Related papers: Two step estimations via the Dantzig selector for …
This paper generalizes a part of the theory of $Z$-estimation which has been developed mainly in the context of modern empirical processes to the case of stochastic processes, typically, semimartingales. We present a general theorem to…
Lasso and Dantzig selector are standard procedures able to perform variable selection and estimation simultaneously. This paper is concerned with extending these procedures to spatial point process intensity estimation. We propose adaptive…
We study the problem of parameter estimation for a univariate discretely observed ergodic diffusion process given as a solution to a stochastic differential equation. The estimation procedure we propose consists of two steps. In the first…
To successfully work on variable selection, sparse model structure has become a basic assumption for all existing methods. However, this assumption is questionable as it is hard to hold in most of cases and none of existing methods may…
For consistency (even oracle properties) of estimation and model prediction, almost all existing methods of variable/feature selection critically depend on sparsity of models. However, for ``large $p$ and small $n$" models sparsity…
In this paper, a linear model of diffusion processes with unknown drift and diagonal diffusion matrices is discussed. We will consider the estimation problems for unknown parameters based on the discrete time observation in high-dimensional…
The Dantzig selector has received popularity for many applications such as compressed sensing and sparse modeling, thanks to its computational efficiency as a linear programming problem and its nice sampling properties. Existing results…
We consider learning high-dimensional multi-response linear models with structured parameters. By exploiting the noise correlations among responses, we propose an alternating estimation (AltEst) procedure to estimate the model parameters…
We propose a generalized version of the Dantzig selector. We show that it satisfies sparsity oracle inequalities in prediction and estimation. We consider then the particular case of high-dimensional linear regression model selection with…
The goal of this paper is to construct ergodic estimators for the parameters in the double exponential Ornstein-Uhlenbeck process, observed at discrete time instants with time step size h. The existence and uniqueness, the strong…
Transductive methods are useful in prediction problems when the training dataset is composed of a large number of unlabeled observations and a smaller number of labeled observations. In this paper, we propose an approach for developing…
Inference and prediction under the sparsity assumption have been a hot research topic in recent years. However, in practice, the sparsity assumption is difficult to test, and more importantly can usually be violated. In this paper, to study…
This paper studies a Dantzig-selector type regularized estimator for linear functionals of high-dimensional linear processes. Explicit rates of convergence of the proposed estimator are obtained and they cover the broad regime from i.i.d.…
We propose a new method of the construction of the asymptotically efficient estimator-processes asymptotically equivalent to the MLE and the same time much more easy to calculate. We suppose that the observed process is ergodic diffusion…
Statistical inference for stochastic processes has advanced significantly due to applications in diverse fields, but challenges remain in high-dimensional settings where parameters are allowed to grow with the sample size. This paper…
We consider a class of linear-programming based estimators in reconstructing a sparse signal from linear measurements. Specific formulations of the reconstruction problem considered here include Dantzig selector, basis pursuit (for the case…
In this paper, we study a simple iterative method for finding the Dantzig selector, which was designed for linear regression problems. The method consists of two main stages. The first stage is to approximate the Dantzig selector through a…
Penalized estimation methods for diffusion processes and dependent data have recently gained significant attention due to their effectiveness in handling high-dimensional stochastic systems. In this work, we introduce an adaptive…
In many important statistical applications, the number of variables or parameters $p$ is much larger than the number of observations $n$. Suppose then that we have observations $y=X\beta+z$, where $\beta\in\mathbf{R}^p$ is a parameter…
We propose a novel high-dimensional linear regression estimator: the Discrete Dantzig Selector, which minimizes the number of nonzero regression coefficients subject to a budget on the maximal absolute correlation between the features and…