STATISTICAL INFERENCE WITH F-STATISTICS WHEN FITTING SIMPLE MODELS TO HIGH-DIMENSIONAL DATA

We study linear subset regression in the context of the high-dimensional overall model $y = \vartheta +\theta ' z + \epsilon $ with univariate response y and a d-vector of random regressors z, independent of $\epsilon $ . Here, “high-dimensional” means that the number d of available explanatory variables is much larger than the number n of observations. We consider simple linear submodels where y is regressed on a set of p regressors given by $x = M'z$ , for some $d \times p$ matrix M of full rank $p < n$ . The corresponding simple model, that is, $y=\alpha +\beta ' x + e$ , is usually justified by imposing appropriate restrictions on the unknown parameter $\theta $ in the overall model; otherwise, this simple model can be grossly misspecified in the sense that relevant variables may have been omitted. In this paper, we establish asymptotic validity of the standard F-test on the surrogate parameter $\beta $ , in an appropriate sense, even when the simple model is misspecified, that is, without any restrictions on $\theta $ whatsoever and without assuming Gaussian data.

Bootstrap-based Budget Allocation for Nested Simulation

Nested simulation (also referred to as two-level simulation) finds a variety of applications such as financial risk measurement, and a central issue of nested simulation is how to allocate a finite amount of simulation budget to achieve the highest accuracy. In “Bootstrap-based Budget Allocation for Nested Simulation”, Zhang, Liu, and Wang propose a bootstrap-based rule for simulation budget allocation for nested simulation. By utilizing the asymptotically optimal inner- and outer-level sample sizes that are typically unknown, the proposed method employs bootstrap sampling on a small amount of initial samples to estimate the unknown optimal sample sizes, thus providing a reasonably good allocation rule for the main simulation. An allocation rule to ensure the asymptotic validity of confidence intervals is also given.

An Introduction to Bootstrap Theory in Time Series Econometrics

While often simple to implement in practice, application of the bootstrap in econometric modeling of economic and financial time series requires establishing validity of the bootstrap. Establishing bootstrap asymptotic validity relies on verifying often nonstandard regularity conditions. In particular, bootstrap versions of classic convergence in probability and distribution, and hence of laws of large numbers and central limit theorems, are critical ingredients. Crucially, these depend on the type of bootstrap applied (e.g., wild or independently and identically distributed (i.i.d.) bootstrap) and on the underlying econometric model and data. Regularity conditions and their implications for possible improvements in terms of (empirical) size and power for bootstrap-based testing differ from standard asymptotic testing, which can be illustrated by simulations.

Monte Carlo Inference on Two-Sided Matching Models

This paper considers two-sided matching models with nontransferable utilities, with one side having homogeneous preferences over the other side. When one observes only one or several large matchings, despite the large number of agents involved, asymptotic inference is difficult because the observed matching involves the preferences of all the agents on both sides in a complex way, and creates a complicated form of cross-sectional dependence across observed matches. When we assume that the observed matching is a consequence of a stable matching mechanism with homogeneous preferences on one side, and the preferences are drawn from a parametric distribution conditional on observables, the large observed matching follows a parametric distribution. This paper shows in such a situation how the method of Monte Carlo inference can be a viable option. Being a finite sample inference method, it does not require independence or local dependence among the observations which are often used to obtain asymptotic validity. Results from a Monte Carlo simulation study are presented and discussed.

BOOTSTRAPPING PRE-AVERAGED REALIZED VOLATILITY UNDER MARKET MICROSTRUCTURE NOISE

The main contribution of this paper is to propose a bootstrap method for inference on integrated volatility based on the pre-averaging approach, where the pre-averaging is done over all possible overlapping blocks of consecutive observations. The overlapping nature of the pre-averaged returns implies that the leading martingale part in the pre-averaged returns arekn-dependent withkngrowing slowly with the sample sizen. This motivates the application of a blockwise bootstrap method. We show that the “blocks of blocks” bootstrap method is not valid when volatility is time-varying. The failure of the blocks of blocks bootstrap is due to the heterogeneity of the squared pre-averaged returns when volatility is stochastic. To preserve both the dependence and the heterogeneity of squared pre-averaged returns, we propose a novel procedure that combines the wild bootstrap with the blocks of blocks bootstrap. We provide a proof of the first order asymptotic validity of this method for percentile and percentile-tintervals. Our Monte Carlo simulations show that the wild blocks of blocks bootstrap improves the finite sample properties of the existing first order asymptotic theory. We use empirical work to illustrate its use in practice.