We obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes. A precise order magnitude is derived spectral radius sample matrices. also consider thresholded estimator that can better characterize sparsity if the true sparse. As our main tool, we implement Toeplitz [Math. Ann. 70 (1911) 351–376] idea and relate eigenvalues matrices to densities or Fourier transforms covariances. develop large deviation result quadratic forms processes using m-dependence...

Summary Statistical inferences for sample correlation matrices are important in high dimensional data analysis. Motivated by this, the paper establishes a new central limit theorem linear spectral statistic of case where dimension p and size n comparable. This result is independent interest large random-matrix theory. We also further investigate vector whose elements have special correlated structure corresponding developed. Meanwhile, we apply to an independence test random variables, then...

Abstract Network data are prevalent in many contemporary big applications which a common interest is to unveil important latent links between different pairs of nodes. Yet simple fundamental question how precisely quantify the statistical uncertainty associated with identification still remains largely unexplored. In this paper, we propose method inference on membership profiles large networks (SIMPLE) setting degree-corrected mixed model, where null hypothesis assumes that pair nodes share...

We establish Nagaev and Rosenthal-type inequalities for dependent ran- dom variables. The imposed dependence conditions, which are expressed in terms of functional measures, directly related to the physical mechanisms underlying processes easy work with. Our results applied nonlinear time series kernel density estimates linear processes.

We study the asymptotic distributions of spiked eigenvalues and largest nonspiked eigenvalue sample covariance matrix under a general model with divergent eigenvalues, while other are bounded but otherwise arbitrary. The limiting normal distribution for is established. It has distinct features that mean relies on not only population spikes also nonspikes variance in depends eigenvectors. In addition, Tracy–Widom law obtained. Estimation number convergence leading eigenvectors considered....

Let ${\mathbf{A}}_{p}=\frac{{\mathbf{Y}}{\mathbf{Y}}^{*}}{m}$ and ${\mathbf{B}}_{p}=\frac{{\mathbf{X}}{\mathbf{X}}^{*}}{n}$ be two independent random matrices where ${\mathbf{X}}=(X_{ij})_{p\times n}$ ${\mathbf{Y}}=(Y_{ij})_{p\times m}$ respectively consist of real (or complex) variables with $\mathbb{E}X_{ij}=\mathbb{E}Y_{ij}=0$, $\mathbb{E}|X_{ij}|^{2}=\mathbb{E}|Y_{ij}|^{2}=1$. Denote by $\lambda_{1}$ the largest root determinantal equation...

Motivated by the problem of testing tetrad constraints in factor analysis, we study large-sample distribution Wald statistics at parameter points which gradient tested constraint vanishes. When based on an asymptotically normal estimator, statistic converges to a rational function random vector. The is determined homogeneous polynomial and covariance matrix. For quadratic forms bivariate monomials arbitrary degree, show unexpected relationships chi-square distributions that explain...

The paper presents a systematic theory for asymptotic inferences based on autocovariances of stationary processes.We consider nonparametric tests se rial correlations using the maximum (or C°°) and quadratic £?) deviations sample autocovariances.For these cases, with proper centering rescaling, distributions are Gumbel Gaussian, respec tively.To establish such an theory, as byproducts, we develop normal comparison principle propose sufficient condition summability joint cumulants adapt...

Characterizing the asymptotic distributions of eigenvectors for large random matrices poses important challenges yet can provide useful insights into a range statistical applications. To this end, in paper we introduce general framework theory (ATE) spiked with diverging spikes and heterogeneous variances, establish properties eigenvalues scenario generalized Wigner matrix noise. Under some mild regularity conditions, expansions show that they are asymptotically normal after normalization....

Determining the precise rank is an important problem in many large-scale applications with matrix data exploiting low-rank plus noise models. In this paper, we suggest a universal approach to inference via residual subsampling (RIRS) for testing and estimating wide family of models, including popularly used network models such as degree corrected mixed membership model special case. Our procedure constructs test statistic entries after extracting spiked components. The converges distribution...

Let $\mathbf{Z}_{M_{1}\times N}=\mathbf{T}^{\frac{1}{2}}\mathbf{X}$ where $(\mathbf{T}^{\frac{1}{2}})^{2}=\mathbf{T}$ is a positive definite matrix and $\mathbf{X}$ consists of independent random variables with mean zero variance one. This paper proposes unified model \[\mathbf{\Omega}=(\mathbf{Z}\mathbf{U}_{2}\mathbf{U}_{2}^{T}\mathbf{Z}^{T})^{-1}\mathbf{Z}\mathbf{U}_{1}\mathbf{U}_{1}^{T}\mathbf{Z}^{T},\] $\mathbf{U}_{1}$ $\mathbf{U}_{2}$ are isometric dimensions $N\times N_{1}$...

We introduce a real-time measure of conditional biases in firms' earnings forecasts. The is defined as the difference between analysts' expectations and statistically optimal unbiased machine-learning benchmark. Analysts' are, on average, biased upwards, bias increases forecast horizon. These are associated with negative cross-sectional return predictability, short legs many anomalies contain firms excessively optimistic earnings. Further, managers companies greatest upward-biased forecasts...

Let $B=(b_{jk})_{p\times n}=(Y_{1},Y_{2},\ldots,Y_{n})$ be a collection of independent real random variables with mean zero and variance one. Suppose that $\Sigma$ is $p$ by population covariance matrix. $X_{k}=\Sigma^{1/2}Y_{k}$ for $k=1,2,\ldots,n$ $\hat{\Sigma}_{1}=\frac{1}{n}\sum_{k=1}^{n}X_{k}X_{k}^{T}$. Under the moment condition $\mathop{\mathrm{sup}}_{p,n}\max_{1\leq j\leq p,1\leq k\leq n}\mathbb{E}b_{jk}^{4}<\infty$, we prove log determinant sample matrix $\hat{\Sigma}_{1}$...

We study the asymptotic distributions of spiked eigenvalues and largest nonspiked eigenvalue sample covariance matrix under a general model with divergent eigenvalues, while other are bounded but otherwise arbitrary. The limiting normal distribution for is established. It has distinct features that mean relies on not only population spikes also nonspikes variance in depends eigenvectors. In addition, Tracy-Widom law obtained. Estimation number convergence leading eigenvectors considered....

Using survey forecasts, we find that subjective expectations of earnings growth and price account for over 90% cross-sectional variation in stock price-earnings ratios. This is largely due to expected growth, which more volatile correlated with P/E ratios than growth. Due forecasters consistently overestimating the high firms, errors 36-43% all In contrast previous findings aggregate market, cross-section correctly expect lower stocks but understate magnitude relationship. 22 anomaly...

Characterizing the asymptotic distributions of eigenvectors for large random matrices poses important challenges yet can provide useful insights into a range statistical applications. To this end, in paper we introduce general framework theory (ATE) spiked with diverging spikes and heterogeneous variances, establish properties eigenvalues scenario generalized Wigner matrix noise. Under some mild regularity conditions, expansions show that they are asymptotically normal after normalization....

Contemporary time series analysis has seen more and tensor type data, from many fields. For example, stocks can be grouped according to Size, Book-to-Market ratio, Operating Profitability, leading a 3-way observation at each month. We propose an autoregressive model for the tensor-valued series, with terms depending on multi-linear coefficient matrices. Comparing traditional approach of vectoring observations then applying vector model, preserves structure admits corresponding...