Technological innovations have enabled the collection of massive amounts of complex data, posing new challenges for achieving accurate statistical inference. In this context, this thesis aims to develop statistical methods that can achieve accurate inference when handling large and complex data. It consists of two chapters, each presenting methodological developments for parametric and semiparametric models.

In the first chapter, we introduce an indirect inference based method that can achieve accurate inference for general parametric models, including those where tractable estimators are lacking. The key advantage of this method is that it provides a simple strategy to construct a consistent estimator in a computationally efficient manner, all under the guarantee of a sharp bias bound that yields accurate inference. This method is particularly useful for handling challenging data features (e.g., misclassification, censoring) and constructing robust estimators. The practical usefulness and superior finite sample performance of our proposed method are illustrated in simulation studies and a real data analysis on alcohol consumption.

In the second chapter, we extend the method developed in the first chapter to semiparametric generalized partially linear models. Our proposed estimator is shown to be consistent, asymptotically normal, and semiparametric efficient. More importantly, we show that the proposed estimator has a smaller bias order than standard estimators, which leads to a significant improvement in inference accuracy for both the parametric and nonparametric components. We present simulation studies and a real data analysis on early-stage diabetes to showcase the superior finite sample performance of our proposed method. This methodological development brings forth the importance of bias correction in inference for semiparametric models, providing valuable insights for further potential extensions, such as in survival analysis.