National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Nonparametric regression estimators
Měsíček, Martin ; Hlávka, Zdeněk (advisor) ; Omelka, Marek (referee)
This thesis is focused on local polynomial smoothers of the conditional vari- ance function in a heteroscedastic nonparametric regression model. Both mean and variance functions are assumed to be smooth, but neither is assumed to be in a parametric family. The basic idea is to apply a local linear regression to squa- red residuals. This method, as we have shown, has high minimax efficiency and it is fully adaptive to the unknown conditional mean function. However, the local linear estimator may give negative values in finite samples which makes variance estimation impossible. Hence Xu and Phillips proposed a new variance estimator that is asymptotically equivalent to the local linear estimator for interior points but is guaranteed to be non-negative. We also established asymptotic results of both estimators for boundary points and proved better asymptotic behavior of the local linear estimator. That motivated us to propose a modification of the local li- near estimator that guarantees non-negativity. Finally, simulations are conducted to evaluate the finite sample performances of the mentioned estimators.
Nash's equillibrium in a game of several players
Měsíček, Martin ; Lachout, Petr (advisor) ; Adam, Lukáš (referee)
This thesis is concerned with finding the Nash`s equilibrium in specific situations of card game poker texas holdem. It lays solid theoretical foundations illustrated on simple problems for understanding the notion of Nash`s equilibrium. Then we try to prove the existence of Nash`s equilibrium in the situations of two or more players in the game. It turns out that the two-player game can be represented by two- person zero-sum game and the game with more players by uncooperative game of N players. We describe a method for finding the Nash`s equilibrium for two-person zero-sum game game based on a method of solving problems of linear programming and we find the equilibrium for particular situations. Considering the extent of the problem, computing device is used when calculating some problems. Powered by TCPDF (www.tcpdf.org)