Related papers: Semi-parametric estimation of the hazard function …
Identifying a biomarker or treatment-dose threshold that marks a specified level of risk is an important problem, especially in clinical trials. This risk, viewed as a function of thresholds and possibly adjusted for covariates, we call the…
Consider the task of matrix estimation in which a dataset $X \in \mathbb{R}^{n\times m}$ is observed with sparsity $p$, and we would like to estimate $\mathbb{E}[X]$, where $\mathbb{E}[X_{ui}] = f(\alpha_u, \beta_i)$ for some Holder smooth…
The density ratio is an important metric for evaluating the relative likelihood of two probability distributions, with extensive applications in statistics and machine learning. However, existing estimation theories for density ratios often…
This paper is concerned with a semiparametric partially linear regression model with unknown regression coefficients, an unknown nonparametric function for the non-linear component, and unobservable Gaussian distributed random errors. We…
In reliability and life testing studies, the topic of estimating hazard rate has received great attention in recent years since an estimate of hazard rate is a quite useful tool for making decisions. Some works have included nonparametric…
Quantum mechanics provides extraordinarily accurate probabilistic predictions, yet the framework remains silent on what distinguishes quantum systems from definite measurement outcomes. This paper develops a measurement-theoretic framework…
In studies involving lifetimes, observed survival times are frequently censored and possibly subject to biased sampling. In this paper, we model survival times under biased sampling (a.k.a., biased survival data) by a semi-parametric model,…
In survival analysis, the hazard function often depends on a set of covariates. Martingale and deviance residual are most widely used for examining the validity of the function form of covariates by checking whether there is a discernible…
We present an argument based on the multidimensional and the uniform central limit theorems, proving that, under some geometrical assumptions between the target function $T$ and the learning class $F$, the excess risk of the empirical risk…
We present and study semi-parametric estimators for the mean of functional outcomes in situations where some of these outcomes are missing and covariate information is available on all units. Assuming that the missingness mechanism depends…
We propose an estimator of a concave cumulative distribution function under the measurement error model, where the non-negative variables of interest are perturbed by additive independent random noise. The estimator is defined as the least…
Considering the problem of risk-sensitive parameter estimation, we propose a fairly wide family of lower bounds on the exponential moments of the quadratic error, both in the Bayesian and the non--Bayesian regime. This family of bounds,…
We study semiparametric varying-coefficient partially linear models when some linear covariates are not observed, but ancillary variables are available. Semiparametric profile least-square based estimation procedures are developed for…
Interval-censored competing risks data arise when each study subject may experience an event or failure from one of several causes and the failure time is not observed exactly but rather known to lie in an interval between two successive…
This paper considers the problem of semi-parametric proportional hazards model fitting for interval, left and right censored survival times. We adopt a more versatile penalized likelihood method to estimate the baseline hazard and the…
Frailty models are often the model of choice for heterogeneous survival data. A frailty model contains both random effects and fixed effects, with the random effects accommodating for the correlation in the data. Different estimation…
We consider the observations of an unknown $s$-sparse vector ${\boldsymbol \theta}$ corrupted by Gaussian noise with zero mean and unknown covariance matrix ${\boldsymbol \Sigma}$. We propose minimax optimal methods of estimating the…
Hazard rate functions of natural and manufactured systems often show a bathtub shaped failure rate. A high early rate of failures is followed by an extended period of useful working life where failures are rare, and finally the failure rate…
We consider the Cox regression model and prove some properties of the maximum partial likelihood estimator $\hat\beta_n$ and of the the Breslow estimator $\Lambda_n$. The asymptotic properties of these estimators have been widely studied in…
Structural failure time models are causal models for estimating the effect of time-varying treatments on a survival outcome. G-estimation and artificial censoring have been proposed to estimate the model parameters in the presence of…