Related papers: Semiparametric stationarity tests based on adaptiv…
For $N,n\in\mathbb N$, consider the sample covariance matrix $$S_N(T)=\frac{1}{N}XX^*$$ from a data set $X=C_N^{1/2}ZT_n^{1/2}$, where $Z=(Z_{i,j})$ is a $N\times n$ matrix having i.i.d. entries with mean zero and variance one, and $C_N,…
Traditional methods for determining assessment item parameters, such as difficulty and discrimination, rely heavily on expensive field testing to collect student performance data for Item Response Theory (IRT) calibration. This study…
Nonparametric regression models with locally stationary covariates have received increasing interest in recent years. As a nice relief of "curse of dimensionality" induced by large dimension of covariates, additive regression model is…
Semiparametric language models (LMs) have shown promise in continuously learning from new text data by combining a parameterized neural LM with a growable non-parametric memory for memorizing new content. However, conventional…
Given a functional central limit (fCLT) for an estimator and a parameter transformation, we construct random processes, called functional delta residuals, which asymptotically have the same covariance structure as the limit process of the…
In this paper we propose a new approach to the central limit theorem (CLT), based on functions of bounded F\'echet variation for the continuously differentiable linear statistics of random matrix ensembles which relies on: a weaker form of…
This paper proposes a new test for covariance matrices structure based on the correction to Rao's score test in large dimensional framework. By generalizing the CLT for the linear spectral statistics of large dimensional sample covariance…
The accelerated failure time (AFT) model is widely used to analyze relationships between variables in the presence of censored observations. However, this model relies on some assumptions such as the error distribution, which can lead to…
From a wavelet analysis, one derives a nonparametrical estimator for the spectral density of a Gaussian process with stationary increments. First, the idealistic case of a continuous time path of the process is considered. A punctual…
In this paper, change-point problems for long memory stochastic volatility models are considered. A general testing problem which includes various alternative hypotheses is discussed. Under the hypothesis of stationarity the limiting…
We consider stochastic approximations of sampling algorithms, such as Stochastic Gradient Langevin Dynamics (SGLD) and the Random Batch Method (RBM) for Interacting Particle Dynamcs (IPD). We observe that the noise introduced by the…
With regard to a three-step estimation procedure, proposed without theoretical discussion by Li and You in Journal of Applied Statistics and Management, for a nonparametric regression model with time-varying regression function, local…
Sample covariance matrices are widely used in multivariate statistical analysis. The central limit theorems (CLT's) for linear spectral statistics of high-dimensional non-centered sample covariance matrices have received considerable…
Chain-of-Thought (CoT) prompting and its variants have gained popularity as effective methods for solving multi-step reasoning problems using pretrained large language models (LLMs). In this work, we analyze CoT prompting from a statistical…
We consider a time series model involving a fractional stochastic component, whose integration order can lie in the stationary/invertible or nonstationary regions and be unknown, and an additive deterministic component consisting of a…
Item response theory (IRT) is a class of interpretable factor models that are widely used in computerized adaptive tests (CATs), such as language proficiency tests. Traditionally, these are fit using parametric mixed effects models on the…
We present a new approach, inspired by Stein's method, to prove a central limit theorem (CLT) for linear statistics of $\beta$-ensembles in the one-cut regime. Compared with the previous proofs, our result requires less regularity on the…
Continual instruction tuning(CIT) during the post-training phase is crucial for adapting multimodal large language models (MLLMs) to evolving real-world demands. However, the progress is hampered by the lack of benchmarks with rigorous,…
In this paper an easy to implement method of stochastically weighing short and long memory linear processes is introduced. The method renders asymptotically exact size confidence intervals for the population mean which are significantly…
In this work, we show that uniform integrability is not a necessary condition for central limit theorems (CLT) to hold for normalized multilevel Monte Carlo (MLMC) estimators and we provide near optimal weaker conditions under which the CLT…