Moment convergence in regularized estimation under multiple and mixed-rates asymptotics

Masuda, H.; Shimizu, Yusuke

doi:10.3103/s1066530717020016

Cited by 26 publications

(13 citation statements)

References 35 publications

(73 reference statements)

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“…Under this approximation, we show that our estimators are consistent but might have biases in the asymptotic distribution depending on the relative rate of convergence of N and T . We apply the theory of M-estimators (e.g., Newey and McFadden, 1994), and use well-established results to handle the following non-standard features of our problem: (i) the estimators of θ, φ and α N converge at different rates (e.g., Radchenko, 2008;Cheng and Shang, 2015;Masuda and Shimizu, 2017); and (ii) additional conditions are required on the relative growth rate of N and T (e.g., Hahn and Newey, 2004;Fernández-Val, 2005;Newey, 2007).…”

Section: Inferencementioning

confidence: 99%

Parametric Modeling of Quantile Regression Coefficient Functions With Longitudinal Data

Frumento

Bottai

Fernández‐Val

2021

Journal of the American Statistical Association

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In ordinary quantile regression, quantiles of different order are estimated one at a time. An alternative approach, which is referred to as quantile regression coefficients modeling (qrcm), is to model quantile regression coefficients as parametric functions of the order of the quantile. In this paper, we describe how the qrcm paradigm can be applied to longitudinal data. We introduce a two-level quantile function, in which two different quantile regression models are used to describe the (conditional) distribution of the within-subject response and that of the individual effects. We propose a novel type of penalized fixed-effects estimator, and discuss its advantages over standard methods based on ℓ 1 and ℓ 2 penalization. We provide model identifiability conditions, derive asymptotic properties, describe goodness-of-fit measures and model selection criteria, present simulation results, and discuss an application. The proposed method has been implemented in the R package qrcm.

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Section: Inferencementioning

confidence: 99%

Parametric Modeling of Quantile Regression Coefficient Functions With Longitudinal Data

Frumento

Bottai

Fernández‐Val

2021

Journal of the American Statistical Association

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“…The matrix notation repeats S i s twice for the quadratic form, thrice for the cubic form, and so on. This notation was introduced by [52] and already adopted by many papers, e.g., [45], [48], [53], [31], [23], [32], [13], [37], [36], [35], just to name a few.…”

Section: Adaptive Estimation Of θmentioning

confidence: 99%

Adaptive estimation for degenerate diffusion processes

Gloter

Yoshida

2021

Electron. J. Statist.

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We discuss parametric estimation of a degenerate diffusion system from time-discrete observations. The first component of the degenerate diffusion system has a parameter θ 1 in a non-degenerate diffusion coefficient and a parameter θ 2 in the drift term. The second component has a drift term parameterized by θ 3 and no diffusion term. Asymptotic normality is proved in two different situations for an adaptive estimator for θ 3 with some initial estimators for (θ 1 , θ 2 ), and an adaptive one-step estimator for (θ 1 , θ 2 , θ 3 ) with some initial estimators for them. Our estimators incorporate information of the increments of both components. Thanks to this construction, the asymptotic variance of the estimators for θ 1 is smaller than the standard one based only on the first component. The convergence of the estimators for θ 3 is much faster than the other parameters. The resulting asymptotic variance is smaller than that of an estimator only using the increments of the second component.

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“…We shall mention that penalized estimation has recently become an active research topic in the setting of asymptotic statistics for stochastic processes. For example, penalized quasi-likelihood estimation for stochastic processes has been developed in the fixed-dimensional setting by [ 27 , 28 , 29 , 30 ], while estimation for linearly parameterized high-dimensional diffusion models has been studied in [ 31 , 32 ]. Compared to these articles, this paper is novel in the respect that we develop an asymptotic distribution theory in a high-dimensional setting .…”

Section: Introductionmentioning

confidence: 99%

De-Biased Graphical Lasso for High-Frequency Data

Koike

2020

Entropy

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This paper develops a new statistical inference theory for the precision matrix of high-frequency data in a high-dimensional setting. The focus is not only on point estimation but also on interval estimation and hypothesis testing for entries of the precision matrix. To accomplish this purpose, we establish an abstract asymptotic theory for the weighted graphical Lasso and its de-biased version without specifying the form of the initial covariance estimator. We also extend the scope of the theory to the case that a known factor structure is present in the data. The developed theory is applied to the concrete situation where we can use the realized covariance matrix as the initial covariance estimator, and we obtain a feasible asymptotic distribution theory to construct (simultaneous) confidence intervals and (multiple) testing procedures for entries of the precision matrix.[19] and subsequently built up by, among others, [2,17,20]. Other common methods used in i.i.d. settings have also been investigated in the literature of high-frequency financial econometrics. Hautsch et al. [25] and Morimoto & Nagata [41] formally apply eigenvalue regularization methods based on random matrix theory to high-frequency data. Lam et al. [37] accommodate the non-linear shrinkage estimator of [39] to a high-frequency data setting with the help of the spectral distribution theory for the realized covariance matrix developed in [58]. Brownlees et al. [8] employ the ℓ 1 -penalized Gaussian MLE, which is known as the graphical Lasso, to estimate the precision matrix (the inverse of the covariance matrix) of high-frequency data. The latter approach is closely related to the methodology we will focus on.Despite the recent advances in this topic as above, most studies in this area focus only on point estimation of covariance and precision matrices, and there are little work about interval estimation and hypothesis testing for these objects. A few exceptions are [36,44] and [34]. The first two articles are concerned with continuous-time factor models: Kong & Liu [36] propose a test for the constancy of the factor loading matrix, while Pelger [44] assumes constant loadings and develops an asymptotic distribution theory to make inference for the factors and loadings. Meanwhile, Koike [34] establishes a high-dimensional central limit theorem for the realized covariance matrix which allows us to construct simultaneous confidence regions or carry out multiple testing for entries of the high-dimensional covariance matrix of high-frequency data. The aim of this study is to develop such a statistical inference theory for the precision matrix of high-frequency data. This is naturally motivated by the fact that the precision matrix of asset returns plays an important role in mean-variance analysis of portfolio allocation (see e.g. [16, Chapter 5]). We accomplish this purpose by imposing a sparsity assumption on the precision matrix. Such an assumption has a clear interpretation in connection with Gaussian graphical models: For a Gaussian random v...

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Moment convergence in regularized estimation under multiple and mixed-rates asymptotics

Cited by 26 publications

References 35 publications

Parametric Modeling of Quantile Regression Coefficient Functions With Longitudinal Data

Parametric Modeling of Quantile Regression Coefficient Functions With Longitudinal Data

Adaptive estimation for degenerate diffusion processes

De-Biased Graphical Lasso for High-Frequency Data

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