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We revisit the method of cumulants for analysing dynamic light scattering data in particle sizing applications. Here the data, in the form of the time correlation function of scattered light, is written as a series involving the first few…

Confidence sets play a fundamental role in statistical inference. In this paper, we consider confidence intervals for high dimensional linear regression with random design. We first establish the convergence rates of the minimax expected…

Machine learning models are often evaluated using point estimates of performance metrics such as accuracy, F1 score, or mean squared error. Such summaries fail to capture the inherent variability induced by stochastic elements of the…

We consider the problem of parameter estimation in the case of observation of the trajectory of diffusion process. We suppose that the drift coefficient has a singularity of cusp-type and the unknown parameter corresponds to the position of…

Stable subordinators, and more general subordinators possessing power law probability tails, have been widely used in the context of subdiffusions, where particles get trapped or immobile in a number of time periods, called constant…

We construct honest confidence regions for a Hilbert space-valued parameter in various statistical models. The confidence sets can be centered at arbitrary adaptive estimators, and have diameter which adapts optimally to a given selection…

This paper develops a threshold regression model where an unknown relationship between two variables nonparametrically determines the threshold. We allow the observations to be cross-sectionally dependent so that the model can be applied to…

Ratios of random variables often appear in probability and statistical applications. We aim to approximate the moments of such ratios under several dependence assumptions. Extending the ideas in Collomb [C. R. Acad. Sci. Paris 285 (1977)…

Spectrum estimation is a fundamental methodology in the analysis of time-series data, with applications including medicine, speech analysis, and control design. The asymptotic theory of spectrum estimation is well-understood, but the theory…

In this paper, we propose a covariate-adjusted nonlinear regression model. In this model, both the response and predictors can only be observed after being distorted by some multiplicative factors. Because of nonlinearity, existing methods…

We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…

Unlike the previous papers of the author, which are in an evenly spaced data setting, we present an approach which predicts the optimal value of the shape parameter contained in the muiltiquadrics and inverse multiquadrics in a purely…

For more than half a century, moments have attracted lot ot interest in the pattern recognition community.The moments of a distribution (an object) provide several of its characteristics as center of gravity, orientation, disparity, volume.…

We propose a novel approach to parameter estimation for simulator-based statistical models with intractable likelihood. Our proposed method involves recursive application of kernel ABC and kernel herding to the same observed data. We…

Assuming that a reflected Ornstein-Uhlenbeck state process is observed at discrete time instants, we propose generalized moment estimators to estimate all drift and diffusion parameters via the celebrated ergodic theorem. With the sampling…

The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…

Model approximations are common practice when estimating structural or quasi-structural models. The paper considers the econometric properties of estimators that utilize projections to reimpose information about the exact model in the form…

We study the problem of parameter estimation in time series stemming from general stochastic processes, where the outcomes may exhibit arbitrary temporal correlations. In particular, we address the question of how much Fisher information is…

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…

Random variables in metric spaces indexed by time and observed at equally spaced time points are receiving increased attention due to their broad applicability. The absence of inherent structure in metric spaces has resulted in a literature…