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Core partitions have attracted much attention since Anderson's work (2002) on the number of $(s,t)$-core partitions for coprime $s,t$. Recently, there has been a growing interest in studying the limiting distributions of the sizes of random…
Kernel methods are an extremely popular set of techniques used for many important machine learning and data analysis applications. In addition to having good practical performances, these methods are supported by a well-developed theory.…
We establish local asymptotic estimates of partial Bergman kernels on closed, $S^1$-symmetric K\"{a}hler manifolds. The main result concerns the scaling asymptotics of partial Bergman kernels at generic off-diagonal points in which they are…
This paper provides new uniform rate results for kernel estimators of absolutely regular stationary processes that are uniform in the bandwidth and in infinite-dimensional classes of dependent variables and regressors. Our results are…
We study asymptotic performance of distributed detection in large scale connected sensor networks. Contrasting to the canonical parallel network where a single node has access to local decisions from all other nodes, each node can only…
The random Fourier features (RFFs) method is a powerful and popular technique in kernel approximation for scalability of kernel methods. The theoretical foundation of RFFs is based on the Bochner theorem that relates symmetric, positive…
Linearizing the Heisenberg equations of motion around the ground state of an interacting quantum many-body system, one gets a time-evolution generator in the positive cone of a real symplectic Lie algebra. The presence of disorder in the…
We consider kernel smoothed Grenander-type estimators for a monotone hazard rate and a monotone density in the presence of randomly right censored data. We show that they converge at rate $n^{2/5}$ and that the limit distribution at a fixed…
We study some properties of smoothing kernels and their local expression as they appear in the construction of Colombeau-type generalized function algebras which are diffeomorphism invariant.
Variable kernel density estimation allows the approximation of a probability density by the mean of differently stretched and rotated kernels centered at given sampling points $y_n\in\mathbb{R}^d,\ n=1,\dots,N$. Up to now, the choice of the…
We propose a new estimator for nonparametric binary choice models that does not impose a parametric structure on either the systematic function of covariates or the distribution of the error term. A key advantage of our approach is its…
Although approximate Bayesian computation (ABC) has become a popular technique for performing parameter estimation when the likelihood functions are analytically intractable there has not as yet been a complete investigation of the…
Discrete mixture models are one of the most successful approaches for density estimation. Under a Bayesian nonparametric framework, Dirichlet process location-scale mixture of Gaussian kernels is the golden standard, both having nice…
We investigate asymptotic properties of least-absolute-deviation or median quantile estimates of the location and scale functions in nonparametric regression models with dependent data from multiple subjects. Under a general dependence…
The asymptotic normality in multi-dimension of the nonparametric estimator of the transition probabilities of a Markov renewal chain is proved, and is applied to that of other nonparametric estimators involved with the associated…
This paper considers the asymptotic behavior in $\beta$-H\"older spaces, and under $L^p$ losses, of a Dirichlet kernel density estimator proposed by Aitchison and Lauder (1985) for the analysis of compositional data. In recent work, Ouimet…
The kernel-based regularization method has two core issues: kernel design and hyperparameter estimation. In this paper, we focus on the second issue and study the properties of several hyperparameter estimators including the empirical Bayes…
We consider asymptotic behavior of the correlation functions of the characteristic polynomials of the hermitian sample covariance matrices $H_n=n^{-1}A_{m,n}^*A_{m,n}$, where $A_{m,n}$ is a $m\times n$ complex matrix with independent and…
In these lecture notes we present some connections between random matrices, the asymmetric exclusion process, random tilings. These three apparently unrelated objects have (sometimes) a similar mathematical structure, an interlacing…
We develop a framework for function classes generated by parametric ridge kernels: one-dimensional kernels composed with affine projections and averaged over a parameter measure. The induced kernels are positive definite, and the resulting…