Sieve Inference on Semi-nonparametric Time Series Models

The method of sieves has been widely used in estimating semiparametric and nonparametric models. In this paper, we first provide a general theory on the asymptotic normality of plug-in sieve M estimators of possibly irregular functionals of semi/nonparametric time series models. Next, we establish a surprising result that the asymptotic variances of plug-in sieve M estimators of irregular (i.e., slower than root-T estimable) functionals do not depend on temporal dependence. Nevertheless, ignoring the temporal dependence in small samples may not lead to accurate inference. We then propose an easy-to-compute and more accurate inference procedure based on a "pre-asymptotic" sieve variance estimator that captures temporal dependence. We construct a "pre-asymptotic" Wald statistic using an orthonormal series long run variance (OS-LRV) estimator. For sieve M estimators of both regular (i.e., root-T estimable) and irregular functionals, a scaled "pre-asymptotic" Wald statistic is asymptotically F distributed when the series number of terms in the OS-LRV estimator is held fixed. Simulations indicate that our scaled "pre-asymptotic" Wald test with F critical values has more accurate size in finite samples than the usual Wald test with chi-square critical values.Weak dependence, Sieve M estimation, Sieve Riesz representor, Irregular functional, Misspecification, Pre-asymptotic variance, Orthogonal series long run variance estimation, F distribution

Efficient Numerical Algorithm for Large-Scale Damped Natural Gradient Descent

We propose a new algorithm for efficiently solving the damped Fisher matrix in large-scale scenarios where the number of parameters significantly exceeds the number of available samples. This problem is fundamental for natural gradient descent and stochastic reconfiguration. Our algorithm is based on Cholesky decomposition and is generally applicable. Benchmark results show that the algorithm is significantly faster than existing methods

Sieve Inference on Semi-nonparametric Time Series Models

The method of sieves has been widely used in estimating semiparametric and nonparametric models. In this paper, we first provide a general theory on the asymptotic normality of plug-in sieve M estimators of possibly irregular functionals of semi/nonparametric time series models. Next, we establish a surprising result that the asymptotic variances of plug-in sieve M estimators of irregular (i.e., slower than root-T estimable) functionals do not depend on temporal dependence. Nevertheless, ignoring the temporal dependence in small samples may not lead to accurate inference. We then propose an easy-to-compute and more accurate inference procedure based on a “pre-asymptotic” sieve variance estimator that captures temporal dependence. We construct a “pre-asymptotic” Wald statistic using an orthonormal series long run variance (OS-LRV) estimator. For sieve M estimators of both regular (i.e., root-T estimable) and irregular functionals, a scaled “pre-asymptotic” Wald statistic is asymptotically F distributed when the series number of terms in the OS-LRV estimator is held fixed. Simulations indicate that our scaled “pre-asymptotic” Wald test with F critical values has more accurate size in finite samples than the usual Wald test with chi-square critical values

Sieve inference on semi-nonparametric time series models

The method of sieves has been widely used in estimating semiparametric and nonparametric models. In this paper, we first provide a general theory on the asymptotic normality of plug-in sieve M estimators of possibly irregular functionals of semi/nonparametric time series models. Next, we establish a surprising result that the asymptotic variances of plug-in sieve M estimators of irregular (i.e., slower than root-T estimable) functionals do not depend on temporal dependence. Nevertheless, ignoring the temporal dependence in small samples may not lead to accurate inference. We then propose an easy-to-compute and more accurate inference procedure based on a “pre-asymptotic” sieve variance estimator that captures temporal dependence. We construct a “pre-asymptotic” Wald statistic using an orthonormal series long run variance (OS-LRV) estimator. For sieve M estimators of both regular (i.e., root-T estimable) and irregular functionals, a scaled “pre-asymptotic” Wald statistic is asymptotically F distributed when the series number of terms in the OS-LRV estimator is held fixed. Simulations indicate that our scaled “pre-asymptotic” Wald test with F critical values has more accurate size in finite samples than the usual Wald test with chi-square critical values

How can health science popularization KOL better produce professional voices?

Health science popularization, as an effective strategy for transmitting health knowledge and improving audience health literacy, has received increasing attention in the past two years. This paper takes the official account - "Oria, a specially grounded nutritionist" as an example, and uses the communication research method of online ethnography and content analysis to explore how blogger Xie Lifeng, as a KOL in the field of health science popularization, can make a professional voice and do a good job in the path and method of health nutrition science popularization in the We Media era. The study ultimately found that in terms of content production and dissemination, it is necessary to do a good job in health and nutrition science popularization. Self media users need to work together from multiple aspects such as segmented vertical production, creating personalized and distinctive IPs, establishing online community forms, and expanding communication channels and platforms

Vision-Language Instruction Tuning: A Review and Analysis

Instruction tuning is a crucial supervised training phase in Large Language Models (LLMs), aiming to enhance the LLM's ability to generalize instruction execution and adapt to user preferences. With the increasing integration of multi-modal data into LLMs, there is growing interest in Vision-Language Instruction Tuning (VLIT), which presents more complex characteristics compared to pure text instruction tuning. In this paper, we systematically review the latest VLIT settings and corresponding datasets in multi-modal LLMs and provide insights into the intrinsic motivations behind their design. For the first time, we offer a detailed multi-perspective categorization for existing VLIT datasets and identify the characteristics that high-quality VLIT data should possess. By incorporating these characteristics as guiding principles into the existing VLIT data construction process, we conduct extensive experiments and verify their positive impact on the performance of tuned multi-modal LLMs. Furthermore, we discuss the current challenges and future research directions of VLIT, providing insights for the continuous development of this field. The code and dataset related to this paper have been open-sourced at https://github.com/palchenli/VL-Instruction-Tuning.Comment: 34 pages, 6 figure