Comparison of causal effect estimators under exposure misclassification

Over the past decades, various principles for causal effect estimation have been proposed, all differing in terms of how they adjust for measured confounders: either via traditional regression adjustment, by adjusting for the expected exposure given those confounders (e.g., the propensity score), or by inversely weighting each subject's data by the likelihood of the observed exposure, given those confounders. When the exposure is measured with error, this raises the question whether these different estimation strategies might be differently affected and whether one of them is to be preferred for that reason. In this article, we investigate this by comparing inverse probability of treatment weighted (IPTW) estimators and doubly robust estimators for the exposure effect in linear marginal structural mean models (MSM) with G-estimators, propensity score (PS) adjusted estimators and ordinary least squares (OLS) estimators for the exposure effect in linear regression models. We find analytically that these estimators are equally affected when exposure misclassification is independent of the confounders, but not otherwise. Simulation studies reveal similar results for time-varying exposures and when the model of interest includes a logistic link.     

Asymptotics of the Finite-time Ruin Probability for the Sparre Andersen Risk Model Perturbed by an Inflated Stationary Chi-process

In this article, we consider the Sparre Andersen risk model that is perturbed by an inflated chi-process with non-negative random inflator R. Under some conditions on the perturbation and the random inflator, which allow for both small and large fluctuations, exact asymptotic behaviour of the finite-time ruin probability is obtained when initial reserve tends to infinity.     

Unemployment duration and the measurement of unemployment

We propose a framework in which the welfare bases of various unemployment measures available in the literature can be analyzed and a decomposition of these measures can be made into aggregate unemployment and the concentration of its distribution. A set of axioms for an unemployment measure is then introduced, which relate to the sensitivity of an unemployment measure to the inequality in the distribution of the unemployment. An unemployment measure is derived on the basis of these axioms that captures the distributional considerations in the measurement of unemployment.      

Convergence Rate of Wavelet Expansions of Gaussian Random Processes

This article characterizes uniform convergence rate for general classes of wavelet expansions of stationary Gaussian random processes. The convergence in probability is considered.     

Uniform asymptotics for ruin probability of a two-dimensional dependent renewal risk model

ABSTRACT

In this paper we consider the tail behavior of a two-dimensional dependent renewal risk model with two dependent classes of insurance business, in which the claim sizes are governed by a common renewal counting process, and their inter-arrival times are dependent, identically distributed. For the case that the claim size distribution belongs to the intersection of long-tailed distribution class and dominant variation class, we obtain an asymptotic formula, which holds uniformly for all time in an infinite interval. Moreover, we point out that the formula still holds uniformly for all time in an infinite interval for widely dependent random variables (r.v.s) under some conditions.     

Inference for the scale parameter of lifetime distribution of k-unit parallel system based on progressively censored data

In this paper, inference for the scale parameter of lifetime distribution of a k-unit parallel system is provided. Lifetime distribution of each unit of the system is assumed to be a member of a scale family of distributions. Maximum likelihood estimator (MLE) and confidence intervals for the scale parameter based on progressively Type-II censored sample are obtained. A β-expectation tolerance interval for the lifetime of the system is obtained. As a member of the scale family, half-logistic distribution is considered and the performance of the MLE, confidence intervals and tolerance intervals are studied using simulation.     

On shrinkage m-estimators of location parameters

For a general class of continuous ( and marginally symmetric ) inultivariate distributions, based on suitable M-statistics ( involving bounded but possibly discontinuous score generating functions), shrinkage estimators of location are considered. These estimators are based on the James-Stein type rule and incorporates the idea of preliminary test estimation too. The main emphasis is laid on the study of asymptotic tdistributional ) risk properties of these est-innators, and asymptotic tin-) adraissibility results are also studied under fairly general regularity conditions.     

On Comparison Of Estimates Of Dispersion Using Generalized Pitman Nearness Criterion

In this paper, estimates QP dispersion matrix and its functions are compared based on generalized Pitman nearness criterion, Various Iosa functions are considered for the purpose. Locally superior estimates are defined and obtained. Comparison of these estimates are made with other standard ones. It is snown that within certain classes, defined in the paper, these are the best estimatcrs ia the generalized Fitman nearness sense     

Recent and classical goodness-of-fit tests for the Poisson distribution

We give a critical synopsis of classical and recent tests for Poissonity, our emphasis being on procedures which are consistent against general alternatives. Two classes of weighted Cramér–von Mises type test statistics, based on the empirical probability generating function process, are studied in more detail. Both of them generalize already known test statistics by introducing a weighting parameter, thus providing more flexibility with regard to power against specific alternatives. In both cases, we prove convergence in distribution of the statistics under the null hypothesis in the setting of a triangular array of rowwise independent and identically distributed random variables as well as consistency of the corresponding test against general alternatives. Therefore, a sound theoretical basis is provided for the parametric bootstrap procedure, which is applied to obtain critical values in a large-scale simulation study. Each of the tests considered in this study, when implemented via the parametric bootstrap method, maintains a nominal level of significance very closely, even for small sample sizes. The procedures are applied to four well-known data sets.     

论诉讼中的"二元"证明标准

诉讼中的证明标准问题是证据法学研究中的一个重要问题.近年来,一些学者从比较研究的角度提出在我国证据法中移植英美法上的"二元"证明标准.本文在理论和实践两个层次分析的基础上提出反驳理由,并指出,这种移植既无必要性,也缺乏可操作性.