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The normality assumption on data set is very restrictive approach for modelling. The generalized form of normal distribution, named as an exponential power (EP) distribution, and its scale mixture form have been considered extensively to…
In the causal adjustment setting, variable selection techniques based on one of either the outcome or treatment allocation model can result in the omission of confounders, which leads to bias, or the inclusion of spurious variables, which…
Evidential Deep Learning (EDL) is a popular framework for uncertainty-aware classification that models predictive uncertainty via Dirichlet distributions parameterized by neural networks. Despite its popularity, its theoretical foundations…
We consider the problem of estimating parameters of stochastic differential equations (SDEs) with discrete-time observations that are either completely or partially observed. The transition density between two observations is generally…
Let $(X,Y)$ be a random vector whose conditional excess probability $\theta(x,y):=P(Y\leq y | X>x)$ is of interest. Estimating this kind of probability is a delicate problem as soon as $x$ tends to be large, since the conditioning event…
Empirical likelihood approach is one of non-parametric statistical methods, which is applied to the hypothesis testing or construction of confidence regions for pivotal unknown quantities. This method has been applied to the case of…
Determinantal point processes (DPPs) have wide-ranging applications in machine learning, where they are used to enforce the notion of diversity in subset selection problems. Many estimators have been proposed, but surprisingly the basic…
The maximum-likelihood estimator of nonlinear panel data models with fixed effects is consistent but asymptotically-biased under rectangular-array asymptotics. The literature has thus far concentrated its effort on devising methods to…
In finite mixtures of location-scale distributions, if there is no constraint or penalty on the parameters, then the maximum likelihood estimator does not exist because the likelihood is unbounded. To avoid this problem, we consider a…
Maximum pseudo-likelihood (MPL) is a semiparametric estimation method often used to obtain the dependence parameters in copula models from data. It has been shown that despite being consistent, and in some cases efficient, MPL estimation…
We develop a set of variable selection methods for the Cox model under interval censoring, in the ultra-high dimensional setting where the dimensionality can grow exponentially with the sample size. The methods select covariates via a…
Most of the existing methods for estimating the local intrinsic dimension of a data distribution do not scale well to high-dimensional data. Many of them rely on a non-parametric nearest neighbors approach which suffers from the curse of…
In this paper, we study fluctuations of conditionally centered statistics of the form $$N^{-1/2}\sum_{i=1}^N c_i(g(\sigma_i)-\mathbb{E}_N[g(\sigma_i)|\sigma_j,j\neq i])$$ where $(\sigma_1,\ldots ,\sigma_N)$ are sampled from a dependent…
Interval-censored multi-state data arise in many studies of chronic diseases, where the health status of a subject can be characterized by a finite number of disease states and the transition between any two states is only known to occur…
This paper studies the high-dimensional mixed linear regression (MLR) where the output variable comes from one of the two linear regression models with an unknown mixing proportion and an unknown covariance structure of the random…
Change-point processes are one flexible approach to model long time series. We propose a method to uncover which model parameter truly vary when a change-point is detected. Given a set of breakpoints, we use a penalized likelihood approach…
We propose an $\ell_1$-penalized estimation procedure for high-dimensional linear mixed-effects models. The models are useful whenever there is a grouping structure among high-dimensional observations, i.e. for clustered data. We prove a…
Likelihood-based inferences have been remarkably successful in wide-spanning application areas. However, even after due diligence in selecting a good model for the data at hand, there is inevitably some amount of model misspecification:…
In the context of a linear model with a sparse coefficient vector, exponential weights methods have been shown to be achieve oracle inequalities for prediction. We show that such methods also succeed at variable selection and estimation…
We consider the problem of simultaneous variable selection and estimation in additive, partially linear models for longitudinal/clustered data. We propose an estimation procedure via polynomial splines to estimate the nonparametric…