We present a new adaptive kernel density estimator based on linear diffusion processes. The proposed builds existing ideas for smoothing by incorporating information from pilot estimate. In addition, we propose plug-in bandwidth selection method that is free the arbitrary normal reference rules used methods. simulation examples in which approach outperforms methods terms of accuracy and reliability.

Summary Simulation from the truncated multivariate normal distribution in high dimensions is a recurrent problem statistical computing and typically only feasible by using approximate Markov chain Monte Carlo sampling. We propose minimax tilting method for exact independently identically distributed data simulation distribution. The new methodology provides both an efficient estimator to hitherto intractable Gaussian integrals. prove that has rare vanishing relative error asymptotic...

We propose a novel simulation-based method that exploits generalized splitting (GS) algorithm to estimate the reliability of graph (or network), defined here as probability given set nodes are connected, when each link fails with (small) probability. For large graphs, in general, computing exact is an intractable problem and estimating it by standard Monte Carlo methods poses serious difficulties, because unreliability (one minus reliability) often rare-event show proposed GS can accurately...

The generation of random spatial data on a computer is an important tool for understanding the behavior processes. In this paper we describe how to generate realizations from main types processes, including Gaussian and Markov fields, point Wiener Levy fields. Concrete MATLAB code provided.

The cross-entropy and minimum methods are well-known Monte Carlo simulation techniques for rare-event probability estimation optimization. In this paper, we investigate how these can be eXtended to provide a general non-parametric framework based on φ-divergence distance measures. We show the χ 2 distance, in particular, yields viable alternative Kullback—Leibler distance. theory is illustrated with various eXamples from density estimation, continuous multi-eXtremal

Global likelihood maximization is an important aspect of many statistical analyses. Often the function highly multi-extremal. This presents a significant challenge to standard search procedures, which often settle too quickly into inferior local maximum. We present new approach based on cross-entropy (CE) method, and illustrate its use for analysis mixture models.

In a static network reliability model, one typically assumes that the failures of components are independent. This simplifying assumption makes it possible to estimate efficiently via specialized Monte Carlo algorithms. Hence, natural question consider is whether this independence can be relaxed while still attaining an elegant and tractable model permits efficient algorithm for unreliability estimation. article, we provide answer by considering with dependent link failures, based on...

Abstract Kernel density estimation on a finite interval poses an outstanding challenge because of the well‐recognized bias at boundaries interval. Motivated by application in cancer research, we consider boundary constraint linking values unknown target function boundaries. We provide kernel estimator (KDE) that successfully incorporates this linked condition, leading to non‐self‐adjoint diffusion process and expansions nonseparable generalized eigenfunctions. The solution is rigorously...

We propose an exponential tilting method for the accurate estimation of probability that a random vector with multivariate student-t distribution falls in convex polytope. The can also be used to simulate exactly from corresponding truncated distribution, thus providing alternative approximate Markov Chain Monte Carlo simulation. Numerical experiments show suggested is significantly more and reliable than its competitors.

Global likelihood maximization is an important aspect of many statistical analyses. Often the function highly multiextremal. This presents a significant challenge to standard search procedures, which often settle too quickly into inferior local maximum. We present new approach based on cross-entropy (CE) method, and illustrate its use for analysis mixture models.

Static network reliability models typically assume that the failures of their components are independent. This assumption allows for design efficient Monte Carlo algorithms can estimate in settings where it is a rare-event probability. Despite this computational benefit, independent component frequently not realistic modeling real-life networks. In article we show how splitting methods simulation be used to model incorporates dependence structure via Marshal-Olkin copula.

We consider the problem of evaluating cumulative distribution function (CDF) sum order statistics, which serves to compute outage probability (OP) values at output generalized selection combining receivers. Generally, closed-form expressions CDF statistics are unavailable for many practical distributions. Moreover, naive Monte Carlo (MC) method requires a substantial computational effort when interest is sufficiently small. In region small OP values, we instead propose two effective variance...