E quantile sensitivities is important in many optimization applications, from hedging in financial engineering to service-level constraints in inventory control to more general chance constraints in stochastic programming. Recently, Hong (Hong, L. J. 2009. Estimating quantile sensitivities. Oper. Res. 57 118–130) derived a batched infinitesimal perturbation analysis estimator for quantile sensi...

In this paper, we provide an asymptotic expression for mean integrated squared error (MISE) of nonlinear wavelet density estimator for a truncation model. It is assumed that the lifetime observations form a stationary α-mixing sequence. Unlike for kernel estimator, the MISE expression of the nonlinear wavelet estimator is not affected by the presence of discontinuities in the curves. Also, we e...

Abstract: We consider estimation of the structural distribution function of the cell probabilities of a multinomial sample in situations where the number of cells is large. We review the performance of the natural estimator, an estimator based on grouping of the cells, and a kernel type estimator. Inconsistency of the natural estimator and weak consistency of the other two estimators is derived...

In this paper, we analyze methods for estimating the density of a conditional expectation. We compare an estimator based on a straightforward application of kernel density estimation to a bias-corrected estimator that we propose. We prove convergence results for these estimators and show that the bias-corrected estimator has a superior rate of convergence. In a simulated test case, we show that...

Let X1, . . . , Xn be i.i.d. observations, where Xi = Yi + Zi and Yi and Zi are independent. Assume that unobservable Y ’s are distributed as a random variable UV, where U has a Bernoulli distribution with probability of zero equal to p and V has a distribution function F with density f and U and V are independent. Furthermore, let the random variables Zi have the standard normal distribution. ...

Various consistency proofs for the kernel density estimator have been developed over the last few decades. Important milestones are the pointwise consistency and almost sure uniform convergence with a fixed bandwidth on the one hand and the rate of convergence with a fixed or even a variable bandwidth on the other hand. While considering global properties of the empirical distribution functions...

As sample quantiles can be obtained as maximum likelihood estimates of location parameters in suitable asymmetric Laplace distributions, so kernel estimates of quantiles can be obtained as maximum likelihood estimates of location parameters in a general class of distributions with simple exponential tails. In this paper, this observation is applied to kernel quantile regression. In so doing, a ...

The generalized varying coefficient partially linear model with a growing number of predictors arises in many contemporary scientific endeavor. In this paper we set foot on both theoretical and practical sides of profile likelihood estimation and inference. When the number of parameters grows with sample size, the existence and asymptotic normality of the profile likelihood estimator are establ...

The generalized varying coefficient partially linear model with growing number of predictors arises in many contemporary scientific endeavor. In this paper we set foot on both theoretical and practical sides of profile likelihood estimation and inference. When the number of parameters grows with sample size, the existence and asymptotic normality of the profile likelihood estimator are establis...