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We investigate two training-set methods: support vector machines (SVMs) and Kernel Regression (KR) for photometric redshift estimation with the data from the Sloan Digital Sky Survey Data Release 5 and Two Micron All Sky Survey databases.…
Averaging neural network weights sampled by a backbone stochastic gradient descent (SGD) is a simple yet effective approach to assist the backbone SGD in finding better optima, in terms of generalization. From a statistical perspective,…
Inference for models with recursively defined likelihoods is computationally demanding, limiting scalability to large datasets. We propose a stabilised weighted subsampling methodology for accelerated inference based on an unbiased…
A new smoothing method for solving ? -support vector regression (?-SVR), tolerating a small error in fitting a given data sets nonlinearly is proposed in this study. Which is a smooth unconstrained optimization reformulation of the…
Fully robust OSCV is a modification of the OSCV method that produces consistent bandwidth in the cases of smooth and nonsmooth regression functions. The current implementation of the method uses the kernel $H_I$ that is almost…
In the context of estimating local modes of a conditional density based on kernel density estimators, we show that existing bandwidth selection methods developed for kernel density estimation are unsuitable for mode estimation. We propose…
One of the limiting factors of using support vector machines (SVMs) in large scale applications are their super-linear computational requirements in terms of the number of training samples. To address this issue, several approaches that…
The support vector machine (SVM) has an asymptotic behavior that parallels that of the quasi-maximum likelihood estimator (QMLE) for binary outcomes generated by a binary choice model (BCM), although it is not a QMLE. We show that, under…
We study the nonparametric least squares estimator (LSE) of a multivariate convex regression function. The LSE, given as the solution to a quadratic program with $O(n^2)$ linear constraints ($n$ being the sample size), is difficult to…
The spatial error model (SEM) is a type of simultaneous autoregressive (SAR) model for analysing spatially correlated data. Markov chain Monte Carlo (MCMC) is one of the most widely used Bayesian methods for estimating SEM, but it has…
To overcome the tradeoff of the conventional normalized least mean square (NLMS) algorithm between fast convergence rate and low steady-state misalignment, this paper proposes a variable step size (VSS) NLMS algorithm by devising a new…
We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes which are observed discretely with additive observation noise. The eligibility of this approach to lead to an…
The instability in the selection of models is a major concern with data sets containing a large number of covariates. This paper deals with variable selection methodology in the case of high-dimensional problems where the response variable…
This study introduces a novel formulation to enhance Support Vector Machines (SVMs) in handling class imbalance and noise. Unlike the conventional Soft Margin SVM, which penalizes the magnitude of constraint violations, the proposed model…
We propose simultaneous mean-variance regression for the linear estimation and approximation of conditional mean functions. In the presence of heteroskedasticity of unknown form, our method accounts for varying dispersion in the regression…
We address high dimensional covariance estimation for elliptical distributed samples, which are also known as spherically invariant random vectors (SIRV) or compound-Gaussian processes. Specifically we consider shrinkage methods that are…
This paper provides a new methodology to analyze unobserved heterogeneity when observed characteristics are modeled nonlinearly. The proposed model builds on varying random coefficients (VRC) that are determined by nonlinear functions of…
This paper studies non inf-sup stable finite element approximations to the evolutionary Navier--Stokes equations. Several local projection stabilization (LPS) methods corresponding to different stabilization terms are analyzed, thereby…
Multiclass probability estimation is the problem of estimating conditional probabilities of a data point belonging to a class given its covariate information. It has broad applications in statistical analysis and data science. Recently a…
We consider estimating the density of a response conditioning on an error-prone covariate. Motivated by two existing kernel density estimators in the absence of covariate measurement error, we propose a method to correct the existing…