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有限维 higher criticism 检验的解析 p 值计算AI 解读

The higher criticism test is effective for testing a joint null hypothesis against a sparse alternative, e.g., for testing the effect of a gene or genetic pathway that consists of d genetic markers. Accurate p-value calculations for the higher criticism test based on the asymptotic distribution require a very large d, which is not the case for the number of genetic variants in a gene or a pathway. In this paper we propose an analytical method for accurately computing the…

线性模型中的独立性与拟合优度检验AI 解读

We consider a linear regression model and propose an omnibus test to simultaneously check the assumption of independence between the error and predictor variables and the goodness-of-fit of the parametric model. Our approach is based on testing for independence between the predictor and the residual obtained from the parametric fit by using the Hilbert–Schmidt independence criterion (Gretton et al., 2008). The proposed method requires no user-defined regularization, is…

风险差的广义 Cornfield 条件AI 解读

A central question in causal inference with observational studies is the sensitivity of conclusions to unmeasured confounding. The classical Cornfield condition allows us to assess whether an unmeasured binary confounder can explain away the observed relative risk of the exposure on the outcome. It states that for an unmeasured confounder to explain away an observed relative risk, the association between the unmeasured confounder and the exposure and the association between…

多线性主成分分析中 Kronecker 包络模型的检验AI 解读

We develop likelihood methods for the Kronecker envelope model in the principal components analysis of matrix observations that have a multivariate normal distribution. Maximum likelihood estimates are derived and the associated likelihood ratio statistic for a test of this Knonecker envelope model is obtained. The asymptotic null distribution of the likelihood ratio statistic is derived as some nuisance parameters approach infinity, and a saddlepoint approximation for this…

分数噪声回归模型的渐近等价性AI 解读

Consider estimation of the regression function based on a model with equidistant design and measurement errors generated from a fractional Gaussian noise process. In previous literature, this model has been heuristically linked to an experiment, where the anti-derivative of the regression function is continuously observed under additive perturbation by a fractional Brownian motion. Based on a reformulation of the problem using reproducing kernel Hilbert spaces, we derive…

地统计回归模型选择中广义信息准则的渐近理论AI 解读

Information criteria, such as Akaike’s information criterion and Bayesian information criterion are often applied in model selection. However, their asymptotic behaviors for selecting geostatistical regression models have not been well studied, particularly under the fixed domain asymptotic framework with more and more data observed in a bounded fixed region. In this article, we study the generalized information criterion (GIC) for selecting geostatistical regression models…

笛卡尔符号法则与基因组变异数据中种群历史模型的可识别性AI 解读

The sample frequency spectrum (SFS) is a widely-used summary statistic of genomic variation in a sample of homologous DNA sequences. It provides a highly efficient dimensional reduction of large-scale population genomic data and its mathematical dependence on the underlying population demography is well understood, thus enabling the development of efficient inference algorithms. However, it has been recently shown that very different population demographies can actually…

奇异值阈值矩阵去噪的极小极大风险AI 解读

An unknown $m$ by $n$ matrix $X_{0}$ is to be estimated from noisy measurements $Y=X_{0}+Z$, where the noise matrix $Z$ has i.i.d. Gaussian entries. A popular matrix denoising scheme solves the nuclear norm penalization problem $\operatorname{min}_{X}\|Y-X\|_{F}^{2}/2+\lambda\|X\|_{*}$, where $\|X\|_{*}$ denotes the nuclear norm (sum of singular values). This is the analog, for matrices, of $\ell_{1}$ penalization in the vector case. It has been empirically observed that if $X_{0}$…

偏距离相关及其对相异度数据的方法扩展AI 解读

Distance covariance and distance correlation are scalar coefficients that characterize independence of random vectors in arbitrary dimension. Properties, extensions and applications of distance correlation have been discussed in the recent literature, but the problem of defining the partial distance correlation has remained an open question of considerable interest. The problem of partial distance correlation is more complex than partial correlation partly because the…

持续图的置信集合AI 解读

Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features (2000) as one varies a tuning parameter. Features with short lifetimes are informally considered to be “topological noise,” and those with a long lifetime are considered to be “topological signal.” In this paper, we bring some statistical ideas to persistent homology. In particular, we derive confidence…

利用面板bootstrap改进共同基金绩效评价推断AI 解读

Two new methodologies are introduced to improve inference in the evaluation of mutual fund performance against benchmarks. First, the benchmark models are estimated using panel methods with both fund and time effects. Second, the non-normality of individual mutual fund returns is accounted for by using panel bootstrap methods. We also augment the standard benchmark factors with fund-specific characteristics, such as fund size. Using a dataset of UK equity mutual fund…

利用线性累积量方程对测量误差模型进行最小距离估计AI 解读

We consider a multiple mismeasured regressor errors-in-variables model. We develop closed-form minimum distance estimators from any number of estimating equations, which are linear in the third and higher cumulants of the observable variables. Using the cumulant estimators alters qualitative inference relative to ordinary least squares in two applications related to investment and leverage regressions. The estimators perform well in Monte Carlos calibrated to resemble the…

通过最优组合分位数信息实现高效回归估计AI 解读

We develop a generally applicable framework for constructing efficient estimators of regression models via quantile regressions. The proposed method is based on optimally combining information over multiple quantiles and can be applied to a broad range of parametric and nonparametric settings. When combining information over a fixed number of quantiles, we derive an upper bound on the distance between the efficiency of the proposed estimator and the Fisher information. As…

固定效应动态面板模型的非参数估计AI 解读

This paper considers nonparametric estimation of autoregressive panel data models with fixed effects. A within-group type series estimator is developed and its convergence rate and asymptotic normality are derived. It is found that the series estimator is asymptotically biased and the bias could reduce the mean-square convergence rate compared with the cross-section cases. A bias corrected nonparametric estimator is developed.

密度加权平均导数的 Bootstrap 推断AI 解读

We investigate the properties of several bootstrap-based inference procedures for semiparametric density-weighted average derivatives. The key innovation in this paper is to employ an alternative asymptotic framework to assess the properties of these inference procedures. This theoretical approach is conceptually distinct from the traditional approach (based on asymptotic linearity of the estimator and Edgeworth expansions), and leads to different theoretical prescriptions…

退化 ARCH 模型参数推断的一族对比准则AI 解读

In this paper, we introduce a family of contrasts for parametric inference in ARCH models the volatility of which exhibits some degeneracy. We focus specifically on ARCH processes with a linear volatility (called LARCH processes), for which the Gaussian quasi-likelihood estimator may be inconsistent. Our approach generalizes that of Beran and Schützner (2009) and gives an interesting alternative to the WLSE used by Francq and Zakoïan (2010) for an autoregressive process with…

条件平均处理效应的估计AI 解读

We consider a functional parameter called the conditional average treatment effect (CATE), designed to capture heterogeneity of a treatment effect across subpopulations when the unconfoundedness assumption applies. In contrast to quantile regressions, the subpopulations of interest are defined in terms of the possible values of a set of continuous covariates rather than the quantiles of the potential outcome distributions. We show that the CATE parameter is nonparametrically…

构造二项与泊松参数置信区间的样本分割方法AI 解读

Summary We introduce a new method for improving the coverage accuracy of confidence intervals for means of lattice distributions. The technique can be applied very generally to enhance existing approaches, although we consider it in greatest detail in the context of estimating a binomial proportion or a Poisson mean, where it is particularly effective. The method is motivated by a simple theoretical result, which shows that, by splitting the original sample of size n into…

贝叶斯模型选择中的相关摘要统计量AI 解读

Summary The choice of the summary statistics that are used in Bayesian inference and in particular in approximate Bayesian computation algorithms has bearings on the validation of the resulting inference. Those statistics are nonetheless customarily used in approximate Bayesian computation algorithms without consistency checks. We derive necessary and sufficient conditions on summary statistics for the corresponding Bayes factor to be convergent, namely to select the true…

利用商品价格指数预测通货膨胀AI 解读

This paper shows that for five small commodity-exporting countries that have adopted inflation targeting monetary policies, world commodity price aggregates have predictive power for their CPI and PPI inflation, particularly once possible structural breaks are taken into account. This conclusion is robust to using either disaggregated or aggregated commodity price indexes (although the former perform better), the currency denomination of the commodity prices, and to using…

利用分数多项式逼近正规经济函数的似然推断AI 解读

This paper shows that regular fractional polynomials can approximate regular cost, production and utility functions and their first two derivatives on closed compact subsets of the strictly positive orthant of Euclidean space arbitrarily well. These functions therefore can provide reliable approximations to demand functions and other economically relevant characteristics of tastes and technology. Using canonical cost function data, it shows that full Bayesian inference for…

意见分歧与资产价格AI 解读

How do differences of opinion affect asset prices? Do investors earn a risk premium when disagreement arises in the market? Despite their fundamental importance, these questions are among the most controversial issues in finance. In this paper, we use a novel data set that allows us to directly measure the level of disagreement among Wall Street mortgage dealers about prepayment speeds. We examine how disagreement evolves over time and study its effects on expected returns,…

断点回归设计的稳健非参数置信区间AI 解读

In the regression-discontinuity (RD) design, units are assigned to treatment based on whether their value of an observed covariate exceeds a known cutoff. In this design, local polynomial estimators are now routinely employed to construct confidence intervals for treatment effects. The performance of these confidence intervals in applications, however, may be seriously hampered by their sensitivity to the specific bandwidth employed. Available bandwidth selectors typically…

两步广义矩估计框架下的固定平滑渐近理论AI 解读

This paper develops the fixed-smoothing asymptotics in a two-step generalized method of moments (GMM) framework. Under this type of asymptotics, the weighting matrix in the second-step GMM criterion function converges weakly to a random matrix and the two-step GMM estimator is asymptotically mixed normal. Nevertheless, the Wald statistic, the GMM criterion function statistic, and the Lagrange multiplier statistic remain asymptotically pivotal. It is shown that critical…