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VIF回归：面向大规模数据的快速回归算法AI 解读

We propose a fast and accurate algorithm, VIF regression, for doing feature selection in large regression problems. VIF regression is extremely fast; it uses a one-pass search over the predictors and a computationally efficient method of testing each potential predictor for addition to the model. VIF regression provably avoids model overfitting, controlling the marginal false discovery rate. Numerical results show that it is much faster than any other published algorithm for…

滚动样本方差估计量的连续记录渐近理论AI 解读

It is widely known that conditional covariances of asset returns change over time. Researchers doing empirical work have adopted many strategies for accommodating conditional heteroskedasticity. One popular strategy is performing rolling regressions in which only data from, say, the preceding five year period is used to estimate the conditional covariance of returns at a given date. The authors develop continuous record asymptotic approximations for the measurement error in…

误设 ARCH 模型的滤波与预测：第二篇AI 解读

A companion paper (Nelson, 1992) showed that in data observed at high frequencies, an ARCH model may perform well in estimating the conditional variance of a process, even when the ARCH model is severely misspecified. While such models may perform reasonably well at filtering (i.e., at estimating unobserved instantaneous conditional variances), they may perform disastrously at medium- and long-term forecasting of the process and its volatility. In this paper, we develop…

多元回归的风险膨胀准则AI 解读

A new criterion is proposed for the evaluation of variable selection procedures in multiple regression. This criterion, which we call the risk inflation, is based on an adjustment to the risk. Essentially, the risk inflation is the maximum increase in risk due to selecting rather than knowing the "correct" predictors. A new variable selection procedure is obtained which, in the case of orthogonal predictors, substantially improves on AIC, $C_p$ and BIC and is close to…

单变量 ARCH 模型的渐近滤波理论AI 解读

Researchers often employ ARCH models to estimate conditional variances and covariances. How successfully can misspecified ARCH models carry out this estimation? This paper employs continuous record asymptotics to approximate the distribution of the measurement error. This allows the authors to (1) compare the efficiency of various ARCH models, (2) characterize the impact of different kinds of misspecification on efficiency, and (3) characterize asymptotically optimal ARCH…

未知变点之前的参数估计AI 解读

Consider the problem of estimating $\mu$, based on the observation of $Y_0, Y_1, \ldots, Y_n$, where it is assumed only that $Y_0, Y_1, \ldots, Y_\kappa \operatorname{iid} N(\mu, \sigma^2)$ for some unknown $\kappa$. Unlike the traditional change-point problem, the focus here is not on estimating $\kappa$, which is now a nuisance parameter. When it is known that $\kappa = k$, the sample mean $\bar{Y}_k = \sum^k_0Y_i/(k + 1)$, provides, in addition to wonderful efficiency…