Related papers: The central limit theorem under random truncation
In this paper we study uniform versions of two limit theorems in random left truncation model (RLTM). The law of large numbers (LLN) and the central limit theorem (CLT) have been obtained under the bracketing entropy conditions in this…
Linear Mixed Effects (LME) models have been widely applied in clustered data analysis in many areas including marketing research, clinical trials, and biomedical studies. Inference can be conducted using maximum likelihood approach if…
We consider the problem of estimating functionals of discrete distributions, and focus on tight nonasymptotic analysis of the worst case squared error risk of widely used estimators. We apply concentration inequalities to analyze the random…
The maximum likelihood estimation of the left-truncated log-logistic distribution with a given truncation point is analyzed in detail from both mathematical and numerical perspectives. These maximum likelihood equations often do not possess…
Maximum likelihood estimation of linear functionals in the inverse problem of deconvolution is considered. Given observations of a random sample from a distribution $P_0\equiv P_{F_0}$ indexed by a (potentially infinite-dimensional)…
Distributional regression aims to find the best candidate in a given parametric family of conditional distributions to model a given dataset. As each candidate in the distribution family can be identified by the corresponding distribution…
This work deals with the estimation of the extreme value index and extreme quantiles for heavy tailed data,randomly right truncated by another heavy tailed variable. Under mild assumptions and the condition thatthe truncated variable is…
Proper econometric analysis should be informed by data structure. Many forms of financial data are recorded in discrete-time and relate to products of a finite term. If the data comes from a financial trust, it will often be further subject…
We use Stein characterisations to derive new moment-type estimators for the parameters of several truncated multivariate distributions in the i.i.d. case; we also derive the asymptotic properties of these estimators. Our examples include…
If the log likelihood is approximately quadratic with constant Hessian, then the maximum likelihood estimator (MLE) is approximately normally distributed. No other assumptions are required. We do not need independent and identically…
The Central Limit Theorem (CLT) is one of the most fundamental results in statistics. It states that the standardized sample mean of a sequence of $n$ mutually independent and identically distributed random variables with finite first and…
This paper deals with the problem of inference associated with linear fractional diffusion process with random effects in the drift. In particular we are concerned with the maximum likelihood estimators (MLE) of the random effect…
In this work, a generalised version of the central limit theorem is proposed for nonlinear functionals of the empirical measure of i.i.d. random variables, provided that the functional satisfies some regularity assumptions for the…
We find limiting distributions of the nonparametric maximum likelihood estimator (MLE) of a log-concave density, that is, a density of the form $f_0=\exp\varphi_0$ where $\varphi_0$ is a concave function on $\mathbb{R}$. The pointwise…
For a L\'evy basis $L$ on $\mathbb{R}^d$ and a suitable kernel function $f:\mathbb{R}^d \to \mathbb{R}$, consider the continuous spatial moving average field $X=(X_t)_{t\in \mathbb{R}^d}$ defined by $X_t = \int_{\mathbb{R}^d} f(t-s) \,…
We study the non-parametric estimation of the value ${\theta}(f )$ of a linear functional evaluated at an unknown density function f with support on $R_+$ based on an i.i.d. sample with multiplicative measurement errors. The proposed…
The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes. The central limit theorem and functional central limit theorem are obtained for martingale like random variables under…
A sharp, distribution free, non-asymptotic result is proved for the concentration of a random function around the mean function, when the randomization is generated by a finite sequence of independent data and the random functions satisfy…
By means of a Lynden-Bell integral with deterministic threshold, Worms and Worms [A Lynden-Bell integral estimator for extremes of randomly truncated data. Statist. Probab. Lett. 2016; 109: 106-117] recently introduced an asymptotically…
We study the convergence in distribution norms in the Central Limit Theorem for non identical distributed random variables that is $$ \varepsilon_{n}(f):={\mathbb{E}}\Big(f\Big(\frac 1{\sqrt…