Related papers: On the minimal penalty for Markov order estimation

We develop a constant-tracking likelihood theory for two nonregular models: the folded normal and finite Gaussian mixtures. For the folded normal, we prove boundary coercivity for the profiled likelihood, show that the profile path of the…

Assume one observes independent categorical variables or, equivalently, one observes the corresponding multinomial variables. Estimating the distribution of the observed sequence amounts to estimating the expectation of the multinomial…

We consider the estimation of high-dimensional network structures from partially observed Markov random field data using a penalized pseudo-likelihood approach. We fit a misspecified model obtained by ignoring the missing data problem. We…

Consider a probability measure supported by a regular geodesic ball in a manifold. For any p larger than or equal to 1 we define a stochastic algorithm which converges almost surely to the p-mean of the measure. Assuming furthermore that…

We develop a penalized likelihood estimation framework to estimate the structure of Gaussian Bayesian networks from observational data. In contrast to recent methods which accelerate the learning problem by restricting the search space, our…

This paper focuses on exploring the sparsity of the inverse covariance matrix $\bSigma^{-1}$, or the precision matrix. We form blocks of parameters based on each off-diagonal band of the Cholesky factor from its modified Cholesky…

The Skolem problem and the related Positivity problem for linear recurrence sequences are outstanding number-theoretic problems whose decidability has been open for many decades. In this paper, the inherent mathematical difficulty of a…

Empirical likelihood is a powerful semi-parametric method increasingly investigated in the literature. However, most authors essentially focus on an i.i.d. setting. In the case of dependent data, the classical empirical likelihood method…

In many empirical studies of a large two-sided matching market (such as in a college admissions problem), the researcher performs statistical inference under the assumption that they observe a random sample from a large matching market. In…

Scaled type Markov renewal processes generalize classical renewal processes: renewal times come from a one parameter family of probability laws and the sequence of the parameters is the trajectory of an ergodic Markov chain. Our primary…

We consider Markov decision processes where the state of the chain is only given at chosen observation times and of a cost. Optimal strategies involve the optimisation of observation times as well as the subsequent action values. We…

If the log likelihood is approximately quadratic with constant Hessian, then the maximum likelihood estimator (MLE) is approximately normally distributed. No other assumptions are required. We do not need independent and identically…

This paper introduces a graph-based algorithm for solving single-item, single-location inventory lot-sizing problems under non-stationary stochastic demand using the $(R_t, S_t)$ policy and a penalty cost scheme. The proposed method relaxes…

Sparse reconstruction approaches using the re-weighted l1-penalty have been shown, both empirically and theoretically, to provide a significant improvement in recovering sparse signals in comparison to the l1-relaxation. However, numerical…

Suppose the edges of the complete graph on $n$ vertices are assigned a uniformly chosen random ordering. Let $X$ denote the corresponding number of Hamiltonian paths that are increasing in this ordering. It was shown in a recent paper by…

We consider the problem of estimation of a covariance matrix for Gaussian data in a high dimensional setting. Existing approaches include maximum likelihood estimation under a pre-specified sparsity pattern, l_1-penalized loglikelihood…

Information theoretic criteria (ITC) have been widely adopted in engineering and statistics for selecting, among an ordered set of candidate models, the one that better fits the observed sample data. The selected model minimizes a penalized…

In this paper we consider high-dimensional multiclass classification by sparse multinomial logistic regression. We propose first a feature selection procedure based on penalized maximum likelihood with a complexity penalty on the model size…

This paper is devoted to studying the average optimality in continuous-time Markov decision processes with fairly general state and action spaces. The criterion to be maximized is expected average rewards. The transition rates of underlying…

Let X,X_1,X_2,... be independent identically distributed random variables and let h(x,y)=h(y,x) be a measurable function of two variables. It is shown that the bounded law of the iterated logarithm, $\limsup_n (n\log\log n)^{-1}|\sum_{1<=…