Annals of the Institute of Statistical Mathematics最新文献

In this study, we propose a model averaging approach to estimating the conditional quantiles based on a set of semiparametric varying coefficient models. Different from existing literature on the subject, we consider a particular form for all candidates, where there is only one varying coefficient in each sub-model, and all the candidates under investigation may be misspecified. We propose a weight choice criterion based on a leave-more-out cross-validation objective function. Moreover, the resulting averaging estimator is more robust against model misspecification due to the weighted coefficients that adjust the relative importance of the varying and constant coefficients for the same predictors. We prove out statistical properties for each sub-model and asymptotic optimality of the weight selection method. Simulation studies show that the proposed procedure has satisfactory prediction accuracy. An analysis of a skin cutaneous melanoma data further supports the merits of the proposed approach.

An (alpha)-slash distribution built upon a random variable X is a heavy tailed distribution corresponding to (Y=X/U^{1/alpha }), where U is standard uniform random variable, independent of X. We point out and explore a connection between (alpha)-slash distributions, which are gaining popularity in statistical practice, and generalized convolutions, which come up in the probability theory as generalizations of the standard concept of the convolution of probability measures and allow for the operation between the measures to be random itself. The stochastic interpretation of Kendall convolution discussed in this work brings this theoretical concept closer to statistical practice, and leads to new results for (alpha)-slash distributions connected with extremes. In particular, we show that the maximum of independent random variables with (alpha)-slash distributions is also a random variable with an (alpha)-slash distribution. Our theoretical results are illustrated by several examples involving standard and novel probability distributions and extremes.

In this paper, we estimate the high-dimensional precision matrix under the weak sparsity condition where many entries are nearly zero. We revisit the sparse column-wise inverse operator estimator and derive its general error bounds under the weak sparsity condition. A unified framework is established to deal with various cases including the heavy-tailed data, the non-paranormal data, and the matrix variate data. These new methods can achieve the same convergence rates as the existing methods and can be implemented efficiently.

This paper is about the one-step ahead prediction of the future of observations drawn from an infinite-order autoregressive AR((infty )) process. It aims to design penalties (fully data driven) ensuring that the selected model verifies the efficiency property but in the non-asymptotic framework. We show that the excess risk of the selected estimator enjoys the best bias-variance trade-off over the considered collection. To achieve these results, we needed to overcome the dependence difficulties by following a classical approach which consists in restricting to a set where the empirical covariance matrix is equivalent to the theoretical one. We show that this event happens with probability larger than (1-c_0/n^2) with (c_0>0). The proposed data-driven criteria are based on the minimization of the penalized criterion akin to the Mallows’s (C_p).

In this paper, we consider possibly misspecified stochastic differential equation models driven by Lévy processes. Regardless of whether the driving noise is Gaussian or not, Gaussian quasi-likelihood estimator can estimate unknown parameters in the drift and scale coefficients. However, in the misspecified case, the asymptotic distribution of the estimator varies by the correction of the misspecification bias, and consistent estimators for the asymptotic variance proposed in the correctly specified case may lose theoretical validity. As one of its solutions, we propose a bootstrap method for approximating the asymptotic distribution. We show that our bootstrap method theoretically works in both correctly specified case and misspecified case without assuming the precise distribution of the driving noise.

In this paper, we propose tests for the existence of random effects and interactions for two-way models with dependent errors. We prove that the proposed tests are asymptotically distribution-free which have asymptotically size ({{tau }}) and are consistent. We elucidate the nontrivial power under the local alternative when a sample size tends to infinity and the number of groups is fixed. A simulation study is performed to investigate the finite-sample performance of the proposed tests. In the real data analysis, we apply our tests to the daily log-returns of 24 stock prices from six countries and four sectors. We find that there is no strong evidence to support the existence of substantial differences in the log-return across countries, nor to the existence of interactions between countries and sectors. However, there exists random effect differences in the daily log-return series across different sectors.

In recent years, many methodologies for distributed data have been developed. However, there are two problems. First, most of these methods require the data to be randomly and uniformly distributed across different machines. Second, the methods are mainly not robust. To solve these problems, we propose a distributed pilot modal regression estimator, which achieves robustness and can adapt when the data are stored nonrandomly. First, we collect a random pilot sample from different machines; then, we approximate the global MR objective function by a communication-efficient surrogate that can be efficiently evaluated by the pilot sample and the local gradients. The final estimator is obtained by minimizing the surrogate function in the master machine, while the other machines only need to calculate their gradients. Theoretical results show the new estimator is asymptotically efficient as the global MR estimator. Simulation studies illustrate the utility of the proposed approach.

Multivariate nonresponse is often encountered in complex survey sampling, and simply ignoring it leads to erroneous inference. In this paper, we propose a new matrix completion method for complex survey sampling. Different from existing works either conducting row-wise or column-wise imputation, the data matrix is treated as a whole which allows for exploiting both row and column patterns simultaneously. A column-space-decomposition model is adopted incorporating a low-rank structured matrix for the finite population with easy-to-obtain demographic information as covariates. Besides, we propose a computationally efficient projection strategy to identify the model parameters under complex survey sampling. Then, an augmented inverse probability weighting estimator is used to estimate the parameter of interest, and the corresponding asymptotic upper bound of the estimation error is derived. Simulation studies show that the proposed estimator has a smaller mean squared error than other competitors, and the corresponding variance estimator performs well. The proposed method is applied to assess the health status of the U.S. population.

A general class of inhomogeneous hidden semi-Markov models (IHSMMs) is proposed for modelling partially observed processes that do not necessarily behave in a stationary and memoryless manner. The key feature of the proposed model is that the sojourn times of the states in the semi-Markov chain are time-dependent, making it an inhomogeneous semi-Markov chain. Conjectured consistency of the parameter estimators is checked by simulation study using direct numerical optimization of the log-likelihood function. The proposed models are applied to a global volcanic eruption catalogue to investigate the time-dependent incompleteness of the record by introducing a particular case of IHSMMs with time-dependent shifted Poisson state durations and a renewal process as the observed process. The Akaike Information Criterion and residual analysis are used to choose the best model. The selected IHSMM provides useful insights into the completeness of the global record of volcanic eruptions, demonstrating the effectiveness of this method.

Over the last four decades, the cluster regression analysis in a finite population (FP) setup for an exponential family such as linear or binary data was done by using a two-stage cluster sample chosen from the FP but by treating the sample as though it is a single-stage cluster sample from a super-population (SP) which contains the FP as a hypothetical sample. Because the responses within a cluster in the FP are correlated, the aforementioned sample mis-specification makes the sample-based so-called GLS (generalized least square) estimators design biased and inconsistent. In this paper, we demonstrate for the exponential family data how to avoid the sampling mis-specification and accommodate the cluster correlations to obtain unbiased and consistent estimates for the FP parameters. The asymptotic normality of the regression estimators is also given for the construction of confidence intervals when needed.