D-trace estimation of a precision matrix using adaptive Lasso penalties

Abstract In this paper, we propose a new approach to model structural change in cointegrating regressions using penalized regression techniques. First, we consider a setting with known breakpoint candidates and show that a modified adaptive lasso estimator can consistently estimate structural breaks in the intercept and slope coefficient of a cointegrating regression. Second, we extend our approach to a diverging number of breakpoint candidates and provide simulation evidence that timing and magnitude of structural breaks are consistently estimated. Third, we use the adaptive lasso estimation to design new tests for cointegration in the presence of multiple structural breaks, derive the asymptotic distribution of our test statistics and show that the proposed tests have power against the null of no cointegration. Finally, we use our new methodology to study the effects of structural breaks on the long-run PPP relationship.

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On Randomized Trace Estimates for Indefinite Matrices with an Application to Determinants

Foundations of Computational Mathematics ◽

10.1007/s10208-021-09525-9 ◽

2021 ◽

Author(s):

Alice Cortinovis ◽

Daniel Kressner

Keyword(s):

Large Scale ◽

Gaussian Process Regression ◽

Likelihood Estimation ◽

Random Vectors ◽

Symmetric Positive Definite ◽

Matrix Logarithm ◽

The Matrix ◽

Trace Estimation ◽

Scale Matrix ◽

Existing Result

AbstractRandomized trace estimation is a popular and well-studied technique that approximates the trace of a large-scale matrix B by computing the average of $$x^T Bx$$ x T B x for many samples of a random vector X. Often, B is symmetric positive definite (SPD) but a number of applications give rise to indefinite B. Most notably, this is the case for log-determinant estimation, a task that features prominently in statistical learning, for instance in maximum likelihood estimation for Gaussian process regression. The analysis of randomized trace estimates, including tail bounds, has mostly focused on the SPD case. In this work, we derive new tail bounds for randomized trace estimates applied to indefinite B with Rademacher or Gaussian random vectors. These bounds significantly improve existing results for indefinite B, reducing the number of required samples by a factor n or even more, where n is the size of B. Even for an SPD matrix, our work improves an existing result by Roosta-Khorasani and Ascher (Found Comput Math, 15(5):1187–1212, 2015) for Rademacher vectors. This work also analyzes the combination of randomized trace estimates with the Lanczos method for approximating the trace of f(B). Particular attention is paid to the matrix logarithm, which is needed for log-determinant estimation. We improve and extend an existing result, to not only cover Rademacher but also Gaussian random vectors.

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Resolving the ambiguity of random‐effects models with singular precision matrix

Statistica Neerlandica ◽

10.1111/stan.12244 ◽

2021 ◽

Author(s):

Woojoo Lee ◽

Hans‐Peter Piepho ◽

Youngjo Lee

Keyword(s):

Random Effects ◽

Precision Matrix ◽

Random Effects Models

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Penalized Averaging of Parametric and Non-Parametric Quantile Forecasts

Journal of Time Series Econometrics ◽

10.1515/jtse-2019-0021 ◽

2019 ◽

Vol 0 (0) ◽

Author(s):

Jan G. De Gooijer ◽

Dawit Zerom

Keyword(s):

Risk Premium ◽

Empirical Studies ◽

Forecast Accuracy ◽

Equity Premium ◽

Adaptive Lasso ◽

Large Set ◽

Usual Practice ◽

Conditional Quantile ◽

Equity Risk ◽

Non Parametric

Abstract We propose a hybrid penalized averaging for combining parametric and non-parametric quantile forecasts when faced with a large number of predictors. This approach goes beyond the usual practice of combining conditional mean forecasts from parametric time series models with only a few predictors. The hybrid methodology adopts the adaptive LASSO regularization to simultaneously reduce predictor dimension and obtain quantile forecasts. Several recent empirical studies have considered a large set of macroeconomic predictors and technical indicators with the goal of forecasting the S&P 500 equity risk premium. To illustrate the merit of the proposed approach, we extend the mean-based equity premium forecasting into the conditional quantile context. The application offers three main findings. First, combining parametric and non-parametric approaches adds quantile forecast accuracy over and above the constituent methods. Second, a handful of macroeconomic predictors are found to have systematic forecasting power. Third, different predictors are identified as important when considering lower, central and upper quantiles of the equity premium distribution.

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Factors Affecting Salt Reduction Measure Adoption among Chinese Residents

International Journal of Environmental Research and Public Health ◽

10.3390/ijerph18020445 ◽

2021 ◽

Vol 18 (2) ◽

pp. 445

Author(s):

Zeying Huang ◽

Di Zeng

Keyword(s):

Logistic Regression ◽

Food Intake ◽

Nutrition Education ◽

Online Survey ◽

Adaptive Lasso ◽

Stepwise Logistic Regression ◽

Salt Reduction ◽

Salt Restriction ◽

Salt Diet ◽

Factors Affecting

China has the highest mortality rate caused by diseases and conditions associated with its high-salt diet. Since 2016, China has initiated a national salt reduction campaign that aims at promoting the usage of salt information on food labels and salt-restriction spoons and reducing condiment and pickled food intake. However, factors affecting individuals’ decisions to adopt these salt reduction measures remain largely unknown. By comparing the performances of logistic regression, stepwise logistic regression, lasso logistic regression and adaptive lasso logistic regression, this study aims to fill this gap by analyzing the adoption behaviour of 1610 individuals from a nationally representative online survey. It was found that the practices were far from adopted and only 26.40%, 22.98%, 33.54% and 37.20% reported the adoption of labelled salt information, salt-restriction spoons, reduced condiment use in home cooking and reduced pickled food intake, respectively. Knowledge on salt, the perceived benefits of salt reduction, participation in nutrition education and training programs on sodium reduction were positively associated with using salt information labels. Adoption of the other measures was largely explained by people’s awareness of hypertension risks and taste preferences. It is therefore recommended that policy interventions should enhance Chinese individuals’ knowledge of salt, raise the awareness of the benefits associated with a low-salt diet and the risks associated with consuming excessive salt and reshape their taste choices.

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