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The non-null distribution of the sample correlation coefficient under bivariate normality is derived when each of the associated two sample variances is subject to stripe truncation including usual single and double truncation as special cases. The probability density function is obtained using series expressions as in the untruncated case with new definitions of weighted hypergeometric functions. Formulas of the moments of arbitrary orders are given using the weighted hypergeometric functions. It is shown that the null joint distribution of the sample correlation coefficients under multivariate untruncated normality holds also in the variance-truncated cases. Some numerical illustrations are shown.

The popularity of modern portfolio theory has decreased among practitioners because of its unfavorable out-of-sample performance. Estimation risk tends to affect the optimal weight calculation noticeably, especially when a large number of assets are considered. To overcome these issues, many methods have been proposed in recent years, but only a few address practically relevant questions related to portfolio allocation. This study therefore uses different covariance estimation techniques, combines them with sparse model approaches, and includes a turnover constraint that induces stability. We use two datasets of the S&P 500 to create a realistic data foundation for our empirical study. We discover that it is possible to maintain the low-risk profile of efficient estimation methods while automatically selecting only a subset of assets and further inducing low portfolio turnover. Moreover, we find that simply using LASSO is insufficient to lower turnover when the model’s tuning parameter can change over time.

In this paper, we study the limiting behavior of eigenvalues of the variance-covariance matrix of a random sample from a multivariate subordinator heavy-tailed Lévy process, and use large deviations of a heavy-tailed stochastic process to derive the limit distributions of its components. We confine our study to multivariate Lévy processes with regularly varying random components and possibly different indices of regularity. Assuming that the product of increments of the marginal components are also regularly varying random variables, we show that the product of two dependent regularly varying Log-Gamma random variables with integer-valued shape parameters is also a regularly varying random variable with index depending on the correlation between the original variables. This result enables us to derive the limiting tail behavior of sample variance-covariance matrix from a multivariate Lévy process having Log-Gamma components with integer-valued shape parameters and different indices of regularity.

In this study, I used standard statistical tools (such as the various forms of the two-sample Allan variance) to characterize the clocks in computers, and I show how the results of this study are used to design algorithms to synchronize the computer clocks. These synchronization algorithms can be used to synchronize the time of a computer to a local reference clock or to a remote server. The algorithms by themselves are not intended to be a simple replacement for software that implements the Network Time Protocol (NTP) or any other similar application. Instead, they describe the statistical principles that should be used to design an algorithm to synchronize any computer clock by using data from any external reference received in any format. These algorithms have been used to synchronize the clocks of the computers that support the Internet Time Service operated by the National Institute of Standards and Technology (NIST), and I illustrate the performance of the algorithm with real-time data from these servers. In addition to presenting the design principles of the algorithm, I illustrate the principles with two specific examples: synchronizing a computer clock to a local reference signal, and the design of a synchronization process that is based on time-difference data received from a remote server over the public Internet. The message exchange between the local system and the remote server in this configuration is realized in NTP format, but that is not a fundamental requirement.

Purpose This paper aims to propose a hybrid method based on polynomial fitting bias self-compensation, grey forward-backward linear prediction (GFBLP) and moving average filter (MAF) for error compensation in micro-electromechanical system gyroscope signal especially under motion state. Design/methodology/approach The error compensation can be divided into two processes: bias correction and noise reduction. A polynomial drift angle fitting algorithm is used to correct bias before denoising processing. For noise reduction, operation can be taken in two stages: detection and processing. First, sample variances are used to judge motion state. According to the detection results, algorithmic system switches between grey GFBLP and MAF to ensure fast convergence rate and small steady-state error. Findings Experimental results show that the proposed method can correct bias effectively for practical gyroscope signal, and can eliminate noise effectively for both practical gyroscope signal and synthetic signal, which indicates the effectiveness of the proposed method. Originality/value Bias correction and noise reduction are considerations. Noise contained in practical or synthetic signal can be reduced rapidly and effectively, which benefits from the new idea of combination grey GFBLP, MAF and sample variances. And most importantly, it is applicable for signal denoising under arbitrary motion state condition, which is different from other methods where the convergence performance is seldom analyzed.

We present an image analysis based automatic road crack detection method for conducting smooth driving on non-smooth road surfaces. In the new proposal, first the road surface areas which include cracks are extracted as crack images by analyzing the color variance on norm. Then cracks are extracted from those areas by introducing a method on discriminant analysis. According to experiments using the images of different road surfaces, the new proposal showed better performances than the conventional approaches.

In recent work, Wang et al introduced the “Sum of Single Effects” ( SuSiE ) model, and showed that it provides a simple and efficient approach to fine-mapping genetic variants from individual-level data. Here we present new methods for fitting the SuSiE model to summary data, for example to single-SNP z -scores from an association study and linkage disequilibrium (LD) values estimated from a suitable reference panel. To develop these new methods, we first describe a simple, generic strategy for extending any individual-level data method to deal with summary data. The key idea is to replace the usual regression likelihood with an analogous likelihood based on summary data. We show that existing fine-mapping methods such as FINEMAP and CAVIAR also (implicitly) use this strategy, but in different ways, and so this provides a common framework for understanding different methods for fine-mapping. We investigate other common practical issues in fine-mapping with summary data, including problems caused by inconsistencies between the z -scores and LD estimates, and we develop diagnostics to identify these inconsistencies. We also present a new refinement procedure that improves model fits in some data sets, and hence improves overall reliability of the SuSiE fine-mapping results. Detailed evaluations of fine-mapping methods in a range of simulated data sets show that SuSiE applied to summary data is competitive, in both speed and accuracy, with the best available fine-mapping methods for summary data.

Exponentially weighted moving average (EWMA) control charts are regarded as one of the most convenient tools in detecting small process shifts. Although EWMA control charts have been extensively used to monitor the mean of quality characteristics, there are few studies concentrating on the monitoring of process variability by using weighted moving control charts. In this paper, we propose an exponentially weighted moving sample variance (EWMSV) control chart for monitoring process variability when the sample size is equal to 1. The results are compared numerically with other similar methods using the average run length (ARL). Through an example, the practical considerations are presented to implement EWMSV control charts.

Meta-analyses frequently include studies with small sample sizes. Researchers usually fail to account for sampling error in the reported within-study variances; they model the observed study-specific effect sizes with the within-study variances and treat these sample variances as if they were the true variances. However, this sampling error may be influential when sample sizes are small. This article illustrates that the sampling error may lead to substantial bias in meta-analysis results. We conducted extensive simulation studies to assess the bias caused by sampling error. Meta-analyses with continuous and binary outcomes were simulated with various ranges of sample size and extents of heterogeneity. We evaluated the bias and the confidence interval coverage for five commonly-used effect sizes (i.e., the mean difference, standardized mean difference, odds ratio, risk ratio, and risk difference). Sampling error did not cause noticeable bias when the effect size was the mean difference, but the standardized mean difference, odds ratio, risk ratio, and risk difference suffered from this bias to different extents. The bias in the estimated overall odds ratio and risk ratio was noticeable even when each individual study had more than 50 samples under some settings. Also, Hedges' g, which is a bias-corrected estimate of the standardized mean difference within studies, might lead to larger bias than Cohen's d in meta-analysis results. Cautions are needed to perform meta-analyses with small sample sizes. The reported within-study variances may not be simply treated as the true variances, and their sampling error should be fully considered in such meta-analyses.