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In this paper, we introduce a family of robust estimates for the parametric and nonparametric components under a generalized partially linear model, where the data are modeled by $y_i|(\mathbf{x}_i,t_i)\sim F(\cdot,\mu_i)$ with…
The accuracy of probability distributions inferred using machine-learning algorithms heavily depends on data availability and quality. In practical applications it is therefore fundamental to investigate the robustness of a statistical…
Consider a two-class classification problem where we observe samples $(X_i, Y_i)$ for i = 1, ..., n, $X_i \in R^p$ and $Y_i$ in {0, 1}. Given $Y_i = k$, $X_i$ is assumed to follow a multivariate normal distribution with mean $\mu_k \in R^k$…
In this article, the estimation of reliability of a system is discussed $p(y<x)$ when strength, $X$, and stress, $Y$, are two independent exponential distribution with different scale parameters when the available data are type II Censored…
The inflated beta regression model is widely used for modeling continuous proportions with values at the boundaries. Maximum likelihood estimation for these models is well-known for its sensitivity to outliers, which can severely distort…
Traditional methods for linear regression generally assume that the underlying error distribution, equivalently the distribution of the responses, is normal. Yet, sometimes real life response data may exhibit a skewed pattern, and assuming…
This paper introduces a new method for testing the statistical significance of estimated parameters in predictive regressions. The approach features a new family of test statistics that are robust to the degree of persistence of the…
This paper presents a model selection technique of estimation in semiparametric regression models of the type Y_i=\beta^{\prime}\underbarX_i+f(T_i)+W_i, i=1,...,n. The parametric and nonparametric components are estimated simultaneously by…
A weighted likelihood technique for robust estimation of a multivariate Wrapped Normal distribution for data points scattered on a p-dimensional torus is proposed. The occurrence of outliers in the sample at hand can badly compromise…
The family of q-Gaussian and q-exponential probability densities fit the statistical behavior of diverse complex self-similar non-equilibrium systems. These distributions, independently of the underlying dynamics, can rigorously be obtained…
In this paper, we consider the problem of parameter estimating for a family of exponential distributions. We develop the improved estimation method, which generalized the James--Stein approach for a wide class of distributions. The proposed…
Learning the distribution of a continuous or categorical response variable $\boldsymbol y$ given its covariates $\boldsymbol x$ is a fundamental problem in statistics and machine learning. Deep neural network-based supervised learning…
We consider the problem of finding anomalies in a $d$-dimensional field of independent random variables $\{Y_i\}_{i \in \left\{1,...,n\right\}^d}$, each distributed according to a one-dimensional natural exponential family $\mathcal F =…
Structured additive distributional regression models offer a versatile framework for estimating complete conditional distributions by relating all parameters of a parametric distribution to covariates. Although these models efficiently…
Many structural econometric models include latent variables on whose probability distributions one may wish to place minimal restrictions. Leading examples in panel data models are individual-specific variables sometimes treated as "fixed…
We present a Bayesian nonparametric model for conditional distribution estimation using Bayesian additive regression trees (BART). The generative model we use is based on rejection sampling from a base model. Typical of BART models, our…
This PhD thesis contains several contributions to the field of statistical causal modeling. Statistical causal models are statistical models embedded with causal assumptions that allow for the inference and reasoning about the behavior of…
Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…
Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited,…
In this paper, we propose a new class of distributions by exponentiating the random variables associated with the probability density functions of composite distributions. We also derive some mathematical properties of this new class of…