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We develop asymptotic approximations that can be applied to sequential estimation and inference problems, adaptive randomized controlled trials, and related settings. In batched adaptive settings where the decision at one stage can affect…
Ever since the proof of asymptotic normality of maximum likelihood estimator by Cramer (1946), it has been understood that a basic technique of the Taylor series expansion suffices for asymptotics of $M$-estimators with…
Frequency domain methods form a ubiquitous part of the statistical toolbox for time series analysis. In recent years, considerable interest has been given to the development of new spectral methodology and tools capturing dynamics in the…
We propose a method for estimating the asymptotic phase and amplitude functions of limit-cycle oscillators using observed time series data without prior knowledge of their dynamical equations. The estimation is performed by polynomial…
This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are…
Data-driven methods for modeling dynamic systems have received considerable attention as they provide a mechanism for control synthesis directly from the observed time-series data. In the absence of prior assumptions on how the time-series…
Spectral estimators are fundamental in lowrank matrix models and arise throughout machine learning and statistics, with applications including network analysis, matrix completion and PCA. These estimators aim to recover the leading…
Method of moment estimators exhibit appealing statistical properties, such as asymptotic unbiasedness, for nonconvex problems. However, they typically require a large number of samples and are extremely sensitive to model misspecification.…
For time series data observed at non-random and possibly non-equidistant time points, we estimate the trend function nonparametrically. Under the assumption of a bounded total variation of the function and low-order moment conditions on the…
This paper studies a spectrum estimation method for the case that the samples are obtained at a rate lower than the Nyquist rate. The method is referred to as the correlogram for undersampled data. The algorithm partitions the spectrum into…
In continuous-time system identification, the intersample behavior of the input signal is known to play a crucial role in the performance of estimation methods. One common input behavior assumption is that the spectrum of the input is…
We study the quadratic prediction error method -- i.e., nonlinear least squares -- for a class of time-varying parametric predictor models satisfying a certain identifiability condition. While this method is known to asymptotically achieve…
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…
We present improved methods for calculating confidence intervals and $p$-values in situations where standard asymptotic approaches fail due to small sample sizes. We apply these techniques to a specific class of statistical model that can…
We present a general framework for studying regularized estimators; such estimators are pervasive in estimation problems wherein "plug-in" type estimators are either ill-defined or ill-behaved. Within this framework, we derive, under…
This paper studies two spectrum estimation methods for the case that the samples are obtained at a rate lower than the Nyquist rate. The first method is the correlogram method for undersampled data. The algorithm partitions the spectrum…
We consider the problem of parameter estimation in a high-dimensional generalized linear model. Spectral methods obtained via the principal eigenvector of a suitable data-dependent matrix provide a simple yet surprisingly effective…
Doubly robust estimators have gained widespread popularity in various fields due to their ability to provide unbiased estimates under model misspecification. However, the asymptotic theory for doubly robust estimators with continuous-time…
Multi-index models provide a popular framework to investigate the learnability of functions with low-dimensional structure and, also due to their connections with neural networks, they have been object of recent intensive study. In this…
The Wallace--Freeman estimator is a classical invariant point estimator whose large-sample properties have not been fully developed in a modern asymptotic framework. We show that the estimator can be formulated as a penalised M-estimator…