Related papers: Quasi-MLE for quadratic ARCH model with long memor…

Long-context Large Language Models (LLMs) face significant memory bottlenecks during inference due to the linear growth of key-value (KV) cache with sequence length. While individual optimization techniques like KV cache quantization,…

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…

Quantum amplitude estimation is a key subroutine in a number of powerful quantum algorithms, including quantum-enhanced Monte Carlo simulation and quantum machine learning. Maximum-likelihood quantum amplitude estimation (MLQAE) is one of a…

This paper proposes a closed-form optimal estimator based on the theory of estimating functions for a class of linear ARCH models. The estimating function (EF) estimator has the advantage over the widely used maximum likelihood (ML) and…

Empirical economic research frequently applies maximum likelihood estimation in cases where the likelihood function is analytically intractable. Most of the theoretical literature focuses on maximum simulated likelihood (MSL) estimators,…

We introduce a recursive algorithm of conveniently general form for estimating the coefficient of a moving average model of order one and obtain convergence results for both correct and misspecified MA(1) models. The algorithm encompasses…

Andresen and Spokoiny's (2013) ``critical dimension in semiparametric estimation`` provide a technique for the finite sample analysis of profile M-estimators. This paper uses very similar ideas to derive two convergence results for the…

We present the first comprehensive study of latent multi-head attention (MLA) for small language models, revealing interesting efficiency-quality trade-offs. Training 30M-parameter GPT models on 100,000 synthetic stories, we benchmark three…

A new method of quasi-optimal observables allows one to approach the quality of data processing usually associated with the method of maximal likelihood within the simpler algorithmic context of generalized moments.

This paper develops a quasi-maximum likelihood estimator for genuinely unbalanced dynamic network panel data models with individual fixed effects. We propose a model that accommodates contemporaneous and lagged network spillovers, temporal…

We consider a process $ X= (X_t)_{t\in \Z}$ belonging to a large class of causal models including AR($\infty$), ARCH($\infty$), TARCH($\infty$),... models. We assume that the model depends on a parameter $\theta_0 \in \R^d$ and consider the…

We study the parameter estimation method for linear regression models with possibly skewed stable distributed errors. Our estimation procedure consists of two stages: first, for the regression coefficients, the Cauchy quasi-maximum…

This paper studies nonparametric regression with long memory (LRD) errors and predictors. First, we formulate general conditions which guarantee the standard rate of convergence for a nonparametric kernel estimator. Second, we calculate the…

Large Language Models (LLMs) are often evaluated against ideals of perfect Bayesian inference, yet growing evidence suggests that their in-context reasoning exhibits systematic forgetting of past information. Rather than viewing this…

This paper investigates the properties of Quasi Maximum Likelihood estimation of an approximate factor model for an $n$-dimensional vector of stationary time series. We prove that the factor loadings estimated by Quasi Maximum Likelihood…

Amplitude Estimation (AE) is a critical subroutine in many quantum algorithms, allowing for a quadratic speedup in various applications like those involving estimating statistics of various functions as in financial Monte Carlo simulations.…

Interval-censored multi-state data arise in many studies of chronic diseases, where the health status of a subject can be characterized by a finite number of disease states and the transition between any two states is only known to occur…

This paper explores seasonal and long-memory time series properties by using the seasonal fractional ARIMA model when the seasonal data has one and two seasonal periods and short-memory counterparts. The stationarity and invertibility…

This paper studies computationally and theoretically attractive estimators called the Laplace type estimators (LTE), which include means and quantiles of Quasi-posterior distributions defined as transformations of general…

The density ratio model (DRM) provides a flexible and useful platform for combining information from multiple sources. In this paper, we consider statistical inference under two-sample DRMs with additional parameters defined through and/or…