Distance-Based Statistical Inference

Statistical distances, divergences, and similar quantities have an extensive history play important role in the statistical related scientific literature. This shows up estimation, where we often use estimators based on minimizing a distance. Distances also prominent hypothesis testing model selection. We review properties of distances that are used work, present their properties, show how they compare to each other. discuss approximation framework for model-based inference using distances. Emphasis is placed identifying what sense which can be interpreted as loss functions assessment. special class quadratic connect it with classical goodness-of-fit paradigm, demonstrate its problem assessing fit. These methods analyzing very large samples.