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Statistical inferences for high-dimensional regression models have been extensively studied for their wide applications ranging from genomics, neuroscience, to economics. However, in practice, there are often potential unmeasured…
We propose a new model selection method, the posterior averaging information criterion, for Bayesian model assessment from a predictive perspective. The theoretical foundation is built on the Kullback-Leibler divergence to quantify the…
The Kullback-Leibler divergence or relative entropy is an information-theoretic measure between statistical models that play an important role in measuring a distance between random variables. In the study of complex systems, random fields…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
This paper introduces a new biased estimator for the negative binomial regression model that is a generalization of Liu-type estimator proposed for the linear model in [12]. Since the variance of the maximum likelihood estimator (MLE) is…
Optimal dimensionality reduction methods are proposed for the Bayesian inference of a Gaussian linear model with additive noise in presence of overabundant data. Three different optimal projections of the observations are proposed based on…
Diffusion models for continuous state spaces based on Gaussian noising processes are now relatively well understood from both practical and theoretical perspectives. In contrast, results for diffusion models on discrete state spaces remain…
We develop a projected least squares estimator for the change point parameter in a high dimensional time series model with a potential change point. Importantly we work under the setup where the jump size may be near the boundary of the…
The paper develops new methods of non-parametric estimation a compound Poisson distribution. Such a problem arise, in particular, in the inference of a Levy process recorded at equidistant time intervals. Our key estimator is based on…
Many two-sample problems call for a comparison of two distributions from an exponential family. Density ratio estimation methods provide ways to solve such problems through direct estimation of the differences in natural parameters. The…
Considering the increasing size of available data, the need for statistical methods that control the finite sample bias is growing. This is mainly due to the frequent settings where the number of variables is large and allowed to increase…
We present a unified theoretical framework for parametric low-rank approximation, a research area devoted to the development of efficient algorithms that act as adaptive alternatives of traditional methods such as Singular Value…
Small area estimators that ignore the sampling design lack design consistency when the sampling mechanism is complex and may be severely biased under informative designs. Existing procedures that account for the survey weights under…
We present a new method for high-dimensional linear regression when a scale parameter of the additive errors is unknown. The proposed estimator is based on a penalized Huber $M$-estimator, for which theoretical results on estimation error…
We propose a new minimum-distance estimator for linear random coefficient models. This estimator integrates the recently advanced sliced Wasserstein distance with the nearest neighbor methods, both of which enhance computational efficiency.…
In this work we introduce declarative statistics, a suite of declarative modelling tools for statistical analysis. Statistical constraints represent the key building block of declarative statistics. First, we introduce a range of relevant…
Estimation using pooled sampling has long been an area of interest in the group testing literature. Such research has focused primarily on the assumed use of fixed sampling plans (i), although some recent papers have suggested alternative…
When data contains measurement errors, it is necessary to make assumptions relating the observed, erroneous data to the unobserved true phenomena of interest. These assumptions should be justifiable on substantive grounds, but are often…
Consider a nonlinear regression model : y_{i}=g(x_{i},{\theta})+e_{i}, i=1,...,n, where the x_{i} are random predictors x_{i} and {\theta} is the unknown parameter vector ranging in a set {\Theta}\subsetR^{p}. All known results on the…
This paper discusses predictive densities under the Kullback--Leibler loss for high-dimensional Poisson sequence models under sparsity constraints. Sparsity in count data implies zero-inflation. We present a class of Bayes predictive…