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Inference for functional linear models in the presence of heteroscedastic errors has received insufficient attention given its practical importance; in fact, even a central limit theorem has not been studied in this case. At issue,…

The maximum score estimator of Manski (1975) provides an elegant approach to estimate slope coefficient in binary choice models without requiring parametric assumptions on the error distribution. However, under i.i.d. sampling, it admits a…

An algorithm is described that enables efficient deterministic approximate computation of the bootstrap distribution for any linear bootstrap method $T_n^*$, alleviating the need for repeated resampling from observations (resp.…

Accurate statistical inference in logistic regression models remains a critical challenge when the ratio between the number of parameters and sample size is not negligible. This is because approximations based on either classical asymptotic…

To address the difficult problem of multi-step ahead prediction of non-parametric autoregressions, we consider a forward bootstrap approach. Employing a local constant estimator, we can analyze a general type of non-parametric time series…

Fitting parametric models by optimizing frequency domain objective functions is an attractive approach of parameter estimation in time series analysis. Whittle estimators are a prominent example in this context. Under weak conditions and…

In distributed, or privacy-preserving learning, we are often given a set of probabilistic models estimated from different local repositories, and asked to combine them into a single model that gives efficient statistical estimation. A…

This article proposes an online bootstrap scheme for nonparametric level estimation in nonstationary time series. Our approach applies to a broad class of level estimators expressible as weighted sample averages over time windows, including…

Westling and Carone (2020) proposed a framework for studying the large sample distributional properties of generalized Grenander-type estimators, a versatile class of nonparametric estimators of monotone functions. The limiting distribution…

We consider bootstrap inference for estimators which are (asymptotically) biased. We show that, even when the bias term cannot be consistently estimated, valid inference can be obtained by proper implementations of the bootstrap.…

The maximum-likelihood estimator of nonlinear panel data models with fixed effects is consistent but asymptotically-biased under rectangular-array asymptotics. The literature has thus far concentrated its effort on devising methods to…

Bootstrap is a principled and powerful frequentist statistical tool for uncertainty quantification. Unfortunately, standard bootstrap methods are computationally intensive due to the need of drawing a large i.i.d. bootstrap sample to…

We propose an estimator of a concave cumulative distribution function under the measurement error model, where the non-negative variables of interest are perturbed by additive independent random noise. The estimator is defined as the least…

For discrete-valued time series, predictive inference cannot be implemented through the construction of prediction intervals to some predetermined coverage level, as this is the case for real-valued time series. To address this problem, we…

In this paper, we investigate the (in)-consistency of different bootstrap methods for constructing confidence intervals in the class of estimators that converge at rate $n^{1/3}$. The Grenander estimator, the nonparametric maximum…

Background and Objective: Uncertainty in non-linear mixed effect models is often assessed using the Fisher information matrix to derive the standard errors of estimation. The bootstrap is an alternative to the asymptotic method, with…

In this paper, we consider possibly misspecified stochastic differential equation models driven by L\'{e}vy processes. Regardless of whether the driving noise is Gaussian or not, Gaussian quasi-likelihood estimator can estimate unknown…

In this paper, we develop a comprehensive asymptotic and bootstrap theory for checkerboard-based estimation of lower and upper tail copulas under unknown marginal distributions. The estimator is constructed via local bilinear (checkerboard)…

This paper studies simultaneous inference of conditional distributions in nonlinear time series from a sieve M-regression perspective. Existing literature on sieve M-regression has primarily focused on pointwise asymptotics, leaving the…

Estimating nonlinear functionals of probability distributions from samples is a fundamental statistical problem. The "plug-in" estimator obtained by applying the target functional to the empirical distribution of samples is biased.…