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Cure models have been developed as an alternative modelling approach to conventional survival analysis in order to account for the presence of cured subjects that will never experience the event of interest. Mixture cure models, which model…
This paper discusses asymptotic distributions of various estimators of the underlying parameters in some regression models with long memory (LM) Gaussian design and nonparametric heteroscedastic LM moving average errors. In the simple…
Nonparametric methods for the estimation of the Levy density of a Levy process are developed. Estimators that can be written in terms of the ``jumps'' of the process are introduced, and so are discrete-data based approximations. A model…
The Laplace approximation (LA) has been proposed as a method for approximating the marginal likelihood of statistical models with latent variables. However, the approximate maximum likelihood estimators (MLEs) based on the LA are often…
We study non-parametric regression estimates for random fields. The data satisfies certain strong mixing conditions and is defined on the regular $N$-dimensional lattice structure. We show consistency and obtain rates of convergence. The…
Inference methods for computing confidence intervals in parametric settings usually rely on consistent estimators of the parameter of interest. However, it may be computationally and/or analytically burdensome to obtain such estimators in…
This paper studies simultaneous inference of conditional distributions in nonlinear time series from a sieve M-regression perspective. Existing literature on sieve M-regression has primarily focused on pointwise asymptotics, leaving the…
Probabilistic survival analysis models seek to estimate the distribution of the future occurrence (time) of an event given a set of covariates. In recent years, these models have preferred nonparametric specifications that avoid directly…
Multivariate distributions often carry latent structures that are difficult to identify and estimate, and which better reflect the data generating mechanism than extrinsic structures exhibited simply by the raw data. In this paper, we…
With the ubiquitous availability of unstructured data, growing attention is paid as how to adjust for selection bias in such non-probability samples. The majority of the robust estimators proposed by prior literature are either fully or…
We propose a new method for the Maximum Likelihood Estimator (MLE) of nonlinear mixed effects models when the variance matrix of Gaussian random effects has a prescribed pattern of zeros (PPZ). The method consists in coupling the recently…
We study nonparametric maximum likelihood estimation of a log-concave density function $f_0$ which is known to satisfy further constraints, where either (a) the mode $m$ of $f_0$ is known, or (b) $f_0$ is known to be symmetric about a fixed…
The usual parametric models for survival data are of the following form. Some parametrically specified hazard rate $\alpha(s,\theta)$ is assumed for possibly censored random life times $X_1^0,\ldots,X_n^0$; one observes only…
The Negative Binomial distribution becomes highly skewed under extreme dispersion. Even at moderately large sample sizes, the sample mean exhibits a heavy right tail. The standard Normal approximation often does not provide adequate…
The paper develops new methods of non-parametric estimation a compound Poisson distribution. Such a problem arise, in particular, in the inference of a Levy process recorded at equidistant time intervals. Our key estimator is based on…
Latent Gaussian models have a rich history in statistics and machine learning, with applications ranging from factor analysis to compressed sensing to time series analysis. The classical method for maximizing the likelihood of these models…
Time-homogeneous Markov chains are often used as disease progression models in studies of cost-effectiveness and optimal decision-making. Maximum likelihood estimation of these models can be challenging when data are collected at a time…
In this paper, we investigate the (in)-consistency of different bootstrap methods for constructing confidence intervals in the class of estimators that converge at rate $n^{1/3}$. The Grenander estimator, the nonparametric maximum…
The Highly-Adaptive-LASSO Targeted Minimum Loss Estimator (HAL-TMLE) is an efficient plug-in estimator of a pathwise differentiable parameter in a statistical model that at minimal (and possibly only) assumes that the sectional variation…
The characteristic function of the folded normal distribution and its moment function are derived. The entropy of the folded normal distribution and the Kullback--Leibler from the normal and half normal distributions are approximated using…