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In data science, vector autoregression (VAR) models are popular in modeling multivariate time series in the environmental sciences and other applications. However, these models are computationally complex with the number of parameters…
Quantile regression has become a valuable tool to analyze heterogeneous covaraite-response associations that are often encountered in practice. The development of quantile regression methodology for high-dimensional covariates primarily…
Recent advances in autoregressive (AR) generative models have produced increasingly powerful systems for media synthesis. Among them, next-scale prediction has emerged as a popular paradigm, where models generate images in a coarse-to-fine…
Quantile regression is a powerful statistical methodology that complements the classical linear regression by examining how covariates influence the location, scale, and shape of the entire response distribution and offering a global view…
Linear Regression is a seminal technique in statistics and machine learning, where the objective is to build linear predictive models between a response (i.e., dependent) variable and one or more predictor (i.e., independent) variables. In…
The VQE algorithm has turned out to be quite expensive to run given the way we currently access quantum processors (i.e. over the cloud). In order to alleviate this issue, we introduce Quantum Sampling Regression (QSR), an alternative…
In this article, I introduce the sivqr command, which estimates the coefficients of the instrumental variables (IV) quantile regression model introduced by Chernozhukov and Hansen (2005). The sivqr command offers several advantages over the…
Along with the widespread adoption of high-dimensional data, traditional statistical methods face significant challenges in handling problems with high correlation of variables, heavy-tailed distribution, and coexistence of sparse and dense…
The Multi-Kink Quantile Regression (MKQR) model is an important tool for analyzing data with heterogeneous conditional distributions, especially when quantiles of response variable are of interest, due to its robustness to outliers and…
This paper introduces a novel scheme to progressively estimate interferometric phases from a stack of synthetic aperture radar (SAR) images. The scheme is shown to yield comparable performance to full-covariance algorithms for a realistic…
We study one particular type of multivariate spatial autoregression (MSAR) model with diverging dimensions in both responses and covariates. This makes the usual MSAR models no longer applicable due to the high computational cost. To…
We propose a novel framework for fitting additive quantile regression models, which provides well calibrated inference about the conditional quantiles and fast automatic estimation of the smoothing parameters, for model structures as…
We propose regression models for curve-valued responses in two or more dimensions, where only the image but not the parametrization of the curves is of interest. Examples of such data are handwritten letters, movement paths or outlines of…
We introduce a new paradigm for AutoRegressive (AR) image generation, termed Set AutoRegressive Modeling (SAR). SAR generalizes the conventional AR to the next-set setting, i.e., splitting the sequence into arbitrary sets containing…
Time series of individual subjects have become a common data type in psychological research. These data allow one to estimate models of within-subject dynamics, and thereby avoid the notorious problem of making within-subjects inferences…
We propose a new class of spatio-temporal models with unknown and banded autoregressive coefficient matrices. The setting represents a sparse structure for high-dimensional spatial panel dynamic models when panel members represent economic…
This paper proposes a novel conditional heteroscedastic time series model by applying the framework of quantile regression processes to the ARCH(\infty) form of the GARCH model. This model can provide varying structures for conditional…
Constructing valid prediction intervals rather than point estimates is a well-established approach for uncertainty quantification in the regression setting. Models equipped with this capacity output an interval of values in which the ground…
Autoregressive visual generation has garnered increasing attention due to its scalability and compatibility with other modalities compared with diffusion models. Most existing methods construct visual sequences as spatial patches for…
Understanding the time-varying structure of complex temporal systems is one of the main challenges of modern time series analysis. In this paper, we show that every uniformly-positive-definite-in-covariance and sufficiently short-range…