Related papers: On a new robust method of inference for general ti…
We consider the parameter estimation problem of a probabilistic generative model prescribed using a natural exponential family of distributions. For this problem, the typical maximum likelihood estimator usually overfits under limited…
The primary objective of this scholarly work is to develop two estimation procedures - maximum likelihood estimator (MLE) and method of trimmed moments (MTM) - for the mean and variance of lognormal insurance payment severity data sets…
Strong consistency of the quasi-maximum likelihood estimator is given for a general class of multidimensional causal processes based on asyMmetric laplacian innovation.
Linear mixed models (LMMs) are a popular class of methods for analyzing longitudinal and clustered data. However, such models can be sensitive to outliers, and this can lead to biased inference on model parameters and inaccurate prediction…
This research examines the use of Large Language Models (LLMs) in predicting time series, with a specific focus on the LLMTIME model. Despite the established effectiveness of LLMs in tasks such as text generation, language translation, and…
We propose a class of estimators for the parameters of a GARCH(p,q) sequence. We show that our estimators are consistent and asymptotically normal under mild conditions. The quasi-maximum likelihood and the likelihood estimators are…
In this paper, we propose a new statistical inference method for massive data sets, which is very simple and efficient by combining divide-and-conquer method and empirical likelihood. Compared with two popular methods (the bag of little…
Latent class analysis (LCA) is a useful tool to investigate the heterogeneity of a disease population with time-to-event data. We propose a new method based on non-parametric maximum likelihood estimator (NPMLE), which facilitates…
We outline how modern likelihood theory, which provides essentially exact inferences in a variety of parametric statistical problems, may routinely be applied in practice. Although the likelihood procedures are based on analytical…
The linear regression model with a random variable (RV) measurement matrix, where the mean of the random measurement matrix has full column rank, has been extensively studied. In particular, the quasiconvexity of the maximum likelihood…
This paper proposed a new probability distribution named as inverse xgamma distribution (IXGD). Different mathematical and statistical properties,viz., reliability characteristics, moments, inverse moments, stochastic ordering and order…
Sequential change-point detection in non-Gaussian stochastic processes is challenging because the underlying densities are rarely known in real time. Classical parametric procedures such as CUSUM lose optimality under distributional…
Spatial-temporal linear model and the corresponding likelihood-based statistical inference are important tools for the analysis of spatial-temporal lattice data. In this paper, we study the asymptotic properties of maximum likelihood…
Ordinary least square (OLS), maximum likelihood (ML) and robust methods are the widely used methods to estimate the parameters of a linear regression model. It is well known that these methods perform well under some distributional…
In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…
Generalized linear mixed models (GLMMs) are used to model responses from exponential families with a combination of fixed and random effects. For variance components in GLMMs, we propose an approximate restricted likelihood ratio test that…
Estimating the unconstrained mean and covariance matrix is a popular topic in statistics. However, estimation of the parameters of $N_p(\mu,\Sigma)$ under joint constraints such as $\Sigma\mu = \mu$ has not received much attention. It can…
Robust estimators and Wald-type tests are developed for the multinomial logistic regression based on $\phi$-divergence measures. The robustness of the proposed estimators and tests is proved through the study of their influence functions…
We present a new statistical learning paradigm for Boltzmann machines based on a new inference principle we have proposed: the latent maximum entropy principle (LME). LME is different both from Jaynes maximum entropy principle and from…
Regression models based on the log-symmetric family of distributions are particularly useful when the response is strictly positive and asymmetric. In this paper, we propose a class of quantile regression models based on reparameterized…