Estimation and Inference for Linear Panel Data Models Under Misspecification When Both n and T are Large

This article considers fixed effects (FE) estimation for linear panel data models under possible model misspecification when both the number of individuals, n, and the number of time periods, T, are large. We first clarify the probability limit of the FE estimator and argue that this probability limit can be regarded as a pseudo-true parameter. We then establish the asymptotic distributional properties of the FE estimator around the pseudo-true parameter when n and T jointly go to infinity. Notably, we show that the FE estimator suffers from the incidental parameters bias of which the top order is O(T^{? 1}), and even after the incidental parameters bias is completely removed, the rate of convergence of the FE estimator depends on the degree of model misspecification and is either (nT)^{? 1/2} or n^{? 1/2}. Second, we establish asymptotically valid inference on the (pseudo-true) parameter. Specifically, we derive the asymptotic properties of the clustered covariance matrix (CCM) estimator and the cross-section bootstrap, and show that they are robust to model misspecification. This establishes a rigorous theoretical ground for the use of the CCM estimator and the cross-section bootstrap when model misspecification and the incidental parameters bias (in the coefficient estimate) are present. We conduct Monte Carlo simulations to evaluate the finite sample performance of the estimators and inference methods, together with a simple application to the unemployment dynamics in the U.S.     

Bayesian inference for stable Lévy–driven stochastic differential equations with high‐frequency data

In this paper, we consider parametric Bayesian inference for stochastic differential equations driven by a pure‐jump stable Lévy process, which is observed at high frequency. In most cases of practical interest, the likelihood function is not available; hence, we use a quasi‐likelihood and place an associated prior on the unknown parameters. It is shown under regularity conditions that there is a Bernstein–von Mises theorem associated to the posterior. We then develop a Markov chain Monte Carlo algorithm for Bayesian inference, and assisted with theoretical results, we show how to scale Metropolis–Hastings proposals when the frequency of the data grows, in order to prevent the acceptance ratio from going to zero in the large data limit. Our algorithm is presented on numerical examples that help verify our theoretical findings.     

Response of Japanese companies to environmental changes

How is Japanese business responding to environmental changes? This article reports on a survey of 140 major Japanese companies regarding other responses. The author concludes that: These companies are trying to meet the challenge; that there are differences from industry to industry which need to be delineated; out that there is a considerable difference between measures adopted and planned for implementation which suggest a positive attitude towards environmental changes.     

Multilevel particle filters: normalizing constant estimation

In this article, we introduce two new estimates of the normalizing constant (or marginal likelihood) for partially observed diffusion (POD) processes, with discrete observations. One estimate is biased but non-negative and the other is unbiased but not almost surely non-negative. Our method uses the multilevel particle filter of Jasra et al. (Multilevel particle lter, arXiv:1510.04977, 2015). We show that, under assumptions, for Euler discretized PODs and a given \(\varepsilon >0\) in order to obtain a mean square error (MSE) of \({\mathcal {O}}(\varepsilon ^2)\) one requires a work of \({\mathcal {O}}(\varepsilon ^{-2.5})\) for our new estimates versus a standard particle filter that requires a work of \({\mathcal {O}}(\varepsilon ^{-3})\). Our theoretical results are supported by numerical simulations.     

Sample size calculations for single-arm survival studies using transformations of the Kaplan–Meier estimator

In single-arm clinical trials with survival outcomes, the Kaplan–Meier estimator and its confidence interval are widely used to assess survival probability and median survival time. Since the asymptotic normality of the Kaplan–Meier estimator is a common result, the sample size calculation methods have not been studied in depth. An existing sample size calculation method is founded on the asymptotic normality of the Kaplan–Meier estimator using the log transformation. However, the small sample properties of the log transformed estimator are quite poor in small sample sizes (which are typical situations in single-arm trials), and the existing method uses an inappropriate standard normal approximation to calculate sample sizes. These issues can seriously influence the accuracy of results. In this paper, we propose alternative methods to determine sample sizes based on a valid standard normal approximation with several transformations that may give an accurate normal approximation even with small sample sizes. In numerical evaluations via simulations, some of the proposed methods provided more accurate results, and the empirical power of the proposed method with the arcsine square-root transformation tended to be closer to a prescribed power than the other transformations. These results were supported when methods were applied to data from three clinical trials.