52,294 research outputs found
Equilibrium states of the pressure function for products of matrices
Let be a non-trivial family of complex
matrices, in the sense that for any , there exists such that . Let be the pressure function of . We show
that for each , there are at most ergodic -equilibrium states of
, and each of them satisfies certain Gibbs property.Comment: 12 pages. To appear in DCD
The Return of the Repressed: three examples of how Chinese identity is being reconsolidated for the modern world
After setting the scene for an examination of the changes in culture and self-perception in China today, the authors explore three areas of activity which can be interpreted as illustrating these changes: (1) the current treatment of Confucius, as compared to the recent past; (2) the enthusiasm for the Chinese canon, which has developed from a grassroots movement into government policy; and (3) the way in which the presentation and content of public slogans have changed to, apparently, reflect the substitution of Communist nostrums for Confucian mores. In the first and second cases, the authors suggest that the authorities are acceding to the aspirations and prejudices of the people; rather than leading, they are following, and this has the effect of reinforcing the trend. The third—the gradual abandonment of the use of Marxist shibboleths in propaganda, and their replacement by Confucian adages—is not yet an established fact but, again, the trend is evident. China has revised and modernised its traditional culture and the first fruits of that can be seen in the words and behaviour of its political and intellectual leaders
Binscatter Regressions
We introduce the \texttt{Stata} (and \texttt{R}) package \textsf{Binsreg},
which implements the binscatter methods developed in
\citet*{Cattaneo-Crump-Farrell-Feng_2019_Binscatter}. The package includes the
commands \texttt{binsreg}, \texttt{binsregtest}, and \texttt{binsregselect}.
The first command (\texttt{binsreg}) implements binscatter for the regression
function and its derivatives, offering several point estimation, confidence
intervals and confidence bands procedures, with particular focus on
constructing binned scatter plots. The second command (\texttt{binsregtest})
implements hypothesis testing procedures for parametric specification and for
nonparametric shape restrictions of the unknown regression function. Finally,
the third command (\texttt{binsregselect}) implements data-driven number of
bins selectors for binscatter implementation using either quantile-spaced or
evenly-spaced binning/partitioning. All the commands allow for covariate
adjustment, smoothness restrictions, weighting and clustering, among other
features. A companion \texttt{R} package with the same capabilities is also
available
On Binscatter
Binscatter is very popular in applied microeconomics. It provides a flexible,
yet parsimonious way of visualizing and summarizing large data sets in
regression settings, and it is often used for informal evaluation of
substantive hypotheses such as linearity or monotonicity of the regression
function. This paper presents a foundational, thorough analysis of binscatter:
we give an array of theoretical and practical results that aid both in
understanding current practices (i.e., their validity or lack thereof) and in
offering theory-based guidance for future applications. Our main results
include principled number of bins selection, confidence intervals and bands,
hypothesis tests for parametric and shape restrictions of the regression
function, and several other new methods, applicable to canonical binscatter as
well as higher-order polynomial, covariate-adjusted and smoothness-restricted
extensions thereof. In particular, we highlight important methodological
problems related to covariate adjustment methods used in current practice. We
also discuss extensions to clustered data. Our results are illustrated with
simulated and real data throughout. Companion general-purpose software packages
for \texttt{Stata} and \texttt{R} are provided. Finally, from a technical
perspective, new theoretical results for partitioning-based series estimation
are obtained that may be of independent interest
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