Cumulative Conditional Expectation Index

A comparison of the accuracy of saddlepoint conditional cumulative distribution function approximations

Consider a model parameterized by a scalar parameter of interest and a nuisance parameter vector. Inference about the parameter of interest may be based on the signed root of the likelihood ratio statistic R. The standard normal approximation to the conditional distribution of R typically has error of order O(n^{-1/2}), where n is the sample size. There are several modifications for R, which reduce the order of error in the approximations. In this paper, we mainly investigate Barndorff-Nielsen's modified directed likelihood ratio statistic, Severini's empirical adjustment, and DiCiccio and Mar…

Characterization of Order Statistics in Two Runs Using Conditional Expectation

The runs test is a well-known test that is used for checking independence between elements of a sample data sequence. Some of runs tests are based on the longest run and others based on the total runs. In this paper, we consider order statistics of two runs statistics, and obtain their probability mass functions. In addition, the means and variances of the order statistics are derived using traditional conditional expectation.

高斯变换建模与分布回归函数的估计

Gaussian Transforms Modeling and the Estimation of Distributional Regression Functions

本文提出高斯变换建模条件累积分布函数，给出凹似然估计准则，统一估计密度、分布和分位数函数，并在美国性别工资差距应用中验证。

An efficient model-free estimation of multiclass conditional probability

Conventional multiclass conditional probability estimation methods, such as Fisher's discriminate analysis and logistic regression, often require restrictive distributional model assumption. In this paper, a model-free estimation method is proposed to estimate multiclass conditional probability through a series of conditional quantile regression functions. Specifically, the conditional class probability is formulated as difference of corresponding cumulative distribution functions, where the cumulative distribution functions can be converted from the estimated conditional quantile regression f…

Computing the variance of a conditional expectation via non-nested Monte Carlo

Computing the variance of a conditional expectation has often been of importance in uncertainty quantification. Sun et al. has introduced an unbiased nested Monte Carlo estimator, which they call $1\frac{1}{2}$-level simulation since the optimal inner-level sample size is bounded as the computational budget increases. In this letter we construct unbiased non-nested Monte Carlo estimators based on the so-called pick-freeze scheme due to Sobol'. An extension of our approach to compute higher order moments of a conditional expectation is also discussed.

Minimum Risk Equivariant Estimation of the Parameters of the General Half-Normal Distribution by Means of a Monte Carlo Method to Approximate Conditional Expectations

This work addresses the problem of estimating the parameters of the general half-normal distribution. Namely, the problem of determining the minimum risk equi\-va\-riant (MRE) estimators of the parameters is explored. Simulation studies are realized to compare the behavior of these estimators with maximum likelihood and unbiased estimators. A natural Monte Carlo method to compute conditional expectations is used to approximate the MRE estimation of the location parameter because its expression involves two conditional expectations not easily computables. The used Monte Carlo method is justifie…