Statistical Inference: The Minimum Distance Approach

In many ways, estimation by an appropriate minimum distance method is one of the most natural ideas in statistics. However, there are many different ways of constructing an appropriate distance between the data and the model: the scope of study referred to by "Minimum Distance Estimation" is literally huge. Filling a statistical resource gap, Statistical Inference: The Minimum Distance Approach comprehensively overviews developments in density-based minimum distance inference for independently and identically distributed data. Extensions to other more complex models are also discussed.

Comprehensively covering the basics and applications of minimum distance inference, this book introduces and discusses:

• The estimation and hypothesis testing problems for both discrete and continuous models
• The robustness properties and the structural geometry of the minimum distance methods
• The inlier problem and its possible solutions, and the weighted likelihood estimation problem
• The extension of the minimum distance methodology in interdisciplinary areas, such as neural networks and fuzzy sets, as well as specialized models and problems, including semi-parametric problems, mixture models, grouped data problems, and survival analysis.

Statistical Inference: The Minimum Distance Approach gives a thorough account of density-based minimum distance methods and their use in statistical inference. It covers statistical distances, density-based minimum distance methods, discrete and continuous models, asymptotic distributions, robustness, computational issues, residual adjustment functions, graphical descriptions of robustness, penalized and combined distances, weighted likelihood, and multinomial goodness-of-fit tests. This carefully crafted resource is useful to researchers and scientists within and outside the statistics arena.

在統計學中，以適當的最小距離方法進行估計在許多方面都是最自然的想法之一。然而，有許多不同的方法可以建構數據和模型之間的適當距離：「最小距離估計」所涵蓋的研究範圍實在是非常廣泛。《統計推論：最小距離方法》填補了統計資源的空白，全面概述了基於密度的最小距離推論在獨立同分佈數據上的發展。書中還討論了對其他更複雜模型的擴展。

本書全面介紹和討論了最小距離推論的基礎和應用，包括：
- 離散和連續模型的估計和假設檢驗問題
- 最小距離方法的魯棒性質和結構幾何
- 異常值問題及其可能的解決方案，以及加權最大概似估計問題
- 在跨學科領域中擴展最小距離方法，如神經網絡和模糊集，以及特殊模型和問題，包括半參數問題、混合模型、分組數據問題和生存分析。

《統計推論：最小距離方法》全面介紹了基於密度的最小距離方法及其在統計推論中的應用。書中涵蓋了統計距離、基於密度的最小距離方法、離散和連續模型、漸近分佈、魯棒性、計算問題、殘差調整函數、魯棒性的圖形描述、懲罰和結合距離、加權概似估計和多項式適合度檢驗。這本精心製作的資源對統計學界內外的研究人員和科學家都非常有用。

Ayanendranath Basu, Hiroyuki Shioya, Chanseok Park

Ayanendranath Basu, Hiroyuki Shioya, Chanseok Park