Further Spitzer’s law for widely orthant dependent random variables

The Spitzer’s law is obtained for the maximum partial sums of widely orthant dependent random variables under more optimal moment conditions.

Topological Entropy of Pseudo-Anosov Maps from a Typical Thurston’s Construction

In this paper, we develop a way to extract information about a random walk associated with a typical Thurston’s construction. We first observe that a typical Thurston’s construction entails a free group of rank 2. We also present a proof of the spectral theorem for random walks associated with Thurston’s construction that have finite 2nd moment with respect to the Teichmüller metric. Its general case was remarked by Dahmani and Horbez. Finally, under a hypothesis not involving moment conditions, we prove that random walks eventually become pseudo-Anosov. As an application, we first discuss a random analogy of Kojima and McShane’s estimation of the hyperbolic volume of a mapping torus with pseudo-Anosov monodromy. As another application, we discuss non-probabilistic estimations of stretch factors from Thurston’s construction and the powers for Salem numbers to become the stretch factors of pseudo-Anosovs from Thurston’s construction.

The role of institutions in private investment: panel data evidence

Purpose This study aims to examine the effects of institutions on private investment (PI) using panel data analysis, where the sample countries consist of 100 countries around the world and the time period is covering from 2007 to 2016. The system generalized method of moments (GMM) estimator, introduced by Arellano and Bond (1991) and further developed by Blundell and Bond (1998) is used to analyze the data sets. Design/methodology/approach This study uses the panel data approach to estimate the empirical model due to the panel nature of the data. In particular, due to the presence of lagged dependent variables and the ability to capture individual country-specific effects, the system GMM estimator, introduced by Arellano and Bond (1991) and further developed by Blundell and Bond (1998), is adopted to analyze the roles of institutions in PI. The system GMM is developed specifically to solve the problems of weak instruments and persistency (Blundell and Bond, 1998). Jointly, they suggest to adopt additional moment conditions where lagged difference of the dependent variable is orthogonal to the level form of the disturbances. The system GMM estimator is able to combine the moment conditions for the different models, as well as the level model, thereby (is capable of) generate consistent and efficient parameters. Due to the dynamic nature of the data, this study uses one-step and two-step system GMM to investigate the roles of institutions in PI. Findings The empirical results based on the two-step system GMM demonstrate that the quality of institutions plays an important role in stimulating PI. The finding is reinforced by the analysis of the institutional sub-components’ effects on PI. Originality/value This study is unique as its measurement of institutions is multi-dimensional (including law and order, rules and regulation, government stability, bureaucratic quality, control of corruption, socio-economic condition, etc.), and hence are more comprehensive. Second, it is different than the previous studies as its sample of countries includes both democracies and non-democracies, as well as both developed and non-developed economies in which policy implications are widely acceptable. Third, this study contributes to the policymakers especially those in the debt-ridden economies where governments are budget-tightening (limited capacity for public investment), as to which practical direction should be focused on so as to attract PI and eventually sustainable growth can take place.

IDENTIFICATION ROBUST INFERENCE FOR MOMENTS-BASED ANALYSIS OF LINEAR DYNAMIC PANEL DATA MODELS

We use identification robust tests to show that difference (Dif), level (Lev), and nonlinear (NL) moment conditions, as proposed by Arellano and Bond (1991, Review of Economic Studies 58, 277–297), Ahn and Schmidt (1995, Journal of Econometrics 68, 5–27), Arellano and Bover (1995, Journal of Econometrics 68, 29–51), and Blundell and Bond (1998, Journal of Econometrics 87, 115–143) for the linear dynamic panel data model, do not separately identify the autoregressive parameter when its true value is close to one and the variance of the initial observations is large. We prove that combinations of these moment conditions, however, do so when there are more than three time series observations. This identification then solely results from a set of, so-called, robust moment conditions. These robust moments are spanned by the combined Dif, Lev, and NL moment conditions and only depend on differenced data. We show that, when only the robust moments contain identifying information on the autoregressive parameter, the discriminatory power of the Kleibergen (2005, Econometrica 73, 1103–1124) Lagrange multiplier (KLM) test using the combined moments is identical to the largest rejection frequencies that can be obtained from solely using the robust moments. This shows that the KLM test implicitly uses the robust moments when only they contain information on the autoregressive parameter.

Ridgelized Hotelling’s T2 test on mean vectors of large dimension

In this paper, a ridgelized Hotelling’s [Formula: see text] test is developed for a hypothesis on a large-dimensional mean vector under certain moment conditions. It generalizes the main result of Chen et al. [A regularized Hotelling’s [Formula: see text] test for pathway analysis in proteomic studies, J. Am. Stat. Assoc. 106(496) (2011) 1345–1360.] by relaxing their Gaussian assumption. This is achieved by establishing an exact four-moment theorem that is a simplified version of Tao and Vu’s [Random matrices: universality of local statistics of eigenvalues, Ann. Probab. 40(3) (2012) 1285–1315] work. Simulation results demonstrate the superiority of the proposed test over the traditional Hotelling’s [Formula: see text] test and its several extensions in high-dimensional situations.

A UNIFORM BOUND ON THE OPERATOR NORM OF SUB-GAUSSIAN RANDOM MATRICES AND ITS APPLICATIONS

For an $N \times T$ random matrix $X(\beta )$ with weakly dependent uniformly sub-Gaussian entries $x_{it}(\beta )$ that may depend on a possibly infinite-dimensional parameter $\beta \in \mathbf {B}$ , we obtain a uniform bound on its operator norm of the form $\mathbb {E} \sup _{\beta \in \mathbf {B}} ||X(\beta )|| \leq CK \left (\sqrt {\max (N,T)} + \gamma _2(\mathbf {B},d_{\mathbf {B}})\right )$ , where C is an absolute constant, K controls the tail behavior of (the increments of) $x_{it}(\cdot )$ , and $\gamma _2(\mathbf {B},d_{\mathbf {B}})$ is Talagrand’s functional, a measure of multiscale complexity of the metric space $(\mathbf {B},d_{\mathbf {B}})$ . We illustrate how this result may be used for estimation that seeks to minimize the operator norm of moment conditions as well as for estimation of the maximal number of factors with functional data.

On Markov Moment Problem and Related Results

We prove new results and complete our recently published theorems on the vector-valued Markov moment problem, by means of polynomial approximation on unbounded subsets, also applying an extension of the positive linear operators’ result. The domain is the Banach lattice of continuous real-valued functions on a compact subset or an space, where is a positive moment determinate measure on a closed unbounded set. The existence and uniqueness of the operator solution are proved. Our solutions satisfy the interpolation moment conditions and are between two given linear operators on the positive cone of the domain space. The norm controlling of the solution is emphasized. The most part of the results are stated and proved in terms of quadratic forms. This type of result represents the first aim of the paper. Secondly, we construct a polynomial solution for a truncated multidimensional moment problem.