arXiv subjects

Chak Fung Choi

Publications and source records attributed to Chak Fung Choi.

3 recordsLinked to original sources

arXiv2026

On Sharpened Convergence Rate of Generalized Sliced Inverse Regression for Nonlinear Sufficient Dimension Reduction

Generalized Sliced Inverse Regression (GSIR) is one of the most important methods for nonlinear sufficient dimension reduction. As shown in Li and Song (2017), it enjoys a convergence rate that is independent of the dimension of the predictor, thus avoiding the curse of dimensionality. In this paper we establish an improved convergence rate of GSIR under additional mild eigenvalue decay rate and smoothness conditions. Our convergence rate can be made arbitrarily close to $n^{-1/3}$ under appropriate decay rate and smoothness parameters. As a comparison, the rate of Li and Song (2017) is $n^{-1/4}$ under the best conditions. This improvement is significant because, for example, in a semiparametric estimation problem involving an infinite-dimensional nuisance parameter, the convergence rate of the estimator of the nuisance parameter is often required to be faster than $n^{-1/4}$ to guarantee desired semiparametric properties such as asymptotic efficiency. This can be achieved by the improved convergence rate, but not by the original rate. The sharpened convergence rate can also be established for GSIR in more general settings, such as functional sufficient dimension reduction.

math.ST↗

arXiv2024

Predicting Future Change-points in Time Series

Change-point detection and estimation procedures have been widely developed in the literature. However, commonly used approaches in change-point analysis have mainly been focusing on detecting change-points within an entire time series (off-line methods), or quickest detection of change-points in sequentially observed data (on-line methods). Both classes of methods are concerned with change-points that have already occurred. The arguably more important question of when future change-points may occur, remains largely unexplored. In this paper, we develop a novel statistical model that describes the mechanism of change-point occurrence. Specifically, the model assumes a latent process in the form of a random walk driven by non-negative innovations, and an observed process which behaves differently when the latent process belongs to different regimes. By construction, an occurrence of a change-point is equivalent to hitting a regime threshold by the latent process. Therefore, by predicting when the latent process will hit the next regime threshold, future change-points can be forecasted. The probabilistic properties of the model such as stationarity and ergodicity are established. A composite likelihood-based approach is developed for parameter estimation and model selection. Moreover, we construct the predictor and prediction interval for future change points based on the estimated model.

stat.ME↗

arXiv2021

Multiple-Output Channel Simulation and Lossy Compression of Probability Distributions

We consider a variant of the channel simulation problem with a single input and multiple outputs, where Alice observes a probability distribution $P$ from a set of prescribed probability distributions $\mathbb{\mathcal{P}}$, and sends a prefix-free codeword $W$ to Bob to allow him to generate $n$ i.i.d. random variables $X_{1},X_{2,}...,X_{n}$ which follow the distribution $P$. This can also be regarded as a lossy compression setting for probability distributions. This paper describes encoding schemes for three cases of $P$: $P$ is a distribution over positive integers, $P$ is a continuous distribution over $[0,1]$ with a non-increasing pdf, and $P$ is a continuous distribution over $[0,\infty)$ with a non-increasing pdf. We show that the growth rate of the expected codeword length is sub-linear in $n$ when a power law bound is satisfied. An application of multiple-outputs channel simulation is the compression of probability distributions.

cs.IT↗