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协变量测量误差下的分位数回归AI 解读

This paper establishes that the availability of instrumental variables enables the identification and the consistent estimation of nonparametric quantile regression models in the presence of measurement error in the regressors. The proposed estimator takes the form of a nonlinear functional of derivatives of conditional expectations and is shown to provide estimated quantile functions that are uniformly consistent over a compact set.

基于 Hellinger 距离的非参数条件独立检验AI 解读

We propose a nonparametric test of conditional independence based on the weighted Hellinger distance between the two conditional densities, f ( y | x , z ) and f ( y | x ), which is identically zero under the null. We use the functional delta method to expand the test statistic around the population value and establish asymptotic normality under β-mixing conditions. We show that the test is consistent and has power against alternatives at distance n −1/2 h − d /4 . The cases…

单调指数模型的排序估计量AI 解读

This paper shows that the finite-dimensional parameters of a monotone-index model can be estimated by minimizing an objective function based on sorting the data. The key observation guiding this procedure is that the sum of distances between pairs of adjacent observations is minimized (over all possible permutations) when the observations are sorted by their values. The resulting estimator is a generalization of Cavanagh and Sherman's monotone rank estimator (MRE) (Cavanagh…

一般混合条件下平方 CUSUM 检验的极限分布AI 解读

We consider the cumulative sum (CUSUM) of squares test in a linear regression model with general mixing assumptions on the regressors and the errors. We derive its limit distribution and show how it depends on the nature of the error process. We suggest a corrected version that has a limit distribution free of nuisance parameters. We also discuss how it provides an improvement over the standard approach to testing for a change in the variance in a univariate times series.…

半非参数区间删失混合比例风险模型：识别与一致性结果AI 解读

In this paper I propose estimating distributions on the unit interval semi-nonparametrically using orthonormal Legendre polynomials. This approach will be applied to the interval-censored mixed proportional hazard (ICMPH) model, where the distribution of the unobserved heterogeneity is modeled semi-nonparametrically. Various conditions for the nonparametric identification of the ICMPH model are derived. I will prove general consistency results for M -estimators of (partly)…

关于 GARCH 模型不等式约束的一则说明AI 解读

We consider the parameter restrictions that need to be imposed to ensure that the conditional variance process of a GARCH( p , q ) model remains nonnegative. Previously, Nelson and Cao (1992, Journal of Business ’ Economic Statistics 10, 229–235) provided a set of necessary and sufficient conditions for the aforementioned nonnegativity property for GARCH( p , q ) models with p ≤ 2 and derived a sufficient condition for the general case of GARCH( p , q ) models with p ≥ 3. In…

依赖数据下核估计的一致收敛速率AI 解读

This paper presents a set of rate of uniform consistency results for kernel estimators of density functions and regressions functions. We generalize the existing literature by allowing for stationary strong mixing multivariate data with infinite support, kernels with unbounded support, and general bandwidth sequences. These results are useful for semiparametric estimation based on a first-stage nonparametric estimator.

密度可能不存在时的核估计AI 解读

Nonparametric kernel estimation of density and conditional mean is widely used, but many of the pointwise and global asymptotic results for the estimators are not available unless the density is continuous and appropriately smooth; in kernel estimation for discrete-continuous cases smoothness is required for the continuous variables. Nonsmooth density and mass points in distributions arise in various situations that are examined in empirical studies; some examples and…

一类分数阶过程向量自回归模型的表示理论AI 解读

Based on an idea of Granger (1986, Oxford Bulletin of Economics and Statistics 48, 213–228), we analyze a new vector autoregressive model defined from the fractional lag operator 1 − (1 − L ) d . We first derive conditions in terms of the coefficients for the model to generate processes that are fractional of order zero. We then show that if there is a unit root, the model generates a fractional process X t of order d , d > 0, for which there are vectors β so that β‼ X t is…

一致区分 I(0) 与 I(1) 过程的不可能性AI 解读

An I(0) process is commonly defined as a process that satisfies a functional central limit theorem, i.e., whose scaled partial sums converge weakly to a Wiener process, and an I(1) process as a process whose first differences are I(0). This paper establishes that with this definition, it is impossible to consistently discriminate between I(0) and I(1) processes. At the same time, on a more constructive note, there exist consistent unit root tests and also nontrivial…

具有无限方差创新的一阶多变量自回归AI 解读

We consider the limiting behavior of a vector autoregressive model of order one (VAR(1)) with independent and identically distributed (i.i.d.) innovations vector with dependent components in the domain of attraction of a multivariate stable law with possibly different indices of stability. It is shown that in some cases the ordinary least squares (OLS) estimates are inconsistent. This inconsistency basically originates from the fact that each coordinate of the partial sum…

有无单位根的 AR(1) 时间序列中的高斯推断AI 解读

This paper introduces a simple first-difference-based approach to estimation and inference for the AR(1) model. The estimates have virtually no finite-sample bias and are not sensitive to initial conditions, and the approach has the unusual advantage that a Gaussian central limit theory applies and is continuous as the autoregressive coefficient passes through unity with a uniform $\sqrt{n}$ rate of convergence. En route, a useful central limit theorem (CLT) for sample…

含低频随机水平跳变与异常值的协整过程渐近理论AI 解读

This is an analytical study of the effect of level-shift and temporary-change components, when present but neglected, on the trace test for cointegration. The contribution is threefold. First, we discuss in a multivariate framework, and jointly, effects that in the previous literature have been discussed in a univariate setting and in isolation. Second, we consider a rather general specification of shifts and outliers with random size, number, and timing and with flexible…

利用宏观数据改善微观预测AI 解读

We consider the problem of combining forecasts from two different levels (called “macro” and “micro”), where we have access to the forecasts and their precisions but not to the full data set. We develop a theoretical framework and provide Monte Carlo evidence in the cases of both perfect and imperfect aggregation. Our proposed procedure is simple and robust. We also extend the procedure to time series and propose a forecast model for the European zero rates, combining…

多元回归的预测密度估计AI 解读

Suppose we observe X ∼ Nm(Aβ,σ2I) and would like to estimate the predictive density p(y|β) of a future Y ∼ Nn(Bβ,σ2I). Evaluating predictive estimates by Kullback–Leibler loss, we develop and evaluate Bayes procedures for this problem. We obtain general sufficient conditions for minimaxity and dominance of the “noninformative” uniform prior Bayes procedure. We extend these results to situations where only a subset of the predictors in A is thought to be potentially…

估计误差的快速收敛率与模型选择的 Oracle 不等式AI 解读

We consider complexity penalization methods for model selection. These methods aim to choose a model to optimally trade off estimation and approximation errors by minimizing the sum of an empirical risk term and a complexity penalty. It is well known that if we use a bound on the maximal deviation between empirical and true risks as a complexity penalty, then the risk of our choice is no more than the approximation error plus twice the complexity penalty. There are many…

回归中的局部化模型选择AI 解读

Research on model/procedure selection has focused on selecting a single model globally. In many applications, especially for high-dimensional or complex data, however, the relative performance of the candidate procedures typically depends on the location, and the globally best procedure can often be improved when selection of a model is allowed to depend on location. We consider localized model selection methods and derive their theoretical properties.This research was…

均值矩阵的自适应估计：总体最小二乘与总体收缩AI 解读

An unknown constant matrix M is observed with additive random error. The basic problem considered is to devise an estimator of M that trades off bias against variance so as to achieve relatively low quadratic risk. This paper develops an adaptive total least squares estimator and an adaptive total shrinkage estimator of M that minimize estimated risk over certain large classes of linear estimators. It is shown that the asymptotic risk of the adaptive total least squares…

回归模型中平均风险的最小化AI 解读

Most model selection mechanisms work in an “overall” modus, providing models without specific concern for how the selected model is going to be used afterward. The focused information criterion (FIC), on the other hand, is geared toward optimum model selection when inference is required for a given estimand. In this paper the FIC method is extended to weighted versions. This allows one to rank and select candidate models for the purpose of handling a range of similar tasks…

基于广义错误率的形式化数据窥探处理AI 解读

It is common in econometric applications that several hypothesis tests are carried out simultaneously. The problem then becomes how to decide which hypotheses to reject, accounting for the multitude of tests. The classical approach is to control the familywise error rate (FWE), which is the probability of one or more false rejections. But when the number of hypotheses under consideration is large, control of the FWE can become too demanding. As a result, the number of false…

最高后验概率模型选择的深入考察AI 解读

We consider the properties of the highest posterior probability model in a linear regression setting. Under a spike and slab hierarchy we find that although highest posterior model selection is total risk consistent, it possesses hidden undesirable properties. One such property is a marked underfitting in finite samples, a phenomenon well noted for Bayesian information criterion (BIC) related procedures but not often associated with highest posterior model selection. Another…

近奇异设计下的收缩估计AI 解读

Shrinkage estimation procedures such as ridge regression and the lasso have been proposed for stabilizing estimation in linear models when high collinearity exists in the design. In this paper, we consider asymptotic properties of shrinkage estimators in the case of “nearly singular” designs.I thank Hannes Leeb and Benedikt Pötscher and also the referees for their valuable comments. This research was supported by a grant from the Natural Sciences and Engineering Research…

能否估计模型选择后估计量的无条件分布？AI 解读

We consider the problem of estimating the unconditional distribution of a post-model-selection estimator. The notion of a post-model-selection estimator here refers to the combined procedure resulting from first selecting a model (e.g., by a model-selection criterion such as the Akaike information criterion [AIC] or by a hypothesis testing procedure) and then estimating the parameters in the selected model (e.g., by least squares or maximum likelihood), all based on the same…

线性协整下区制切换误差修正模型的稳定性AI 解读

The paper obtains conditions that ensure stationarity of linear long-run equilibrium relations and differenced observations in vector autoregressive error correction models with nonlinear short-run dynamics. The considered models include various threshold error correction models and their smooth transition counterparts. These models assume that the form of the short-run dynamics depends on values of observable transition functions that determine the regime in which the…