scholarly journals Inference for the Linear IV Model Ridge Estimator Using Training and Test Samples

Stats ◽  
2021 ◽  
Vol 4 (3) ◽  
pp. 725-744
Author(s):  
Fallaw Sowell ◽  
Nandana Sengupta
Keyword(s):  
Asymptotic Distribution ◽  
Method Of Moments ◽  
Structural Parameters ◽  
Test Sample ◽  
Confidence Regions ◽  
Tuning Parameter ◽  
Ridge Estimator ◽  
Chi Squared ◽  
Special Case ◽  
Iv Model

The asymptotic distribution is presented for the linear instrumental variables model estimated with a ridge penalty and a prior where the tuning parameter is selected with a holdout sample. The structural parameters and the tuning parameter are estimated jointly by method of moments. A chi-squared statistic permits confidence regions for the structural parameters. The form of the asymptotic distribution provides insights on the optimal way to perform the split between the training and test sample. Results for the linear regression estimated by ridge regression are presented as a special case.

scholarly journals On the Asymptotic Distribution of Ridge Regression Estimators Using Training and Test Samples

Econometrics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 39
Author(s):  
Nandana Sengupta ◽  
Fallaw Sowell
Keyword(s):  
Asymptotic Distribution ◽  
Instrumental Variables ◽  
Ridge Regression ◽  
Mixture Distribution ◽  
Tuning Parameter ◽  
Ridge Estimator ◽  
Sampling Distributions ◽  
Education Data ◽  
Regression Estimators ◽  
Better Than

The asymptotic distribution of the linear instrumental variables (IV) estimator with empirically selected ridge regression penalty is characterized. The regularization tuning parameter is selected by splitting the observed data into training and test samples and becomes an estimated parameter that jointly converges with the parameters of interest. The asymptotic distribution is a nonstandard mixture distribution. Monte Carlo simulations show the asymptotic distribution captures the characteristics of the sampling distributions and when this ridge estimator performs better than two-stage least squares. An empirical application on returns to education data is presented.

scholarly journals The extended odd family of probability distributions with practice to a submodel

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3855-3867 ◽  
Author(s):  
Hassan Bakouch ◽  
Christophe Chesneau ◽  
Muhammad Khan
Keyword(s):  
Heavy Tails ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Likelihood Method ◽  
Tuning Parameter ◽  
Data Sets ◽  
New Family ◽  
Rate Functions ◽  
Special Case ◽  
Family Of Distributions

In this paper, we introduce a new family of distributions extending the odd family of distributions. A new tuning parameter is introduced, with some connections to the well-known transmuted transformation. Some mathematical results are obtained, including moments, generating function and order statistics. Then, we study a special case dealing with the standard loglogistic distribution and the modifiedWeibull distribution. Its main features are to have densities with flexible shapes where skewness, kurtosis, heavy tails and modality can be observed, and increasing-decreasing-increasing, unimodal and bathtub shaped hazard rate functions. Estimation of the related parameters is investigated by the maximum likelihood method. We illustrate the usefulness of our extended odd family of distributions with applications to two practical data sets.

scholarly journals A POWERFUL TEST OF THE AUTOREGRESSIVE UNIT ROOT HYPOTHESIS BASED ON A TUNING PARAMETER FREE STATISTIC

2009 ◽  
Vol 25 (6) ◽  
pp. 1515-1544 ◽  
Author(s):  
Morten Ørregaard Nielsen
Keyword(s):  
Asymptotic Distribution ◽  
Unit Root ◽  
Linear Time ◽  
Nonparametric Test ◽  
Tuning Parameter ◽  
Ratio Test ◽  
Local Power ◽  
Finite Sample ◽  
Power Of The Test ◽  
The Family

This paper presents a family of simple nonparametric unit root tests indexed by one parameter,d, and containing the Breitung (2002,Journal of Econometrics108, 342–363) test as the special cased= 1. It is shown that (a) each member of the family withd> 0 is consistent, (b) the asymptotic distribution depends ondand thus reflects the parameter chosen to implement the test, and (c) because the asymptotic distribution depends ondand the test remains consistent for alld> 0, it is possible to analyze the power of the test for different values ofd. The usual Phillips–Perron and Dickey–Fuller type tests are indexed by bandwidth, lag length, etc., but have none of these three properties.It is shown that members of the family withd< 1 have higher asymptotic local power than the Breitung (2002) test, and whendis small the asymptotic local power of the proposed nonparametric test is relatively close to the parametric power envelope, particularly in the case with a linear time trend. Furthermore, generalized least squares (GLS) detrending is shown to improve power whendis small, which is not the case for the Breitung (2002) test. Simulations demonstrate that when applying a sieve bootstrap procedure, the proposed variance ratio test has very good size properties, with finite-sample power that is higher than that of the Breitung (2002) test and even rivals the (nearly) optimal parametric GLS detrended augmented Dickey–Fuller test with lag length chosen by an information criterion.

scholarly journals The Generalised Coupon Collector Problem

2008 ◽  
Vol 45 (03) ◽  
pp. 621-629 ◽  
Author(s):  
Peter Neal
Keyword(s):  
Probability Distribution ◽  
Asymptotic Distribution ◽  
Birthday Problem ◽  
Coupon Collector ◽  
Poisson Limit ◽  
Special Case ◽  
Independent And Identically Distributed

Coupons are collected one at a time from a population containing n distinct types of coupon. The process is repeated until all n coupons have been collected and the total number of draws, Y, from the population is recorded. It is assumed that the draws from the population are independent and identically distributed (draws with replacement) according to a probability distribution X with the probability that a type-i coupon is drawn being P(X = i). The special case where each type of coupon is equally likely to be drawn from the population is the classic coupon collector problem. We consider the asymptotic distribution Y (appropriately normalized) as the number of coupons n → ∞ under general assumptions upon the asymptotic distribution of X. The results are proved by studying the total number of coupons, W(t), not collected in t draws from the population and noting that P(Y ≤ t) = P(W(t) = 0). Two normalizations of Y are considered, the choice of normalization depending upon whether or not a suitable Poisson limit exists for W(t). Finally, extensions to the K-coupon collector problem and the birthday problem are given.

scholarly journals Test configurations and Okounkov bodies

2012 ◽  
Vol 148 (6) ◽  
pp. 1736-1756 ◽  
Author(s):  
David Witt Nyström
Keyword(s):  
Line Bundle ◽  
Recent Work ◽  
Lebesgue Measure ◽  
Asymptotic Distribution ◽  
Concave Function ◽  
Toric Geometry ◽  
Piecewise Polynomial ◽  
Test Configuration ◽  
Special Case

AbstractWe associate to a test configuration for a polarized variety a filtration of the section ring of the line bundle. Using the recent work of Boucksom and Chen we get a concave function on the Okounkov body whose law with respect to Lebesgue measure determines the asymptotic distribution of the weights of the test configuration. We show that this is a generalization of a well-known result in toric geometry. As an application, we prove that the pushforward of the Lebesgue measure on the Okounkov body is equal to a Duistermaat–Heckman measure of a certain deformation of the manifold. Via the Duisteraat–Heckman formula, we get as a corollary that in the special case of an effective ℂ×-action on the manifold lifting to the line bundle, the pushforward of the Lebesgue measure on the Okounkov body is piecewise polynomial.

Poisson convergence and semi-induced properties of random graphs

1987 ◽  
Vol 101 (2) ◽  
pp. 291-300 ◽  
Author(s):  
Michał Karoński ◽  
Andrzej Ruciński
Keyword(s):  
Asymptotic Distribution ◽  
Random Graph ◽  
Random Graphs ◽  
Method Of Moments ◽  
Traditional Method ◽  
General Setting ◽  
Asymptotic Distributions ◽  
New Method ◽  
Isolated Trees ◽  
Ingenious Method

Barbour [l] invented an ingenious method of establishing the asymptotic distribution of the number X of specified subgraphs of a random graph. The novelty of his method relies on using the first two moments of X only, despite the traditional method of moments that involves all moments of X (compare [8, 10, 11, 14]). He also adjusted that new method for counting isolated trees of a given size in a random graph. (For further applications of Barbour's method see [4] and [10].) The main goal of this paper is to show how this method can be extended to a general setting that enables us to derive asymptotic distributions of subsets of vertices of a random graph with various properties.

scholarly journals Theoretical Description Of A Reparamatrization of Discrete Two Parameter Poisson Lindley Distribution for Modeling Waiting And Survival Times Data

2016 ◽  
Vol 29 (1) ◽  
pp. 217-222
Author(s):  
Tanka Raj Adhikari
Keyword(s):  
Poisson Distribution ◽  
Method Of Moments ◽  
Research Paper ◽  
Theoretical Description ◽  
Survival Times ◽  
Lindley Distribution ◽  
Two Parameters ◽  
First Four Moments ◽  
Special Case ◽  
Two Parameter

In this research paper, the theoretical description of are paramatrization of a discrete two-parameter Poisson Lindley Distribution, of which Sankaran’s (1970) one parameter Poisson Lindley Distribution is a special case, is derived by compounding a Poisson Distribution with two parameters Lindley Distribution for modeling waiting and survival times data of Shanker et al. (2012).The first four moments of this distribution have derived. Estimation of the parameters by using method of moments and maximum likely hood method has been discussed.

scholarly journals Further results on non-self-centrality measures of graphs

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 5137-5148 ◽  
Author(s):  
Mahdieh Azari
Keyword(s):  
Structural Parameters ◽  
Cartesian Product ◽  
Upper And Lower Bounds ◽  
Centrality Measures ◽  
Eccentric Connectivity Index ◽  
The Third ◽  
Eccentricity Index ◽  
Strong Product ◽  
Special Cases ◽  
Special Case

For indicating the non-self-centrality extent of graphs, two new eccentricity-based measures namely third Zagreb eccentricity index E3(G) and non-self-centrality number N(G) of a connected graph G have recently been introduced as E3(G) = ?uv?E(G)|?G(u)-?G(v)| and N(G) = ? {u,v}?V(G) |?G(u)-?G(v)|, where ?G(u) denotes the eccentricity of a vertex u in G. In this paper, we find relation between the third Zagreb eccentricity index of graphs with some eccentricity-based invariants such as second Zagreb eccentricity index and second eccentric connectivity index. We also give sharp upper and lower bounds on the nonself-centrality number of graphs in terms of some structural parameters and relate it to two well-known eccentricity-based invariants namely total eccentricity and first Zagreb eccentricity index. Furthermore, we present exact expressions or sharp upper bounds on the third Zagreb eccentricity index and non-selfcentrality number of several graph operations such as join, disjunction, symmetric difference, lexicographic product, strong product, and generalized hierarchical product. The formulae for Cartesian product and rooted product as two important special cases of generalized hierarchical product and the formulae for corona product as a special case of rooted product are also given.

Sign in / Sign up

Export Citation Format

Share Document