A statistical approach to finding a common principle of social and natural phenomena is to model the phenomena by using probabilistic models, estimate unknown parameters from observed data, and provide credibility. A classical way to do so is to construct a probabilistic model with finite-dimensional parameters which is called a parametric method. A major drawback of this is that finding a parametric form of the model that fits the observed phenomenon is not easy. It becomes even more difficult when the prior knowledge of the probabilistic structure is lacking. The finite dimensionality of the model restricts the form of the model, and excessive application of parametric methods often causes fatal error. Besides, many of the modern social and natural phenomena are so complicated that it is impossible to explain them using finite-dimensional probabilistic models.
To overcome such limitations of parametric methods, nonparametric and semiparametric methods are suggested. Unlike for parametric methods, the probabilistic models for nonparametric methods consist of infinite-dimensional components. A semiparametric method is a combination of parametric and nonparametric methods so it also allows the dimension of a model to be infinite. These methods come in handy when finding a parametric model is difficult or when you do exploratory data analysis (EDA) to find an appropriate parametric model.
In Nonparametric Inference Lab, we study statistical models in infinite-dimensional parametric spaces and related asymptotic theory for nonparametric and semiparametric methods. In particular, we study nonparametric structured models, such as additive models, partially linear regression models, varying coefficient regression models, quantile regression models, and etc. Furthermore, we aim to develop statistical methodologies that can be applied to high-dimensional low sample size (HDLSS) data in nonparametric models.
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