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协变量自适应随机化的渐近性质AI 解读

Balancing treatment allocation for influential covariates is critical in clinical trials. This has become increasingly important as more and more biomarkers are found to be associated with different diseases in translational research (genomics, proteomics and metabolomics). Stratified permuted block randomization and minimization methods [Pocock and Simon Biometrics 31 (1975) 103–115, etc.] are the two most popular approaches in practice. However, stratified permuted block…

相关矩阵的谱边缘普适性AI 解读

Let $\widetilde{X}_{M\times N}$ be a rectangular data matrix with independent real-valued entries $[\widetilde{x}_{ij}]$ satisfying $\mathbb{E} \widetilde{x}_{ij}=0$ and $\mathbb{E} \widetilde{x}^{2}_{ij}=\frac{1}{M}$, $N,M\to\infty$. These entries have a subexponential decay at the tails. We will be working in the regime $N/M=d_{N}$, $\lim_{N\to\infty}d_{N}\neq0,1,\infty$. In this paper we prove the edge universality of correlation matrices ${X}^{\dagger}X$, where the…

回归分位数过程的近根号样本量精度近似AI 解读

Traditionally, assessing the accuracy of inference based on regression quantiles has relied on the Bahadur representation. This provides an error of order $n^{-1/4}$ in normal approximations, and suggests that inference based on regression quantiles may not be as reliable as that based on other (smoother) approaches, whose errors are generally of order $n^{-1/2}$ (or better in special symmetric cases). Fortunately, extensive simulations and empirical applications show that…

Grenander型估计量上确界范数误差的极限分布AI 解读

Let $f$ be a nonincreasing function defined on $[0,1]$. Under standard regularity conditions, we derive the asymptotic distribution of the supremum norm of the difference between $f$ and its Grenander-type estimator on sub-intervals of $[0,1]$. The rate of convergence is found to be of order $(n/\log n)^{-1/3}$ and the limiting distribution to be Gumbel.

病态逆问题中的极小极大信号检测AI 解读

Ill-posed inverse problems arise in various scientific fields. We consider the signal detection problem for mildly, severely and extremely ill-posed inverse problems with $l^{q}$-ellipsoids (bodies), $q\in(0,2]$, for Sobolev, analytic and generalized analytic classes of functions under the Gaussian white noise model. We study both rate and sharp asymptotics for the error probabilities in the minimax setup. By construction, the derived tests are, often, nonadaptive. Minimax…

密度线性泛函的 Bernstein–von Mises 定理AI 解读

In this paper, we study the asymptotic posterior distribution of linear functionals of the density by deriving general conditions to obtain a semi-parametric version of the Bernstein–von Mises theorem. The special case of the cumulative distributive function, evaluated at a specific point, is widely considered. In particular, we show that for infinite-dimensional exponential families, under quite general assumptions, the asymptotic posterior distribution of the functional…

稀疏 Ising 模型的非凹惩罚复合条件似然估计AI 解读

The Ising model is a useful tool for studying complex interactions within a system. The estimation of such a model, however, is rather challenging, especially in the presence of high-dimensional parameters. In this work, we propose efficient procedures for learning a sparse Ising model based on a penalized composite conditional likelihood with nonconcave penalties. Nonconcave penalized likelihood estimation has received a lot of attention in recent years. However, such an…

时变回归模型的统计推断AI 解读

We consider parameter estimation, hypothesis testing and variable selection for partially time-varying coefficient models. Our asymptotic theory has the useful feature that it can allow dependent, nonstationary error and covariate processes. With a two-stage method, the parametric component can be estimated with a $n^{1/2}$-convergence rate. A simulation-assisted hypothesis testing procedure is proposed for testing significance and parameter constancy. We further propose an…

含协变量临床试验的多目标最优设计：强化双重自适应偏币设计AI 解读

The present paper deals with the problem of allocating patients to two competing treatments in the presence of covariates or prognostic factors in order to achieve a good trade-off among ethical concerns, inferential precision and randomness in the treatment allocations. In particular we suggest a multipurpose design methodology that combines efficiency and ethical gain when the linear homoscedastic model with both treatment/covariate interactions and interactions among…

高维协方差矩阵的带状性检验与带宽估计AI 解读

Motivated by the latest effort to employ banded matrices to estimate a high-dimensional covariance $\Sigma$, we propose a test for $\Sigma$ being banded with possible diverging bandwidth. The test is adaptive to the “large $p$, small $n$” situations without assuming a specific parametric distribution for the data. We also formulate a consistent estimator for the bandwidth of a banded high-dimensional covariance matrix. The properties of the test and the bandwidth estimator…

基于分位数残差的误设检验AI 解读

We develop quantile residual‐based misspecification tests and apply them to non‐linear time series models for which conventional residuals are unsuited. We formulate a general framework and use it to obtain computationally simple tests aimed at detecting autocorrelation, conditional heteroscedasticity and non‐normality in quantile residuals. These tests are generalizations of similar previous tests based on conventional residuals and the Lagrange Multiplier principle.…

利用大型非平衡期权面板估计与检验非仿射期权定价模型AI 解读

In this paper, we consider joint estimation of objective and risk‐neutral parameters for stochastic volatility option pricing models using both stock and option prices. A common strategy simplifies the task by limiting the analysis to just one option per date. We first discuss its drawbacks on the basis of model interpretation, estimation results and pricing exercises. We then turn the attention to a more flexible approach, that successfully exploits the wealth of…

共爆炸向量自回归中的理性泡沫检验AI 解读

We derive the parameter restrictions that a standard equity market model implies for a bivariate vector autoregression for stock prices and dividends, and we show how to test these restrictions using likelihood ratio tests. The restrictions, which imply that stock returns are unpredictable, are derived both for a model without bubbles and for a model with a rational bubble. In both cases we show how the restrictions can be tested through standard chi-squared inference. The…

均衡价格跳跃与市场微观结构噪声AI 解读

Asset prices observed in financial markets combine equilibrium prices and market microstructure noise. In this paper, we study how to tell apart large shifts in equilibrium prices from noise using high frequency data. We propose a new nonparametric test which allows us to asymptotically remove the noise from observable price data and to discover jumps in fundamental asset values. We provide its asymptotic distribution to decide when such jumps occur. In finite samples, our…

断点回归设计中的分位数处理效应AI 解读

We introduce a nonparametric estimator for local quantile treatment effects in the regression discontinuity (RD) design. The procedure uses local distribution regression to estimate the marginal distributions of the potential outcomes. We illustrate the procedure through Monte Carlo simulations and an application on the distributional effects of a universal pre-K program in Oklahoma. We find that participation in a pre-K program significantly raises the lower end and the…

截断与删失回归模型的半参数稳健估计AI 解读

Many estimation methods of truncated and censored regression models such as the maximum likelihood and symmetrically censored least squares (SCLS) are sensitive to outliers and data contamination as we document. Therefore, we propose a semiparametric general trimmed estimator (GTE) of truncated and censored regression, which is highly robust but relatively imprecise. To improve its performance, we also propose data-adaptive and one-step trimmed estimators. We derive the…

利用趋势回归分割均值非平稳时间序列AI 解读

In this paper, we provide a segmentation procedure for mean-nonstationary time series. The segmentation is obtained by casting the problem into the framework of detecting structural breaks in trending regression models in which the regressors are generated by suitably smooth functions. As test statistics we propose to use the maximally selected likelihood ratio statistics and a related statistics based on partial sums of weighted residuals. The main theoretical contribution…

联合分布与条件分布的贝叶斯建模AI 解读

In this paper, we study a Bayesian approach to flexible modeling of conditional distributions. The approach uses a flexible model for the joint distribution of the dependent and independent variables and then extracts the conditional distributions of interest from the estimated joint distribution. We use a finite mixture of multivariate normals (FMMN) to estimate the joint distribution. The conditional distributions can then be assessed analytically or through simulations.…

弱影响因子下大型因子模型主成分估计量的渐近理论AI 解读

This paper introduces a drifting-parameter asymptotic framework to derive accurate approximations to the finite sample distribution of the principal components (PC) estimator in situations when the factors’ explanatory power does not strongly dominate the explanatory power of the cross-sectionally and temporally correlated idiosyncratic terms. Under our asymptotics, the PC estimator is inconsistent. We find explicit formulae for the amount of the inconsistency, and propose…

非参数协整回归中的动态误设AI 解读

Linear cointegration is known to have the important property of invariance under temporal translation. The same property is shown not to apply for nonlinear cointegration. The limit properties of the Nadaraya–Watson (NW) estimator for cointegrating regression under misspecified lag structure are derived, showing the NW estimator to be inconsistent, in general, with a “pseudo-true function” limit that is a local average of the true regression function. In this respect…

高斯仿射期限结构模型的识别与估计AI 解读

This paper develops new results for identification and estimation of Gaussian affine term structure models. We establish that three popular canonical representations are unidentified, and demonstrate how unidentified regions can complicate numerical optimization. A separate contribution of the paper is the proposal of minimum-chi-square estimation as an alternative to MLE. We show that, although it is asymptotically equivalent to MLE, it can be much easier to compute. In…

非参数前沿估计量的正则化AI 解读

In production theory and efficiency analysis, we estimate the production frontier, the locus of the maximal attainable level of an output (the production), given a set of inputs (the production factors). In other setups, we estimate rather an input (or cost) frontier, the minimal level of the input (cost) attainable for a given set of outputs (goods or services produced). In both cases the problem can be viewed as estimating a surface under shape constraints (monotonicity,…

HESSIAN方法：高效模拟平滑的简明框架AI 解读

I introduce the HESSIAN (highly efficient simulation smoothing in a nutshell) method for numerically efficient simulation smoothing in state space models with univariate states. Given a vector θ of parameters, the vector of states α=(α1,…,αn) is Gaussian and the observed vector y=(y1⊤,…,yn⊤)⊤ need not be. I describe a procedure to construct a close approximation q(α|θ,y) to the target density p(α|θ,y). It requires code to compute five derivatives of logp(yt|θ,αt) with…

含噪高频数据中的跳跃检验AI 解读

This paper proposes a robustification of the test statistic of Aït-Sahalia and Jacod (2009b) for the presence of market microstructure noise in high frequency data, based on the pre-averaging method of Jacod et al. (2010). We show that the robustified statistic restores the test’s discriminating power between jumps and no jumps despite the presence of market microstructure noise in the data.