Related papers: Asymptotic properties in the Probit-Zero-inflated …
In this study, we develop a latent factor model for analysing high-dimensional binary data. Specifically, a standard probit model is used to describe the regression relationship between the observed binary data and the continuous latent…
Analyzing high-dimensional count data is a challenge and statistical model-based approaches provide an adequate and efficient framework that preserves explainability. The (multivariate) Poisson-Log-Normal (PLN) model is one such model: it…
Zero inflation is a common nuisance while monitoring disease progression over time. This article proposes a new observation driven model for zero inflated and over-dispersed count time series. The counts given the past history of the…
There are numerous applications which involve modeling multi-dimensional count data, notably in actuarial science and risk management. When such data exhibit an excess of zeros, common count models are no longer suitable. With multivariate…
We study the law of the iterated logarithm (LIL) for the maximum likelihood estimation of the parameters (as a convex optimization problem) in the generalized linear models with independent or weakly dependent ($\rho$-mixing, $m$-dependent)…
Accurate identification of parameters of load models is essential in power system computations, including simulation, prediction, and stability and reliability analysis. Conventional point estimation based composite load modeling approaches…
The workhorse model for zero-truncated count data (y = 1, 2, ...) is the zero-truncated negative binomial (ZTNB) model. We find it should seldom be used. Instead, we recommend the one-inflated zero-truncated negative binomial (OIZTNB) model…
Several interesting generative learning algorithms involve a complex probability distribution over many random variables, involving intractable normalization constants or latent variable normalization. Some of them may even not have an…
The phenomenon of benign overfitting, where a predictor perfectly fits noisy training data while attaining near-optimal expected loss, has received much attention in recent years, but still remains not fully understood beyond well-specified…
The change-plane Cox model is a popular tool for the subgroup analysis of survival data. Despite the rich literature on this model, there has been limited investigation into the asymptotic properties of the estimators of the…
Probit regression was first proposed by Bliss in 1934 to study mortality rates of insects. Since then, an extensive body of work has analyzed and used probit or related binary regression methods (such as logistic regression) in numerous…
Imputation of missing values is a strategy for handling non-responses in surveys or data loss in measurement processes, which may be more effective than ignoring them. When the variable represents a count, the literature dealing with this…
In this paper, we focus on the COM-type negative binomial distribution with three parameters, which belongs to COM-type $(a,b,0)$ class distributions and family of equilibrium distributions of arbitrary birth-death process. Besides, we show…
Protesting mildly against the notion of an exactly correct parametric model the view is adopted that the logistic regression equation is merely an approximation to the underlying, true function. The behaviour of likelihood based estimators…
Binomial data with unknown sizes often appear in biological and medical sciences and are usually overdispersed. All previous methods used parametric models and only considered overdispersion due to the variation of sizes. The proposed…
We study approximation methods for a large class of mixed models with a probit link function that includes mixed versions of the binomial model, the multinomial model, and generalized survival models. The class of models is special because…
We study a linear high-dimensional regression model in a semi-supervised setting, where for many observations only the vector of covariates $X$ is given with no response $Y$. We do not make any sparsity assumptions on the vector of…
We propose a unified framework for likelihood-based regression modeling when the response variable has finite support. Our work is motivated by the fact that, in practice, observed data are discrete and bounded. The proposed methods assume…
This research deals with the estimation and imputation of missing data in longitudinal models with a Poisson response variable inflated with zeros. A methodology is proposed that is based on the use of maximum likelihood, assuming that data…
The Dirichlet-multinomial (DM) distribution plays a fundamental role in modern statistical methodology development and application. Recently, the DM distribution and its variants have been used extensively to model multivariate count data…