We study a sparse negative binomial regression (NBR) for count data by showing the non-asymptotic advantages of using elastic-net estimator. Two types oracle inequalities are derived NBR's estimates Compatibility Factor Condition and Stabil Condition. The second type inequality is random design can be extended to many $\ell_1 + \ell_2$ regularized M-estimations, with corresponding empirical pro...

Classical target detection schemes are usually obtained by deriving the likelihood ratio under Gaussian hypothesis and replacing the unknown background parameters by their estimates. In most assumed to be Gaussian with zero mean [or with a known mean vector (MV)] and with an unknown covariance matrix (CM). When the MV is unknown, it has to be jointly estimated with the CM. In this paper, adapti...

Consider a two-person zero-sum search game between hider and searcher. The hides among n discrete locations, the searcher successively visits individual locations until finding hider. Known to both players, at location i takes t time units detects hider—if hidden there—independently with probability [Formula: see text] for text]. aims maximize expected detection, whereas minimize it. We prove e...

In this paper, we consider a zero-sum undiscounted stochastic game which has finite state space and finitely many pure actions. Also, assume the transition probability of is controlled by one player all optimal strategies are strictly positive. Under above assumptions, show that $\beta$-discounted games with same payoff matrices $\beta$ sufficiently close to 1 also completely mixed. We give cou...

The problem of correctly predicting the structures of the orthogo nal factorsQ and R from the structure of a matrix A with full column rank is considered in this paper Recently Hare Johnson Olesky and van den Driessche have described a method to predict these structures and they have shown that corresponding to any speci ed nonzero element in the predicted structures of Q or R there exists a ma...

The stochastic spectral expansion method offers a simple framework for calculations in de Sitter spacetimes. We show how to extend its reach metastable vacuum states, both the case when potential is bounded from below, and it unbounded below therefore no stable state exists. In cases, decay rate of given by lowest nonzero eigenvalue associated Fokker--Planck equation. corresponding eigenfunctio...