Statistics and Computing最新文献

In this article, an algorithm for maximum-likelihood estimation of regime-switching diffusions is proposed. The proposed approach uses a Fourier transform to numerically solve the system of Fokker–Planck or forward Kolmogorow equations for the temporal evolution of the state densities. Monte Carlo simulations confirm the theoretically expected consistency of this approach for moderate sample sizes and its practical feasibility for certain regime-switching diffusions used in economics and biology with moderate numbers of states and parameters. An application to animal movement data serves as an illustration of the proposed algorithm.

Hilbert-Schmidt Independence Criterion (HSIC) has recently been introduced to the field of single-index models to estimate the directions. Compared with other well-established methods, the HSIC based method requires relatively weak conditions. However, its performance has not yet been studied in the prevalent high-dimensional scenarios, where the number of covariates can be much larger than the sample size. In this article, based on HSIC, we propose to estimate the possibly sparse directions in the high-dimensional single-index models through a parameter reformulation. Our approach estimates the subspace of the direction directly and performs variable selection simultaneously. Due to the non-convexity of the objective function and the complexity of the constraints, a majorize-minimize algorithm together with the linearized alternating direction method of multipliers is developed to solve the optimization problem. Since it does not involve the inverse of the covariance matrix, the algorithm can naturally handle large p small n scenarios. Through extensive simulation studies and a real data analysis, we show that our proposal is efficient and effective in the high-dimensional settings. The (texttt {Matlab}) codes for this method are available online.

Multivariate Hawkes Processes (MHPs) are a class of point processes that can account for complex temporal dynamics among event sequences. In this work, we study the accuracy and computational efficiency of three classes of algorithms which, while widely used in the context of Bayesian inference, have rarely been applied in the context of MHPs: stochastic gradient expectation-maximization, stochastic gradient variational inference and stochastic gradient Langevin Monte Carlo. An important contribution of this paper is a novel approximation to the likelihood function that allows us to retain the computational advantages associated with conjugate settings while reducing approximation errors associated with the boundary effects. The comparisons are based on various simulated scenarios as well as an application to the study of risk dynamics in the Standard & Poor’s 500 intraday index prices among its 11 sectors.

Phylogenetic trees are key data objects in biology, and the method of phylogenetic reconstruction has been highly developed. The space of phylogenetic trees is a nonpositively curved metric space. Recently, statistical methods to analyze samples of trees on this space are being developed utilizing this property. Meanwhile, in Euclidean space, the log-concave maximum likelihood method has emerged as a new nonparametric method for probability density estimation. In this paper, we derive a sufficient condition for the existence and uniqueness of the log-concave maximum likelihood estimator on tree space. We also propose an estimation algorithm for one and two dimensions. Since various factors affect the inferred trees, it is difficult to specify the distribution of a sample of trees. The class of log-concave densities is nonparametric, and yet the estimation can be conducted by the maximum likelihood method without selecting hyperparameters. We compare the estimation performance with a previously developed kernel density estimator numerically. In our examples where the true density is log-concave, we demonstrate that our estimator has a smaller integrated squared error when the sample size is large. We also conduct numerical experiments of clustering using the Expectation-Maximization algorithm and compare the results with k-means++ clustering using Fréchet mean.

Bootstrap and Jackknife estimates, (T_{n,B}^*) and (T_{n,J},) respectively, of a population parameter (theta ) are both used in statistical computations; n is the sample size, B is the number of Bootstrap samples. For any (n_0) and (B_0,) Bootstrap samples do not add new information about (theta ) being observations from the original sample and when (B_0<infty ,) (T_{n_0,B_0}^*) includes also resampling variability, an additional source of uncertainty not affecting (T_{n_0, J}.) These are neglected in theoretical papers with results for the utopian (T_{n, infty }^*, ) that do not hold for (B<infty .) The consequence is that (T^*_{n_0, B_0}) is expected to have larger mean squared error (MSE) than (T_{n_0,J},) namely (T_{n_0,B_0}^*) is inadmissible. The amount of inadmissibility may be very large when populations’ parameters, e.g. the variance, are unbounded and/or with big data. A palliating remedy is increasing B, the larger the better, but the MSEs ordering remains unchanged for (B<infty .) This is confirmed theoretically when (theta ) is the mean of a population, and is observed in the estimated total MSE for linear regression coefficients. In the latter, the chance the estimated total MSE with (T_{n,B}^*) improves that with (T_{n,J}) decreases to 0 as B increases.

Most scientific publications follow the familiar recipe of (i) obtain data, (ii) fit a model, and (iii) comment on the scientific relevance of the effects of particular covariates in that model. This approach, however, ignores the fact that there may exist a multitude of similarly-accurate models in which the implied effects of individual covariates may be vastly different. This problem of finding an entire collection of plausible models has also received relatively little attention in the statistics community, with nearly all of the proposed methodologies being narrowly tailored to a particular model class and/or requiring an exhaustive search over all possible models, making them largely infeasible in the current big data era. This work develops the idea of forward stability and proposes a novel, computationally-efficient approach to finding collections of accurate models we refer to as model path selection (MPS). MPS builds up a plausible model collection via a forward selection approach and is entirely agnostic to the model class and loss function employed. The resulting model collection can be displayed in a simple and intuitive graphical fashion, easily allowing practitioners to visualize whether some covariates can be swapped for others with minimal loss.

Effective estimation of covariance matrices is crucial for statistical analyses and applications. In this paper, we focus on the robust estimation of covariance matrix for interval-valued data in low and moderately high dimensions. In the low-dimensional scenario, we extend the Minimum Covariance Determinant (MCD) estimator to interval-valued data. We derive an iterative algorithm for computing this estimator, demonstrate its convergence, and theoretically establish that it retains the high breakdown-point property of the MCD estimator. Further, we propose a projection-based estimator and a regularization-based estimator to extend the MCD estimator to moderately high-dimensional settings, respectively. We propose efficient iterative algorithms for solving these two estimators and demonstrate their convergence properties. We conduct extensive simulation studies and real data analysis to validate the finite sample properties of these proposed estimators.

In social sciences, studies are often based on questionnaires asking participants to express ordered responses several times over a study period. We present a model-based clustering algorithm for such longitudinal ordinal data. Assuming that an ordinal variable is the discretization of an underlying latent continuous variable, the model relies on a mixture of matrix-variate normal distributions, accounting simultaneously for within- and between-time dependence structures. The model is thus able to concurrently model the heterogeneity, the association among the responses and the temporal dependence structure. An EM algorithm is developed and presented for parameters estimation, and approaches to deal with some arising computational challenges are outlined. An evaluation of the model through synthetic data shows its estimation abilities and its advantages when compared to competitors. A real-world application concerning changes in eating behaviors during the Covid-19 pandemic period in France will be presented.

To improve the estimation efficiency of high-dimensional regression problems, penalized regularization is routinely used. However, accurately estimating the model remains challenging, particularly in the presence of correlated effects, wherein irrelevant covariates exhibit strong correlation with relevant ones. This situation, referred to as correlated data, poses additional complexities for model estimation. In this paper, we propose the elastic-net multi-step screening procedure (EnMSP), an iterative algorithm designed to recover sparse linear models in the context of correlated data. EnMSP uses a small repeated penalty strategy to identify truly relevant covariates in a few iterations. Specifically, in each iteration, EnMSP enhances the adaptive lasso method by adding a weighted (l_2) penalty, which improves the selection of relevant covariates. The method is shown to select the true model and achieve the (l_2)-norm error bound under certain conditions. The effectiveness of EnMSP is demonstrated through numerical comparisons and applications in financial data.

In this article we consider Bayesian parameter inference for a type of partially observed stochastic Volterra equation (SVE). SVEs are found in many areas such as physics and mathematical finance. In the latter field they can be used to represent long memory in unobserved volatility processes. In many cases of practical interest, SVEs must be time-discretized and then parameter inference is based upon the posterior associated to this time-discretized process. Based upon recent studies on time-discretization of SVEs (e.g. Richard et al. in Stoch Proc Appl 141:109–138, 2021) we use Euler–Maruyama methods for the afore-mentioned discretization. We then show how multilevel Markov chain Monte Carlo (MCMC) methods (Jasra et al. in SIAM J Sci Comp 40:A887–A902, 2018) can be applied in this context. In the examples we study, we give a proof that shows that the cost to achieve a mean square error (MSE) of (mathcal {O}(epsilon ^2)), (epsilon >0), is (mathcal {O}(epsilon ^{-tfrac{4}{2H+1}})), where H is the Hurst parameter. If one uses a single level MCMC method then the cost is (mathcal {O}(epsilon ^{-tfrac{2(2H+3)}{2H+1}})) to achieve the same MSE. We illustrate these results in the context of state-space and stochastic volatility models, with the latter applied to real data.