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There is a growing literature in nonparametric econometrics in the recent two decades. Given the space limitation, it is impossible to survey all the important recent developments in nonparametric econometrics. Therefore, we choose to limit our focus on the following areas. In Section 2, we review the recent developments of nonparametric estimation and testing of regression functions with mixed discrete and continuous covariates. We discuss nonparametric estimation and testing of econometric models for nonstationary data in Section 3. Section 4 is devoted to surveying the literature of nonparametric instrumental variable (IV) models. We review nonparametric estimation of quantile regression models in Section 5. In Sections 2–5, we also point out some open research problems, which might be useful for graduate students to review the important research papers in this field and to search for their own research interests, particularly dissertation topics for doctoral students. Finally, in Section 6 we highlight some important research areas that are not covered in this paper due to space limitation. We plan to write a separate survey paper to discuss some of the omitted topics.

This paper gives a selective review on some recent developments of nonparametric methods in both continuous and discrete time finance, particularly in the areas of nonparametric estimation and testing of diffusion processes, nonparametric testing of parametric diffusion models, nonparametric pricing of derivatives, nonparametric estimation and hypothesis testing for nonlinear pricing kernel, and nonparametric predictability of asset returns. For each financial context, the paper discusses the suitable statistical concepts, models, and modeling procedures, as well as some of their applications to financial data. Their relative strengths and weaknesses are discussed. Much theoretical and empirical research is needed in this area, and more importantly, the paper points to several aspects that deserve further investigation.

The R environment for statistical computing and graphics (R Development Core Team, 2008) offers practitioners a rich set of statistical methods ranging from random number generation and optimization methods through regression, panel data, and time series methods, by way of illustration. The standard R distribution (base R) comes preloaded with a rich variety of functionality useful for applied econometricians. This functionality is enhanced by user-supplied packages made available via R servers that are mirrored around the world. Of interest in this chapter are methods for estimating nonparametric and semiparametric models. We summarize many of the facilities in R and consider some tools that might be of interest to those wishing to work with nonparametric methods who want to avoid resorting to programming in C or Fortran but need the speed of compiled code as opposed to interpreted code such as Gauss or Matlab by way of example. We encourage those working in the field to strongly consider implementing their methods in the R environment thereby making their work accessible to the widest possible audience via an open collaborative forum.

Equilibrium job search models allow for labor markets with homogeneous workers and firms to yield nondegenerate wage densities. However, the resulting wage densities do not accord well with empirical regularities. Accordingly, many extensions to the basic equilibrium search model have been considered (e.g., heterogeneity in productivity, heterogeneity in the value of leisure, etc.). It is increasingly common to use nonparametric forms for these extensions and, hence, researchers can obtain a perfect fit (in a kernel smoothed sense) between theoretical and empirical wage densities. This makes it difficult to carry out model comparison of different model extensions. In this paper, we first develop Bayesian parametric and nonparametric methods which are comparable to the existing non-Bayesian literature. We then show how Bayesian methods can be used to compare various nonparametric equilibrium search models in a statistically rigorous sense.

Identification and inference are central to applied analysis, and two papers examine these issues, the first being theoretical in nature and the second being simulation based.

This paper examines Aman Ullah’s contributions to robust inference, finite sample econometrics, nonparametrics and semiparametrics, and panel and spatial models. His early works on robust inference and finite sample theory were mostly motivated by his thesis advisor, Professor Anirudh Lal Nagar. They eventually led to his most original rethinking of many statistics and econometrics models that developed into the monograph Finite Sample Econometrics published in 2004. His desire to relax distributional and functional-form assumptions lead him in the direction of nonparametric estimation and he summarized his views in his most influential textbook Nonparametric Econometrics (with Adrian Pagan) published in 1999 that has influenced a whole generation of econometricians. His innovative contributions in the areas of seemingly unrelated regressions, parametric, semiparametric and nonparametric panel data models, and spatial models have also inspired a larger literature on nonparametric and semiparametric estimation and inference and spurred on research in robust estimation and inference in these and related areas.

Small- and medium-sized enterprises can be highly affected by losses caused by exchange rate changes. The aim of this paper was to find the optimal Value-at-Risk (VaR) method for estimating future exchange rate losses within one year.

The analysis focuses on five VaR methods, some of them traditional and some of them more up to date with integrated EVT or GARCH. The analysis of VaR methods was concentrated on a time horizon (1–12 months), overestimation predictions and six scenarios based on trends and variability of exchange rates. This study used three currency pairs EUR/CZK, EUR/USD and EUR/JPY for backtesting.

In compliance with the backtesting results, the parametric VaR with random walk has been chosen, despite its shortcomings, as the most accurate for estimating future losses in a medium-term period. The Nonparametric VaR confirmed insensitivity to the current exchange rate development. The EVT-based methods showed overconservatism (overestimation predictions). Every parametric or semiparametric method revealed a severe increase of liberality with increasing time.

This research is limited to the analysis of suitable VaR models in a long- and short-run period without using artificial intelligence.

The result of this paper is the choice of a proper VaR method for the online application for estimating the future exchange rate for enterprises.

The orientation of medium-term period makes the research original and useful for small- and medium-sized enterprises.

Applied econometric analysis is often performed using data collected from large-scale surveys. These surveys use complex sampling plans in order to reduce costs and increase the estimation efficiency for subgroups of the population. These sampling plans result in unequal inclusion probabilities across units in the population. The purpose of this paper is to derive the asymptotic properties of a design-based nonparametric regression estimator under a combined inference framework. The nonparametric regression estimator considered is the local constant estimator. This work contributes to the literature in two ways. First, it derives the asymptotic properties for the multivariate mixed-data case, including the asymptotic normality of the estimator. Second, I use least squares cross-validation for selecting the bandwidths for both continuous and discrete variables. I run Monte Carlo simulations designed to assess the finite-sample performance of the design-based local constant estimator versus the traditional local constant estimator for three sampling methods, namely, simple random sampling, exogenous stratification and endogenous stratification. Simulation results show that the estimator is consistent and that efficiency gains can be achieved by weighting observations by the inverse of their inclusion probabilities if the sampling is endogenous.

Statistical methods are important for meaningful analysis, critique and interpretation of results. The current study aims to investigate the use of statistical methods used in LIS research articles produced by Pakistani authors during 2001–2016.

Content analysis method with both the qualitative and quantitative components was used. LIS articles published by Pakistani authors in national and international journals from 2001 to 2016 were selected. The descriptive and inferential statistics were used to analyze the usage of statistical techniques.

The findings show that use of descriptive statistics remained higher as compared to inferential statistics in the LIS research produced by Pakistani authors. However, a visible growth trend in the use of inferential statistical techniques is found. Males are two times more likely to use inferential statistics as compared to female authors. Articles published in foreign journals and impact factor journals used more inferential statistics as compared to local and nonimpact factor journals. Parametric inferential statistics is more popular among Pakistani authors as compared to nonparametric. Faculty was more inclined toward using parametric statistic. The percentage of collaboration was higher in the papers using parametric statistics. Few articles reported the tests to fulfill the assumptions of parametric and nonparametric statistics.

This study can be used to better understand the trends of statistical techniques used in LIS research and authors' orientation in this regard. It will be helpful for future researchers in the selection of appropriate statistical techniques to be used.