Estimation of time-varying regression model constrained at each time moment by linear inequalities is a natural statistical formulation of a wide class of nonstationary signal processing problems. The presence of linear constraints turns the originally quadratic three-diagonal problem of minimizing the residual squares sum, which is solvable by the linear Kalman-Bucy filtration-smoothing proced...

A Stochastic Variance Reduced Primal Dual Fixed Point Method for Linearly Constrained Separable Optimization

One of the main practical problems of nonparametric regression estimation is the curse of dimensionality. The curse of dimensionality arises because nonparametric regression estimates are dependent variable averages local to the point at which the regression function is to be estimated. The number of observations ‘local’ to the point of estimation decreases exponentially with the number of dime...

We propose a way of testing exogeneity of an explanatory variable without any parametric assumptions in the presence of a conditional "instrumental variable". A testable implication is derived that if an explanatory variable is exogenous, the conditional distribution of the outcome given explanatory variables is independent of the instrumental variable. We propose a consistent nonparametric boo...

We consider N-fold 4-block decomposable integer programs, which simultaneously generalize N-fold integer programs and two-stage stochastic integer programs with N scenarios. In previous work [R. Hemmecke, M. Köppe, R. Weismantel, A polynomial-time algorithm for optimizing over N-fold 4block decomposable integer programs, Proc. IPCO 2010, Lecture Notes in Computer Science, vol. 6080, Springer, 2...

In this paper, we propose a new branch and bound algorithm for the solution of large scale separable concave programming problems. The largest distance bisection (LDB) technique is proposed to divide rectangle into sub-rectangles when one problem is branched into two subproblems. It is proved that the LDB method is a normal rectangle subdivision(NRS). Numerical tests on problems with dimensions...