big-sized ones like Australia and the USA, a car is almost an inevitable necessity to carry out daily activities. Due to this, used cars have become a great alternative to brand new cars because of their cost effectiveness. In this work, estimation of prices of used cars based on numerous factors is studied statistically. Data is based on prices of used cars sold across Australia. Statistical methods like correlation and permutation tests using linear regression model, exact tests and non-parametric bootstrapping is implemented to study the relationship of price with mileage and year of manufacture of the car using p-values and null hypothesis. Predictions are also made on the price by calculating a 95% confidence interval (CI) of median prices in small portions of the dataset. The study presents potential ideas for understanding correlation between variables and parameters in business studies.