We propose a novel smoothing approach for time series analysis to estimate the hidden states of random variables and handle noisy, nonstationary time series data. The method is applicable even when the sample size is small, as is often the case with major macroeconomic time series data. Our approach is based on the frequency decomposition of nonstationary time series, and we address the smoothing challenges specific to such data. In particular, we introduce forward SIML smoothing and backward SIML smoothing, designed to resolve the initial value problem in nonstationary time series analysis. The proposed smoothing methods offer interpretations in both the time and frequency domains. To demonstrate the effectiveness of our approach, we apply our method to the problem of detecting recent breaks in macroeconomic consumption trends.
Structural equation modeling (SEM) is a statistical method for analyzing relationships among latent variables. Since SEM is a confirmatory method, the model needs to be specified in advance. In practice, however, statisticians have several candidate models and aim to select the most appropriate one among them. In this paper, we consider model selection in SEM for jump-diffusion processes. We propose a quasi-Bayesian information criterion (QBIC) for the SEM and show that the proposed criterion has model-selection consistency.
Assume interest is in sampling from a probability distribution μ defined on . We develop a framework for sampling algorithms which take full advantage of ODE numerical integrators, say ψ :→ for one integration step, to explore μ efficiently and robustly. The popular Hamiltonian Monte Carlo (HMC) algorithm and its derivatives are examples of such a use of numerical integrators. A key idea developed here is that of sampling integrator snippets, that is fragments of the orbit of an ODE numerical integrator ψ , and the definition of an associated probability distribution μ̅ such that expectations with respect to μ can be estimated from integrator snippets distributed according to μ̅. The integrator snippet target distribution μ̅ takes the form of a mixture of pushforward distributions which suggest generalisations beyond HMC. Importantly this structure also leads to new, principled and robust strategies to tune the parameters of integrators, such as the discretisation stepsize, effective integration time, or number of integration steps, in a Leapfrog integrator. We illustrate performance and, in particular, robustness through numerical experiments.
Overlap measures are similarity measures that quantify the degree of similarity between two populations. Matusita’s measure is a widely used overlap measure based on the concept of distance between two probability distributions. In this paper, we propose two nonparametric estimators for Matusita’s measure using its quantile-based representation. We study the asymptotic properties of the proposed estimators, relying on the smoothed kernel density estimator of the quasi-relative data. We construct asymptotic confidence intervals for Matusita’s measure. The small sample performance of our proposed estimators is evaluated through simulations, and their application is demonstrated using a real dataset.
Multipath changepoint models are essential tools for analyzing longitudinal data from multiple subjects. While dynamic discrete-time hazard models are widely used in standard survival analysis, existing multipath changepoint methods often rely on the restrictive assumption that the underlying latent probability of a change, or hazard, is constant over time. This paper introduces a significant extension by embedding a dynamic hazard specification within a latent multipath changepoint framework. The hazard rate is allowed to vary over time and is modeled as a function of individual-specific covariates using a logistic link function. We develop a complete frequentist inferential framework based on the method of maximum likelihood and establish rigorous theoretical guarantees for the estimators, including proofs of consistency and asymptotic normality, which are crucial for statistical inference. The finite-sample performance of the proposed method is evaluated through extensive Monte Carlo simulation studies. These studies confirm our theoretical results and demonstrate the substantial estimation bias that can occur when a constant hazard model is incorrectly applied to data with underlying temporal dynamics. The practical utility of our model is illustrated through an application to the Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset. Our analysis of cognitive decline reveals a significant, time-increasing hazard of transition, which is strongly associated with key clinical risk factors, providing highly interpretable insights that might be attenuated by models assuming a constant baseline hazard.
