Nonparametric inference of photon energy distribution from indirect measurements

Nonparametric inference for interventional effects with multiple mediators

Understanding the pathways whereby an intervention has an effect on an outcome is a common scientific goal. A rich body of literature provides various decompositions of the total intervention effect into pathway specific effects. Interventional direct and indirect effects provide one such decomposition. Existing estimators of these effects are based on parametric models with confidence interval estimation facilitated via the nonparametric bootstrap. We provide theory that allows for more flexible, possibly machine learning-based, estimation techniques to be considered. In particular, we establ…

Nonparametric estimation of mark's distribution of an exponential Shot-noise process

In this paper, we consider a nonlinear inverse problem occurring in nuclear science. Gamma rays randomly hit a semiconductor detector which produces an impulse response of electric current. Because the sampling period of the measured current is larger than the mean inter arrival time of photons, the impulse responses associated to different gamma rays can overlap: this phenomenon is known as pileup. In this work, it is assumed that the impulse response is an exponentially decaying function. We propose a novel method to infer the distribution of gamma photon energies from the indirect measureme…

Likelihood ratio type two-sample tests for current status data

We introduce fully nonparametric two-sample tests for testing the null hypothesis that the samples come from the same distribution if the values are only indirectly given via current status censoring. The tests are based on the likelihood ratio principle and allow the observation distributions to be different for the two samples, in contrast with earlier proposals for this situation. A bootstrap method is given for determining critical values and asymptotic theory is developed. A simulation study, using Weibull distributions, is presented to compare the power behavior of the tests with the pow…

Indirect Active Learning

Traditional models of active learning assume a learner can directly manipulate or query a covariate $X$ in order to study its relationship with a response $Y$. However, if $X$ is a feature of a complex system, it may be possible only to indirectly influence $X$ by manipulating a control variable $Z$, a scenario we refer to as Indirect Active Learning. Under a nonparametric model of Indirect Active Learning with a fixed budget, we study minimax convergence rates for estimating the relationship between $X$ and $Y$ locally at a point, obtaining different rates depending on the complexities and no…

The nonparametric location-scale mixture cure model

We propose completely nonparametric methodology to investigate location-scale modelling of two-component mixture cure models, where the responses of interest are only indirectly observable due to the presence of censoring and the presence of so-called long-term survivors that are always censored. We use covariate-localized nonparametric estimators, which depend on a bandwidth sequence, to propose an estimator of the error distribution function that has not been considered before in the literature. When this bandwidth belongs to a certain range of undersmoothing bandwidths, the asymptotic distr…

Indirect Maximum Entropy Bandwidth

This paper proposes a new method of bandwidth selection in kernel estimation of density and distribution functions motivated by the connection between maximisation of the entropy of probability integral transforms and maximum likelihood in classical parametric models. The proposed estimators are designed to indirectly maximise the entropy of the leave-one-out kernel estimates of a distribution function, which are the analogues of the parametric probability integral transforms. The estimators based on minimisation of the Cramer-von Mises discrepancy, near-solution of the moment-based estimating…

Efficient Simulation-Based Minimum Distance Estimation and Indirect Inference

Given a random sample from a parametric model, we show how indirect inference estimators based on appropriate nonparametric density estimators (i.e., simulation-based minimum distance estimators) can be constructed that, under mild assumptions, are asymptotically normal with variance-covarince matrix equal to the Cramer-Rao bound.

基于分类器的非参数序列假设检验

Classifier-Based Nonparametric Sequential Hypothesis Testing

本文提出了一种基于分类器的非参数序列假设检验方法，通过离线数据集训练多类分类器，设计水平α的检验方法，并分析了检验停止时间的上界及分类器分离条件。

Bayesian Nonparametric Density Estimation under Length Bias

A density estimation method in a Bayesian nonparametric framework is presented when recorded data are not coming directly from the distribution of interest, but from a length biased version. From a Bayesian perspective, efforts to computationally evaluate posterior quantities conditionally on length biased data were hindered by the inability to circumvent the problem of a normalizing constant. In this paper we present a novel Bayesian nonparametric approach to the length bias sampling problem which circumvents the issue of the normalizing constant. Numerical illustrations as well as a real dat…

Bayesian Nonparametric Inference for M/G/1 Queueing Systems

In this work, nonparametric statistical inference is provided for the continuous-time M/G/1 queueing model from a Bayesian point of view. The inference is based on observations of the inter-arrival and service times. Beside other characteristics of the system, particular interest is in the waiting time distribution which is not accessible in closed form. Thus, we use an indirect statistical approach by exploiting the Pollaczek-Khinchine transform formula for the Laplace transform of the waiting time distribution. Due to this, an estimator is defined and its frequentist validation in terms of p…

基于双重非参数随机效用模型的动态情境定价

Dynamic Contextual Pricing with Doubly Non-Parametric Random Utility Models

本文提出双重非参数随机效用模型，通过总体方程解决动态在线定价中效用变量间接可观测和一致收敛缺失问题，并证明学习速率极小极大最优，推导遗憾界揭示维度与噪声平滑度的交互关系。

Optimal change-point estimation from indirect observations

We study nonparametric change-point estimation from indirect noisy observations. Focusing on the white noise convolution model, we consider two classes of functions that are smooth apart from the change-point. We establish lower bounds on the minimax risk in estimating the change-point and develop rate optimal estimation procedures. The results demonstrate that the best achievable rates of convergence are determined both by smoothness of the function away from the change-point and by the degree of ill-posedness of the convolution operator. Optimality is obtained by introducing a new technique …

Bayesian Indirect Inference and the ABC of GMM

In this paper we propose and study local linear and polynomial based estimators for implementing Approximate Bayesian Computation (ABC) style indirect inference and GMM estimators. This method makes use of nonparametric regression in the computation of GMM and Indirect Inference models. We provide formal conditions under which frequentist inference is asymptotically valid and demonstrate the validity of the estimated posterior quantiles for confidence interval construction. We also show that in this setting, local linear kernel regression methods have theoretical advantages over local constant…