Local probabilistic sensitivity of input variable X with respect to output variable Z is proportional to the derivative of the conditional expectation E(X|z). This paper reports on experience in computing this conditional expectation. Linearized estimates are found to give acceptable performance, but are not generally applicable. A new method of linearization based on re-weighting a Monte Carlo...

In this paper we explore the bias in the estimation of the Value at Risk and Conditional Tail Expectation risk measures using Monte Carlo simulation. We assess the use of bootstrap techniques to correct the bias for a number of different examples. In the case of the Conditional Tail Expectation, we show that application of the exact bootstrap can improve estimates, and we develop a practical gu...

In a recent paper Longstaff & Schwartz (2001) suggest a method to American option valuation based on simulation. The method is termed the Least Squares Monte-Carlo (LSM) method, and although it has become widely used not much is known about the properties of the estimator. This paper corrects this shortcoming using theory from the literature on seminonparametric series estimators. A central par...

1 Probability “review” 3 1.1 σ-fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Random variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Probability measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Distribution of a random variable . . . . . . . ....

Nonparametric regression estimates a conditional expectation of a response given a predictor variable without requiring parametric assumptions about this conditional expectation. There are many methods of nonparametric regression including kernel estimation, smoothing splines, regression splines, and orthogonal series. Local regression ts parametric models locally by using kernel weights. Local...

Di Piazza and Preiss asked whether every Pettis integrable function defined on [0, 1] and taking values in a weakly compactly generated Ba-nach space is McShane integrable. In this paper we answer this question in the negative.

We demonstrate an intuitive relation between conditional entropy and conditional expectation that is useful when one want to compare them as measurement tools to evaluate secrecy systems. In particular, we give a Security Property applicable to general vector variables in , using measurement based on vector quadratic distance, and we show that one can derive variables that can be measured with ...

Abstract: In this paper, we obtain certain expressions and recurrence relations for two general classes of distributions based on some conditional expectations of k-th lower record values. We consider the necessary and sufficient conditions such that these conditional expectations hold for some distribution functions. Furthermore, an expression of conditional expectation of other general class ...

When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp. functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by actual observations of the response of the real system. In a probabilistic setting, Bayes’s theory is the proper mathematical background for this identification pr...