## V-Matrix Method of Solving Statistical Inference Problems

*Vladimir Vapnik, Rauf Izmailov*; 16(Sep):1683−1730, 2015.

### Abstract

This paper presents direct settings and rigorous solutions of
the main Statistical Inference problems. It shows that rigorous
solutions require solving multidimensional Fredholm integral
equations of the first kind in the situation where not only the
right-hand side of the equation is an approximation, but the
operator in the equation is also defined approximately. Using
Stefanuyk-Vapnik theory for solving such ill-posed operator
equations, constructive methods of empirical inference are
introduced. These methods are based on a new concept called
$V$-matrix. This matrix captures geometric properties of the
observation data that are ignored by classical statistical
methods.

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