On the uniform asymptotic validity of subsampling and the bootstrap

This paper provides conditions under which subsampling and the bootstrap can be used to construct estimators of the quantiles of the distribution of a root that behave well uniformly over a large class of distributions $\mathbf{P}$. These results are then applied (i) to construct confidence regions that behave well uniformly over $\mathbf{P}$ in the sense that the coverage probability tends to at least the nominal level uniformly over $\mathbf{P}$ and (ii) to construct tests that behave well uniformly over $\mathbf{P}$ in the sense that the size tends to no greater than the nominal level uniformly over $\mathbf{P}$. Without these stronger notions of convergence, the asymptotic approximations to the coverage probability or size may be poor, even in very large samples. Specific applications include the multivariate mean, testing moment inequalities, multiple testing, the empirical process and U-statistics.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1051 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

On stepdown control of the false discovery proportion

Consider the problem of testing multiple null hypotheses. A classical approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate ($FWER$), the probability of even one false rejection. However, if $s$ is large, control of the $FWER$ is so stringent that the ability of a procedure which controls the $FWER$ to detect false null hypotheses is limited. Consequently, it is desirable to consider other measures of error control. We will consider methods based on control of the false discovery proportion ($FDP$) defined by the number of false rejections divided by the total number of rejections (defined to be 0 if there are no rejections). The false discovery rate proposed by Benjamini and Hochberg (1995) controls $E(FDP)$. Here, we construct methods such that, for any $\gamma$ and $\alpha$, $P\{FDP>\gamma \}\le \alpha$. Based on $p$-values of individual tests, we consider stepdown procedures that control the $FDP$, without imposing dependence assumptions on the joint distribution of the $p$-values. A greatly improved version of a method given in Lehmann and Romano \citer10 is derived and generalized to provide a means by which any sequence of nondecreasing constants can be rescaled to ensure control of the $FDP$. We also provide a stepdown procedure that controls the $FDR$ under a dependence assumption.Comment: Published at http://dx.doi.org/10.1214/074921706000000383 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Stepup procedures for control of generalizations of the familywise error rate

Consider the multiple testing problem of testing null hypotheses $H_1,...,H_s$. A classical approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate ($\mathit{FWER}$), the probability of even one false rejection. But if $s$ is large, control of the $\mathit{FWER}$ is so stringent that the ability of a procedure that controls the $\mathit{FWER}$ to detect false null hypotheses is limited. It is therefore desirable to consider other measures of error control. This article considers two generalizations of the $\mathit{FWER}$. The first is the $k-\mathit{FWER}$, in which one is willing to tolerate $k$ or more false rejections for some fixed $k\geq 1$. The second is based on the false discovery proportion ($\mathit{FDP}$), defined to be the number of false rejections divided by the total number of rejections (and defined to be 0 if there are no rejections). Benjamini and Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289--300] proposed control of the false discovery rate ($\mathit{FDR}$), by which they meant that, for fixed $\alpha$, $E(\mathit{FDP})\leq\alpha$. Here, we consider control of the $\mathit{FDP}$ in the sense that, for fixed $\gamma$ and $\alpha$, $P\{\mathit{FDP}>\gamma\}\leq \alpha$. Beginning with any nondecreasing sequence of constants and $p$-values for the individual tests, we derive stepup procedures that control each of these two measures of error control without imposing any assumptions on the dependence structure of the $p$-values. We use our results to point out a few interesting connections with some closely related stepdown procedures. We then compare and contrast two $\mathit{FDP}$-controlling procedures obtained using our results with the stepup procedure for control of the $\mathit{FDR}$ of Benjamini and Yekutieli [Ann. Statist. 29 (2001) 1165--1188].Comment: Published at http://dx.doi.org/10.1214/009053606000000461 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Sustainable Cotton Production through Skill Development among Farmers: Evidence from Khairpur District of Sindh, Pakistan

This study on farmers’ training in environment friendly production practices for cotton crop was conducted in the Khairpur district of Sindh province. Data used in this study comprises baseline and post IPM Farmer Field School (FFS) impact surveys conducted during 2001 and 2003 respectively. The programme impacts were estimated on gross margins and changes in farmers’ attitude towards environment and biodiversity. The effect of training on social recognition of farmers, their experimentations abilities, and decision making skills were also examined. Beside single difference comparisons of change in production practices between trained and non-trained farmers, the difference in difference (DD) method was also used for comparisons among FFS farmers, exposed farmers and un-exposed farmers from control villages. The stochastic production frontier model incorporating inefficiency effects is also estimated to analyze the impact of farmers’ training (through FFS) on productivity and efficiency at cotton farms in the study area. Results show better cotton yield and reduction in cost of pesticides and fertilizer inputs enabled FFS farmers to fetch significantly higher gross margins (US$391/ha) than non-FFS (US$ 151/ha) and Control farms (US$ 25/ha). The total application of pesticide chemicals was largely reduced (44%) on FFS farms. The cost of inefficiency at FFS farms was lower (23.71%) as compared to those on non-FFS farms (30.50%) which implies that FFS farmers were able to maintain higher level of technical efficiency. It is concluded that the FFS approach is not only cost efficient but also improves farm level technical efficiency. Information generated through Agro-ecosystem analysis on pest and predator dynamics helps farmers to understand pest-predator interaction to allow nature to work with lesser or most appropriate interventions. A well-planned technical backup support mechanism is recommended to be evolved through integrating research system into farmer-led experimentation. The Programme achievements show that FFS approach in Pakistan has furthered from only crop management to systems management and community development approach and should be supported further to enter into mass scale expansion state.Cotton Production; Skill Development; Production Frontier; Efficiency; Pakistan

Zero-tillage Technology and Farm Profits: A Case Study of Wheat Growers in the Rice Zone of Punjab

The rice-wheat cropping zone of Punjab is the main producer of high-valued and fine quality basmati rice in Pakistan. The rice produced in this area is famous for its grain length and aromatic characteristics. Being an important export item, rice contributes significantly to the national foreign exchange earnings. Wheat is the other major crop of the rice-wheat system and being the staple food is central to national agricultural policies. Rice is grown on a vast area in this zone during Kharif mostly followed by wheat in the Rabi season. Studies have shown that a large gap exists between the potential and yields actually realised by the wheat growers of the area [Byerlee, et al. (1984); Hobbs (1985) and Sheikh, et al. (2000)]. Farmers’ practices regarding land preparation for paddy, wheat planting time, and other conflicts endogenous to the rice-wheat based cropping system were identified as the major factors limiting wheat yield in the area. The flooded and puddled soils that are well suited for paddy production as compared to well-drained conditions required for wheat is such an example of the system conflicts. The farmers in the rice-wheat zone of the Punjab predominantly grow basmati varieties, which are late maturing as compared to coarse varieties of rice. Therefore, paddy harvest is generally delayed at most of the farms in this zone. The late paddy harvest coupled with poor soil structure and loose plant residues create problems for preparation of a good seedbed and planting of wheat often gets late [Byerlee, et al. (1984)]. The farmers also had to resort to the broadcast method for wheat sowing which results in poor and patchy plant stands.

Zero-tillage Technology and Farm Profits: A Case Study of Wheat Growers in the Rice Zone of Punjab

This study presents the results from a field survey of the wheat growers in the rice-wheat zone of Punjab. The late maturing basmati rice varieties and the post paddy-harvest conventional tillage practices to prepare seedbed for wheat sowing often result in delayed planting of the crop. The late sowing is a major factor responsible for low wheat yields obtained by the farmers of the area. Introduction of the new zero-tillage seed drill in the area during early 1980s made it possible to sow wheat in freshly harvested untilled paddy fields utilizing residual moister. Presently, more than eighty thousand hectares of wheat are sown with zero-tillage drill technology. The partial budget analysis showed that zero-tillage is more profitable than conventional wheat sowing methods of ‘wadwatter’ or ‘rauni’. The new technology saves tillage and irrigation costs, results in yield gains through a possible improvement in sowing time and enhanced fertilizer and water use efficiencies. The results showed that the zero-tillage adopters earn an extra income of 253 and 2278 rupees per acre of wheat over that earned from wheat sown with rauni and wadwattar methods respectively. The results of multiple regression analysis confirmed that the zero-tillage technology enhances water and fertilizer use efficiency. However, sufficient evidence was not present to prove any positive or adverse affect of the technology on the incidence of weeds in wheat crop. It is suggested that this aspect of zero-tillage technology be focused more in future research.wheat; Zero-tillage; technology; irrigated Punjab; rice-wheat zone; Pakistan

Adoption of Recommended Varieties: A Farm-level Analysis of Wheat Growers in Irrigated Punjab

This study uses farm level data to analyse the determinants of adoption of recommended wheat varieties in irrigated Punjab, Pakistan. A notable proportion of wheat acreage is sown to non-recommended wheat varieties in the province. These cultivars had either lost (overtime) or did not have resistance against yellow rust. Farm size, education, and size of wheat enterprise on the farm are the important determinants of adoption of recommended wheat varieties while tractor ownership and irrigation source play a positive but insignificant role in the adoption decisions. Age and tenure proved to be less of a constraint towards adoption of the recommended wheat varieties. The likelihood of the adoption of recommended wheat varieties varied among tehsils, with the highest probabilities of adoption in Melsi and Arifwala tehsils of cotton-wheat zones I and II respectively.