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Support Vector Machines (SVMs) are one of the most popular supervised learning models to classify using a hyperplane in an Euclidean space. Similar to SVMs, tropical SVMs classify data points using a tropical hyperplane under the tropical…

We explicitly quantify the empirically observed phenomenon that estimation under a stochastic block model (SBM) is hard if the model contains classes that are similar. More precisely, we consider estimation of certain functionals of random…

The coefficient of variation (CV) is commonly used to measure relative dispersion. However, since it is based on the sample mean and standard deviation, outliers can adversely affect the CV. Additionally, for skewed distributions the mean…

Anomaly detection is defined as the problem of finding data points that do not follow the patterns of the majority. Among the various proposed methods for solving this problem, classification-based methods, including one-class Support…

Because of the advance in technologies, modern statistical studies often encounter linear models with the number of explanatory variables much larger than the sample size. Estimation and variable selection in these high-dimensional problems…

In a missing-data setting, we have a sample in which a vector of explanatory variables x_i is observed for every subject i, while scalar outcomes y_i are missing by happenstance on some individuals. In this work we propose robust estimates…

There has been substantial recent work on methods for estimating the slope function in linear regression for functional data analysis. However, as in the case of more conventional finite-dimensional regression, much of the practical…

We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this…

We propose a new convex loss for Support Vector Machines, both for the binary classification and for the regression models. Therefore, we show the mathematical derivation of the dual problems and we experiment with them on several small…

We present a new approach to obtaining photometric redshifts using a kernel learning technique called Support Vector Machines (SVMs). Unlike traditional spectral energy distribution fitting, this technique requires a large and…

Markov chain Monte Carlo (MCMC) algorithms are used to estimate features of interest of a distribution. The Monte Carlo error in estimation has an asymptotic normal distribution whose multivariate nature has so far been ignored in the MCMC…

The sampling efficiency of MCMC methods in Bayesian inference for stochastic volatility (SV) models is known to highly depend on the actual parameter values, and the effectiveness of samplers based on different parameterizations varies…

We introduce a semiparametric approach for forecasting Value-at-Risk (VaR) and Expected Shortfall (ES) by modeling the conditional scale of financial returns, defined as the difference between two specified quantiles, via restricted…

There is currently an increasing interest in large vector autoregressive (VAR) models. VARs are popular tools for macroeconomic forecasting and use of larger models has been demonstrated to often improve the forecasting ability compared to…

Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…

We develop a pivotal test to assess the statistical significance of the feature variables in a single-layer feedforward neural network regression model. We propose a gradient-based test statistic and study its asymptotics using…

Robust estimators, like the median of a point set, are important for data analysis in the presence of outliers. We study robust estimators for locationally uncertain points with discrete distributions. That is, each point in a data set has…

This paper develops a novel spatial quantile function-on-scalar regression model, which studies the conditional spatial distribution of a high-dimensional functional response given scalar predictors. With the strength of both quantile…

Support Vector Machine (SVM) is powerful classification technique based on the idea of structural risk minimization. Use of kernel function enables curse of dimensionality to be addressed. However, proper kernel function for certain problem…

Maximum likelihood estimation of large Markov-switching vector autoregressions (MS-VARs) can be challenging or infeasible due to parameter proliferation. To accommodate situations where dimensionality may be of comparable order to or…