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This paper utilizes finite Fourier series to represent a time-continuous motion and proposes a novel planning method that adjusts the motion harmonics of each manipulator joint. Primarily, we sum the potential energy for collision detection…
Conformal prediction is a statistical tool for producing prediction regions of machine learning models that are valid with high probability. However, applying conformal prediction to time series data leads to conservative prediction…
In this paper, we analyze the asymptotic behavior of the main characteristics of the mean-variance efficient frontier employing random matrix theory. Our particular interest covers the case when the dimension $p$ and the sample size $n$…
We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…
This paper is devoted to guaranteed estimation (so-called minimax estimation) of linear functions, defined on the solutions domain of the linear descriptor difference equations (LDDE) system, where right-hand part and initial condition are…
This paper analyzes a model in which an outcome equals a frontier function of inputs minus a nonnegative unobserved deviation. The inputs may be endogenous (statistically dependent on the deviation). If zero lies in the support of the…
First order methods endowed with global convergence guarantees operate using global lower bounds on the objective. The tightening of the bounds has been shown to increase both the theoretical guarantees and the practical performance. In…
We consider the problem of estimating the regression function in functional linear regression models by proposing a new type of projection estimators which combine dimension reduction and thresholding. The introduction of a threshold rule…
Compressed Counting (CC) was recently proposed for very efficiently computing the (approximate) $\alpha$th frequency moments of data streams, where $0<\alpha <= 2$. Several estimators were reported including the geometric mean estimator,…
In this paper we show how to use Fourier transform methods to analyze the asymptotic behavior of kernel distribution function estimators. Exact expressions for the mean integrated squared error in terms of the characteristic function of the…
We consider least squares approximation of a function of one variable by a continuous, piecewise-linear approximand that has a small number of breakpoints. This problem was notably considered by Bellman who proposed an approximate algorithm…
The linear programming (LP) approach has a long history in the theory of approximate dynamic programming. When it comes to computation, however, the LP approach often suffers from poor scalability. In this work, we introduce a relaxed…
We consider (robust) inference in the context of a factor model for tensor-valued sequences. We study the consistency of the estimated common factors and loadings space when using estimators based on minimising quadratic loss functions.…
We study the best approximation problem: \[ \displaystyle \min_{\alpha\in \mathbb R^m}\max_{1\leq i\leq n}\left|y_i -\sum_{j=1}^m \alpha_j \Gamma_j ({\bf x}_i) \right|. \] Here: $\Gamma:=\left\{\Gamma_1,...,\Gamma_m\right\}$ is a list of…
We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters.…
A local linear kernel estimator of the regression function x\mapsto g(x):=E[Y_i|X_i=x], x\in R^d, of a stationary (d+1)-dimensional spatial process {(Y_i,X_i),i\in Z^N} observed over a rectangular domain of the form I_n:={i=(i_1,...,i_N)\in…
Semi-functional linear regression models postulate a linear relationship between a scalar response and a functional covariate, and also include a non-parametric component involving a univariate explanatory variable. It is of practical…
Efficient estimation of high-dimensional matrices-including covariance and precision matrices-is a cornerstone of modern multivariate statistics. Most existing studies have focused primarily on the theoretical properties of the estimators…
In finite mixture models, apart from underlying mixing measure, true kernel density function of each subpopulation in the data is, in many scenarios, unknown. Perhaps the most popular approach is to choose some kernel functions that we…
Large-scale sequential data is often exposed to some degree of inhomogeneity in the form of sudden changes in the parameters of the data-generating process. We consider the problem of detecting such structural changes in a high-dimensional…