JournalTOCs

Japanese Journal of Statistics and Data Science
Number of Followers: 0

Hybrid journal (It can contain Open Access articles)
ISSN (Print) 2520-8756 - ISSN (Online) 2520-8764
Published by Springer-Verlag

[2467 journals]

Optimal stable Ornstein–Uhlenbeck regression
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  Abstract: Abstract We prove asymptotically efficient inference results concerning an Ornstein–Uhlenbeck regression model driven by a non-Gaussian stable Lévy process, where the output process is observed at high frequency over a fixed period. The local asymptotics of non-ergodic type for the likelihood function is presented, followed by a way to construct an asymptotically efficient estimator through a suboptimal, yet very simple preliminary estimator.
  PubDate: 2023-03-13
Asymptotic justification of maximum likelihood estimation for the
proportional excess hazard model in analysis of cancer registry data
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  Abstract: Abstract Population-based cancer registry studies are conducted to investigate the various cancer question and have important impacts on cancer control. In order to investigate cancer prognosis from cancer registry data, it is necessary to adjust the effect of deaths from other causes, since cancer registry data include deaths from causes other than cancer. To correct for the effect of deaths from other causes, excess hazard models are often used. The concept of the excess hazard model is that the hazard function for any death in a cancer registry population is the sum of the hazard for cancer deaths, refer to the excess hazard, and the hazard for deaths from other causes. The Cox proportional hazard model for the excess hazard has been developed, and for this model, Perme et al. (Biostatistics 10:136–146, 2009) proposed the inference procedure of the regression coefficients using the techniques of the EM algorithm to compute the maximum likelihood estimator. In this article, we present the large sample properties for the maximum likelihood estimator. We introduce a consistent estimator of the variance for the regression coefficients based on the technique of the semiparametric theory and the consistency and the asymptotic normality of the estimator. The empirical property of variance estimator is investigated by the finite sample simulation studies. We also apply the variance estimator to cancer registry data for stomach, lung, and liver cancer patients from the Surveillance, Epidemiology, and End Results (SEER) database in U.S.
  PubDate: 2023-03-10
Asymptotically efficient estimation for diffusion processes with
nonsynchronous observations
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  Abstract: Abstract We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observations occur in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis of high-frequency data in a financial market. Constructing a quasi-likelihood function to define the estimator, we adaptively estimate the parameter for the diffusion part and the drift part. We consider the asymptotic theory when the terminal time point \(T_n\) and the observation frequency goes to infinity, and show the consistency and the asymptotic normality of the estimator. Moreover, we show local asymptotic normality for the statistical model, and asymptotic efficiency of the estimator as a consequence. To show the asymptotic properties of the maximum-likelihood-type estimator, we need to control the asymptotic behaviors of some functionals of the sampling scheme. Though it is difficult to directly control those in general, we study tractable sufficient conditions when the sampling scheme is generated by mixing processes.
  PubDate: 2023-03-10
On combining unbiased and possibly biased correlated estimators
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  Abstract: Abstract We study estimators that combine an unbiased estimator with a possibly biased correlated estimator of a mean vector. The combined estimators are shrinkage-type estimators that shrink the unbiased estimator towards the biased estimator. Conditions under which the combined estimator dominates the original unbiased estimator are given. Models studied include normal models with a known covariance structure, scale mixtures of normals, and more generally elliptically symmetric models with a known covariance structure. Elliptically symmetric models with a covariance structure known up to a multiple are also considered.
  PubDate: 2023-03-07
Diagnostic test for misspecification of a random-effect distribution using
the gradient function
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  Abstract: Abstract Mixed models typically involve unobserved random-effect variables. Misspecification for a random-effect distribution is hardly avoided and may seriously affect statistical inference. Efendi et al. (2017) proposed a test statistic based on the gradient function developed by Verbeke and Molenberghs (2013) to detect the misspecification. In some situations, however, statistical power of the test is quite low. In this paper, we first studied mathematical properties of the null distribution of the test statistic to identify a possible cause of the shortcoming and then we proposed two new test statistics using the properties. The performance of the test statistics was evaluated by simulation studies, and our proposed test statistics were found to improve the statistical power of the original test in a small or medium sample size.
  PubDate: 2023-02-28
Empirical likelihood inference for monotone index model
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  Abstract: Abstract This paper proposes an empirical likelihood inference method for monotone index models. We construct the empirical likelihood function based on a modified score function developed by Balabdaoui et al. (Scand J Stat 46:517–544, 2019), where the monotone link function is estimated by isotonic regression. It is shown that the empirical likelihood ratio statistic converges to a weighted chi-squared distribution. We suggest inference procedures based on an adjusted empirical likelihood statistic that is asymptotically pivotal, and a bootstrap calibration with recentering. A simulation study illustrates usefulness of the proposed inference methods.
  PubDate: 2023-02-25
General tests of conditional independence based on empirical processes
indexed by functions
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  Abstract: This paper focuses on nonparametric procedures for testing conditional independence between random vectors using Möbius transformation. We derive a method predicated on general empirical processes indexed by a specific class of functions. Conditional half-space and conditional empirical characteristic processes are used to demonstrate two abstract approximation theorems and their applications in real-world situations. We conclude by describing the limiting behavior of the Möbius transformation of the empirical conditional processes indexed by functions under contiguous sequences of alternatives. Our results are proved under some standard structural conditions on the Vapnik-Chervonenkis classes of functions and some mild conditions on the model. Monte Carlo simulation results indicate that the suggested statistical test for independence behaves reasonably well in finite samples.
  PubDate: 2023-02-25
Efficient parameter estimation for parabolic SPDEs based on a log-linear
model for realized volatilities
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  Abstract: Abstract We construct estimators for the parameters of a parabolic SPDE with one spatial dimension based on discrete observations of a solution in time and space on a bounded domain. We establish central limit theorems for a high-frequency asymptotic regime. The asymptotic variances are shown to be substantially smaller compared to existing estimation methods. Moreover, asymptotic confidence intervals are directly feasible. Our approach builds upon realized volatilities and their asymptotic illustration as a response of a log-linear model with spatial explanatory variable. This yields efficient estimators based on realized volatilities with optimal rates of convergence and minimal variances. We demonstrate efficiency gains compared to previous estimation methods numerically and in Monte Carlo simulations.
  PubDate: 2023-02-18
Exact variation and drift parameter estimation for the nonlinear
fractional stochastic heat equation
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  Abstract: Abstract This work concerns the statistical inference for stochastic partial differential equations. We consider the fractional stochastic heat equation driven by a nonlinear Gaussian space–time white noise and analyze its mild solution. We actually study the limit behavior of the spatial quadratic variation of its mild solution, both in the linear and nonlinear noise cases by obtaining the exact limit of this quadratic variation. We apply these results to parameter estimation. More precisely, we construct an estimator for the drift parameter of the fractional stochastic heat equation with nonlinear noise, which is defined in terms of the quadratic variation and based on the observation of the solution at a fixed time and at discrete points in space. The proofs are based on the relation between the solution to the linear fractional stochastic heat equation and the fractional Brownian motion and on a sharp analysis of the Green kernel associated with the fractional Laplacian operator.
  PubDate: 2023-02-18
On the estimation of the jump activity index in the case of random
observation times
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  Abstract: Abstract We propose a nonparametric estimator of the jump activity index \(\beta \) of a pure-jump semimartingale X driven by a \(\beta \) -stable process when the underlying observations are coming from a high-frequency setting at irregular times. The proposed estimator is based on an empirical characteristic function using rescaled increments of X, with a limit that depends in a complicated way on \(\beta \) and the distribution of the sampling scheme. Utilising an asymptotic expansion we derive a consistent estimator for \(\beta \) and prove an associated central limit theorem.
  PubDate: 2023-02-11
Fast and asymptotically efficient estimation in the Hawkes processes
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  Abstract: Abstract Fast and asymptotically efficient methods for the estimation of the parameters in self-excited counting Hawkes processes are considered. They are based on the Le Cam one-step estimation procedure. An initial guess estimator is given to estimate both the intensity baseline and the parameters of the kernel of the Hawkes process which characterize the influence of an event on the intensity. Then, the estimation is corrected by a single step of a Newton-type gradient-descent algorithm on the loglikelihood function. Asymptotic properties of the one-step estimators are studied. Monte Carlo simulations show the performance of the procedures for finite size samples in terms of computing time and efficiency. The methodology is finally used to study the claim frequency in building insurance.
  PubDate: 2023-02-01
Forecasting the housing vacancy rate in Japan using dynamic spatiotemporal
effects models
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  Abstract: Abstract This study attempts to predict and forecast the future heterogeneous increase in the vacant house ratio among prefectures in Japan using spatial panel models with unobserved dynamic spatiotemporal effects. The study formulated models with autoregressive and random-walk spatiotemporal effects, referring to the dynamic spatiotemporal effects (DSE) models. We estimate the model parameters and latent spatiotemporal effects via Markov Chain Monte Carlo algorithm. Simulation studies demonstrated the superior performance of the DSE model in terms of future prediction when spatial and temporal correlation exists. The model is then applied to the prefecturewise ratio of vacant houses to the non-rental housing stock in Japan, and the results imply existence of spatiotemporal correlations that cannot be captured by explanatory variables. Furthermore, it is revealed that the DSE models can provide better forecasting than the existing spatial panel models.
  PubDate: 2022-12-08
  DOI: 10.1007/s42081-022-00184-w
Nonparametric Bayesian volatility learning under microstructure noise
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  Abstract: Abstract In this work, we study the problem of learning the volatility under market microstructure noise. Specifically, we consider noisy discrete time observations from a stochastic differential equation and develop a novel computational method to learn the diffusion coefficient of the equation. We take a nonparametric Bayesian approach, where we a priori model the volatility function as piecewise constant. Its prior is specified via the inverse Gamma Markov chain. Sampling from the posterior is accomplished by incorporating the Forward Filtering Backward Simulation algorithm in the Gibbs sampler. Good performance of the method is demonstrated on two representative synthetic data examples. We also apply the method on a EUR/USD exchange rate dataset. Finally we present a limit result on the prior distribution.
  PubDate: 2022-12-08
  DOI: 10.1007/s42081-022-00185-9
Real world data and data science in medical research: present and future
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  Abstract: Abstract Real world data (RWD) are generating greater interest in recent times despite being not new. There are various purposes of the RWD analytics in medical research as follows: effectiveness and safety of medical treatment, epidemiology such as incidence and prevalence of disease, burden of disease, quality of life and activity of daily living, medical costs, etc. The RWD research in medicine is a mixture of digital transformation, statistics or data science, public health, and regulatory science. Most of the articles describing the RWD or real-world evidence (RWE) in medical research cover only a portion of these specializations, which might lead to an incomplete understanding of the RWD. This article summarizes the overview and challenges of the RWD analysis in medical fields from methodological perspectives. As the first step for the RWD analysis, data source of the RWD should be comprehended. The progress of the RWD is closely related to the digitization, especially of medical administrative data and medical records. Second, the selection of appropriate statistical and epidemiological methods is highly critical for an RWD analysis than those for randomized clinical trials. This is because it contains greater varieties of bias, which should be controlled by balancing the underlying risk between treatment groups. Last, the future of the RWD is discussed in terms of overcoming limited data by proxy confounders, using unstructured text data, linking of multiple databases, using the RWD or RWE for a regulatory purpose, and evaluating values and new aspects in medical research brought by the RWD.
  PubDate: 2022-12-01
  DOI: 10.1007/s42081-022-00156-0
Estimation of order restricted location/scale parameters of a general
bivariate distribution under general loss function: some unified results
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  Abstract: Abstract We consider component-wise equivariant estimation of order restricted location/scale parameters of a general bivariate distribution under quite general conditions on underlying distributions and the loss function. This paper unifies various results in the literature dealing with sufficient conditions for finding improvements over arbitrary location/scale equivariant estimators. The usefulness of these results is illustrated through various examples. A simulation study is considered to compare risk performances of various estimators under bivariate normal and independent gamma probability models. A real-life data analysis is also performed to demonstrate applicability of the derived results.
  PubDate: 2022-12-01
  DOI: 10.1007/s42081-022-00168-w
Shiga University’s endeavor to promote human resources development
for data science in Japan
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  Abstract: Abstract In 2017, Shiga University established the Faculty of Data Science, which was the first faculty in Japan specializing in data science and statistics. This paper reports the Faculty’s historical context, curricula, and collaboration with industry and other universities. The career paths of the graduates and the massive open online courses and textbooks provided by the Faculty of Data Science are also summarized.
  PubDate: 2022-12-01
  DOI: 10.1007/s42081-022-00151-5
Special feature: data science—present and future
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  PubDate: 2022-10-15
  DOI: 10.1007/s42081-022-00180-0
A method for extracting nonlinear structure based on measures of
dependence
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  Abstract: Abstract In this paper, we propose a method for extracting nonlinear structure from multi-dimensional data. In dimension reduction such as principal component analysis (PCA) and projection pursuit (PP) (Friedman in J Am Stat Assoc 82(397):249–266, 1987), we search for projection directions which maximize an index, variance (PCA) or projection indices (PP). Various measures of dependence, including MIC (Reshef et al. in Science 334(6062):1518–1524, 2011) and TIC (Reshef et al. in J Mach Learn Res 17(211):1–63, 2016), have been proposed to evaluate the strength of linear or nonlinear relationships between 2 variables. We adopt them in place of indices in dimension reduction, and extract nonlinear structures. We confirm the performance through numerical examples.
  PubDate: 2022-09-01
  DOI: 10.1007/s42081-022-00177-9
Correction to: Exploring the impact of air pollution on COVID-19 admitted
cases
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  PubDate: 2022-08-18
  DOI: 10.1007/s42081-022-00174-y
Correction to: Asymptotic properties of distance-weighted discrimination
and its bias correction for high-dimension, low-sample-size data
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  Abstract: A Correction to this paper has been published: 10.1007/s42081-021-00135-x
  PubDate: 2022-07-06
  DOI: 10.1007/s42081-022-00167-x