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We introduce and study a new model for functional data. The ARHD is an autoregressive model in which the first order derivative of the random curves appears explicitely. Convergent estimates are obtained through a double penalization…
Producing probabilistic guarantee for several steps of a predicted signal follow a temporal logic defined behavior has its rising importance in monitoring. In this paper, we derive a method to compute the joint probability distribution of…
This work introduces 4 novel probabilistic and reinforcement-driven methods for association rule mining (ARM): Gaussian process-based association rule mining (GPAR), Bayesian ARM (BARM), multi-armed bandit based ARM (MAB-ARM), and…
Among the various procedures used to detect potential changes in a stochastic process the moving sum algorithms are very popular due to their intuitive appeal and good statistical performance. One of the important design parameters of a…
This paper investigates the predictive performance of model averaging in high-dimensional linear regression where the number of regressors is comparable to the sample size. We demonstrate that the double descent trajectory manifests within…
We clarify relationships between conditional (CAR) and simultaneous (SAR) autoregressive models. We review the literature on this topic and find that it is mostly incomplete. Our main result is that a SAR model can be written as a unique…
We use both simulated and real quasar light curves to explore modeling photometric reverberation-mapping (RM) data as a stochastic process. We do this using modifications to our previously developed RM method based on modeling quasar…
We propose new parametric frameworks of regression analysis with the conditional mode of a bounded response as the focal point of interest. Covariate effects estimation and prediction based on the maximum likelihood method under two new…
This paper introduces a new class of robust estimates for ARMA models. They are M-estimates, but the residuals are computed so the effect of one outlier is limited to the period where it occurs. These estimates are closely related to those…
Dynamic inference problems in autoregressive (AR/ARMA/ARIMA), exponential smoothing, and navigation are often formulated and solved using state-space models (SSM), which allow a range of statistical distributions to inform innovations and…
We tackle the problem of automatic calibration of radially distorted cameras in challenging conditions. Accurately determining distortion parameters typically requires either 1) solving the full Structure from Motion (SfM) problem involving…
Diagnostic imaging has gained prominence as potential biomarkers for early detection and diagnosis in a diverse array of disorders including cancer. However, existing methods routinely face challenges arising from various factors such as…
Generation of simulated data is essential for data analysis in particle physics, but current Monte Carlo methods are very computationally expensive. Deep-learning-based generative models have successfully generated simulated data at lower…
The autoregressive moving average (ARMA) model takes the significant position in time series analysis for a wide-sense stationary time series. The difference operator and seasonal difference operator, which are bases of ARIMA and SARIMA…
Real-time magnetic resonance imaging (MRI) methods generally shorten the measuring time by acquiring less data than needed according to the sampling theorem. In order to obtain a proper image from such undersampled data, the reconstruction…
This study reports a statistical analysis of monthly sunspot number time series and observes non homogeneity and asymmetry within it. Using Mann-Kendall test a linear trend is revealed. After identifying stationarity within the time series…
Many stochastic systems in physics and biology are investigated by recording the two-dimensional (2D) positions of a moving test particle in regular time intervals. The resulting sample trajectories are then used to induce the properties of…
We propose convenient inferential methods for potentially nonstationary multivariate unobserved components models with fractional integration and cointegration. Based on finite-order ARMA approximations in the state space representation,…
A new forecasting method based on the concept of the profile predictive the likelihood function is proposed for discrete-valued processes. In particular, generalized autoregressive and moving average (GARMA) models for Poisson distributed…
The paper considers high frequency sampled multivariate continuous-time ARMA (MCARMA) models, and derives the asymptotic behavior of the sample autocovariance function to a normal random matrix. Moreover, we obtain the asymptotic behavior…