Nonparametric Engel Curves and Revealed Preference

This paper applies revealed preference theory to the nonparametric statistical analysis of consumer demand. Knowledge of expansion paths is shown to improve the power of nonparametric tests of revealed preference. The tightest bounds on indifference surfaces and welfare measures are derived using an algorithm for which revealed preference conditions are shown to guarantee convergence. Nonparametric Engel curves are used to estimate expansion paths and provide a stochastic structure within which to examine the consistency of household level data and revealed preference theory. An application is made to a long time series of repeated cross–sections from the Family Expenditure Survey for Britain. The consistency of these data with revealed preference theory is examined. For periods of consistency with revealed preference, tight bounds are placed on true cost of living indices.     

Instrumental Variable Estimation of Nonparametric Models

In econometrics there are many occasions where knowledge of the structural relationship among dependent variables is required to answer questions of interest. This paper gives identification and estimation results for nonparametric conditional moment restrictions. We characterize identification of structural functions as completeness of certain conditional distributions, and give sufficient identification conditions for exponential families and discrete variables. We also give a consistent, nonparametric estimator of the structural function. The estimator is nonparametric two‐stage least squares based on series approximation, which overcomes an ill‐posed inverse problem by placing bounds on integrals of higher‐order derivatives.     

Multiple comparisons in two-factor testing of psychophysical thresholds by the delta test method

We propose an algorithm of multiple comparisons in two-factor testing of psychophysical thresholds. We use logistic regression combined with guessing rate and adopt the step-down procedure with Ryan–Einot–Gabriel–Welsch (REGW) significance levels for multiple test. We test hypotheses of main effects and interaction in two-factor problem by using the delta test statistics.     

对高校双语教学的思考和认识

双语教学已经成为我国课程教学的发展趋势,开展双语教学是培养具有国际合作意识、国际交流能力和具有国际竞争力的外向型人才的客观要求。文章对数理统计双语教学的必要性以及在双语教学的实践中应该注意的问题进行了探讨,并提出了解决问题的方法。     

All Data are Wrong,but Some are Useful? Advocating the Need for Data Auditing

In a recent article from the Annals of Applied Statistics, Cox discussed the main phases of applied statistical research ranging from clarifying study objectives to final data analysis and interpreting results. As an incidental remark to these main phases, we advocate that beyond cleaning and preprocessing the data, it is a good practice to audit the data to determine if they can be trusted at all. A case study based on Ghanaian Official Fishery Statistics is used to illustrate this need, with Benford's law being the tool used to carrying out the data audit. Supplementary materials for this article are available online.     

浅谈统计对高校决策的作用

文章对统计参与高校全方位的决策进行了讨论,并阐明了统计对高校更好地适应当前社会主义市场经济发展,服务社会有一定的应用价值。     

Nonparametric Identification under Discrete Variation

This paper provides weak conditions under which there is nonparametric interval identification of local features of a structural function that depends on a discrete endogenous variable and is nonseparable in latent variates. The function delivers values of a discrete or continuous outcome and instruments may be discrete valued. Application of the analog principle leads to quantile regression based interval estimators of values and partial differences of structural functions. The results are used to investigate the nonparametric identifying power of the quarter‐of‐birth instruments used in Angrist and Krueger's 1991 study of the returns to schooling.     

Nadaraya–Watson estimator for I.I.D. paths of diffusion processes

This paper deals with a nonparametric Nadaraya–Watson (NW) estimator of the drift function computed from independent continuous observations of a diffusion process. Risk bounds on the estimator and its discrete-time approximation are established. The paper also deals with extensions of the PCO and leave-one-out cross-validation bandwidth selection methods for our NW estimator. Finally, some numerical experiments are provided.     

Zero-inflated Poisson model with clustered regression coefficients: Application to heterogeneity learning of field goal attempts of professional basketball players

Although basketball is a dynamic process sport, played between two sides of five players each, learning some static information is essential for professional players, coaches, and team managers. In order to have a deep understanding of field goal attempts among different players, we propose a zero-inflated Poisson model with clustered regression coefficients to learn the shooting habits of different players over the court and the heterogeneity among them. Specifically, the zero-inflated model captures a large portion of the court with zero field goal attempts, and the mixture of finite mixtures model captures the heterogeneity among different players based on clustered regression coefficients and inflated probabilities. Both theoretical and empirical justification through simulation studies validate our proposed method. We apply our proposed model to data from the National Basketball Association (NBA), for learning players' shooting habits and heterogeneity among different players over the 2017–2018 regular season. This illustrates our model as a way of providing insights from different aspects.     

Estimation and prediction for spatial generalized linear mixed models using high order Laplace approximation

Estimation and prediction in generalized linear mixed models are often hampered by intractable high dimensional integrals. This paper provides a framework to solve this intractability, using asymptotic expansions when the number of random effects is large. To that end, we first derive a modified Laplace approximation when the number of random effects is increasing at a lower rate than the sample size. Second, we propose an approximate likelihood method based on the asymptotic expansion of the log-likelihood using the modified Laplace approximation which is maximized using a quasi-Newton algorithm. Finally, we define the second order plug-in predictive density based on a similar expansion to the plug-in predictive density and show that it is a normal density. Our simulations show that in comparison to other approximations, our method has better performance. Our methods are readily applied to non-Gaussian spatial data and as an example, the analysis of the rhizoctonia root rot data is presented.